From e881b78f3dd5c1b9b9255c7267adb076f1ee2a13 Mon Sep 17 00:00:00 2001 From: Wolves Date: Sat, 15 Jun 2024 03:38:29 +0800 Subject: [PATCH] 240615 --- .gitignore | 4 +- week1/C1_W1_Lab01_Python_Jupyter_Soln.ipynb | 160 +++++ ...1_W1_Lab02_Model_Representation_Soln.ipynb | 471 +++++++++++++ week1/C1_W1_Lab03_Cost_function_Soln.ipynb | 352 ++++++++++ week1/C1_W1_Lab04_Gradient_Descent_Soln.ipynb | 657 ++++++++++++++++++ .../C1_W1_Lab01_Python_Jupyter_Soln.ipynb | 159 +++++ .../C1_W1_Lab02_Course_Preview_Soln.ipynb | 33 + ...1_W1_Lab03_Model_Representation_Soln.ipynb | 398 +++++++++++ .../C1_W1_Lab04_Cost_function_Soln.ipynb | 307 ++++++++ .../C1_W1_Lab05_Gradient_Descent_Soln.ipynb | 558 +++++++++++++++ week1/betaversion/images/C1W1L1_Markdown.PNG | Bin 0 -> 32021 bytes week1/betaversion/images/C1W1L1_Run.PNG | Bin 0 -> 7309 bytes week1/betaversion/images/C1W1L1_Tour.PNG | Bin 0 -> 8871 bytes .../images/C1_W1_L3_S1_Lecture_b.png | Bin 0 -> 84816 bytes 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100644 week1/lab_utils_uni.py diff --git a/.gitignore b/.gitignore index ed43ada..21f26f5 100644 --- a/.gitignore +++ b/.gitignore @@ -4,4 +4,6 @@ .DS_Store? -.idea \ No newline at end of file +.idea + +**/.ipynb_checkpoints diff --git a/week1/C1_W1_Lab01_Python_Jupyter_Soln.ipynb b/week1/C1_W1_Lab01_Python_Jupyter_Soln.ipynb new file mode 100644 index 0000000..c9c94e7 --- /dev/null +++ b/week1/C1_W1_Lab01_Python_Jupyter_Soln.ipynb @@ -0,0 +1,160 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Brief Introduction to Python and Jupyter Notebooks\n", + "Welcome to the first optional lab! \n", + "Optional labs are available to:\n", + "- provide information - like this notebook\n", + "- reinforce lecture material with hands-on examples\n", + "- provide working examples of routines used in the graded labs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab, you will:\n", + "- Get a brief introduction to Jupyter notebooks\n", + "- Take a tour of Jupyter notebooks\n", + "- Learn the difference between markdown cells and code cells\n", + "- Practice some basic python\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The easiest way to become familiar with Jupyter notebooks is to take the tour available above in the Help menu:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "
missing
\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Jupyter notebooks have two types of cells that are used in this course. Cells such as this which contain documentation called `Markdown Cells`. The name is derived from the simple formatting language used in the cells. You will not be required to produce markdown cells. Its useful to understand the `cell pulldown` shown in graphic below. Occasionally, a cell will end up in the wrong mode and you may need to restore it to the right state:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + " missing\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The other type of cell is the `code cell` where you will write your code:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "This is a code cell\n" + ] + } + ], + "source": [ + "#This is a 'Code' Cell\n", + "print(\"This is a code cell\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Python\n", + "You can write your code in the code cells. \n", + "To run the code, select the cell and either\n", + "- hold the shift-key down and hit 'enter' or 'return'\n", + "- click the 'run' arrow above\n", + "
\n", + " \n", + "
\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Print statement\n", + "Print statements will generally use the python f-string style. \n", + "Try creating your own print in the following cell. \n", + "Try both methods of running the cell." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "f strings allow you to embed variables right in the strings! 23\n" + ] + } + ], + "source": [ + "# print statements\n", + "variable = \"right in the strings!\"\n", + "var='23'\n", + "print(f\"f strings allow you to embed variables {variable} {var}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Congratulations!\n", + "You now know how to find your way around a Jupyter Notebook." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/C1_W1_Lab02_Model_Representation_Soln.ipynb b/week1/C1_W1_Lab02_Model_Representation_Soln.ipynb new file mode 100644 index 0000000..ad9e199 --- /dev/null +++ b/week1/C1_W1_Lab02_Model_Representation_Soln.ipynb @@ -0,0 +1,471 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Model Representation\n", + "\n", + "
\n", + " \n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab you will:\n", + "- Learn to implement the model $f_{w,b}$ for linear regression with one variable" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notation\n", + "Here is a summary of some of the notation you will encounter. \n", + "\n", + "|General
Notation | Description| Python (if applicable) |\n", + "|: ------------|: ------------------------------------------------------------||\n", + "| $a$ | scalar, non bold ||\n", + "| $\\mathbf{a}$ | vector, bold ||\n", + "| **Regression** | | | |\n", + "| $\\mathbf{x}$ | Training Example feature values (in this lab - Size (1000 sqft)) | `x_train` | \n", + "| $\\mathbf{y}$ | Training Example targets (in this lab Price (1000s of dollars)) | `y_train` \n", + "| $x^{(i)}$, $y^{(i)}$ | $i_{th}$Training Example | `x_i`, `y_i`|\n", + "| m | Number of training examples | `m`|\n", + "| $w$ | parameter: weight | `w` |\n", + "| $b$ | parameter: bias | `b` | \n", + "| $f_{w,b}(x^{(i)})$ | The result of the model evaluation at $x^{(i)}$ parameterized by $w,b$: $f_{w,b}(x^{(i)}) = wx^{(i)}+b$ | `f_wb` | \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tools\n", + "In this lab you will make use of: \n", + "- NumPy, a popular library for scientific computing\n", + "- Matplotlib, a popular library for plotting data" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('./deeplearning.mplstyle')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Statement\n", + " \n", + "\n", + "As in the lecture, you will use the motivating example of housing price prediction. \n", + "This lab will use a simple data set with only two data points - a house with 1000 square feet(sqft) sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000. These two points will constitute our *data or training set*. In this lab, the units of size are 1000 sqft and the units of price are 1000s of dollars.\n", + "\n", + "| Size (1000 sqft) | Price (1000s of dollars) |\n", + "| -------------------| ------------------------ |\n", + "| 1.0 | 300 |\n", + "| 2.0 | 500 |\n", + "\n", + "You would like to fit a linear regression model (shown above as the blue straight line) through these two points, so you can then predict price for other houses - say, a house with 1200 sqft.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Please run the following code cell to create your `x_train` and `y_train` variables. The data is stored in one-dimensional NumPy arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x_train = [1. 2.]\n", + "y_train = [300. 500.]\n" + ] + } + ], + "source": [ + "# x_train is the input variable (size in 1000 square feet)\n", + "# y_train is the target (price in 1000s of dollars)\n", + "x_train = np.array([1.0, 2.0])\n", + "y_train = np.array([300.0, 500.0])\n", + "print(f\"x_train = {x_train}\")\n", + "print(f\"y_train = {y_train}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ">**Note**: The course will frequently utilize the python 'f-string' output formatting described [here](https://docs.python.org/3/tutorial/inputoutput.html) when printing. The content between the curly braces is evaluated when producing the output." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Number of training examples `m`\n", + "You will use `m` to denote the number of training examples. Numpy arrays have a `.shape` parameter. `x_train.shape` returns a python tuple with an entry for each dimension. `x_train.shape[0]` is the length of the array and number of examples as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x_train.shape: (2,)\n", + "Number of training examples is: 2\n" + ] + } + ], + "source": [ + "# m is the number of training examples\n", + "print(f\"x_train.shape: {x_train.shape}\")\n", + "m = x_train.shape[0]\n", + "print(f\"Number of training examples is: {m}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One can also use the Python `len()` function as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of training examples is: 2\n" + ] + } + ], + "source": [ + "# m is the number of training examples\n", + "m = len(x_train)\n", + "print(f\"Number of training examples is: {m}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Training example `x_i, y_i`\n", + "\n", + "You will use (x$^{(i)}$, y$^{(i)}$) to denote the $i^{th}$ training example. Since Python is zero indexed, (x$^{(0)}$, y$^{(0)}$) is (1.0, 300.0) and (x$^{(1)}$, y$^{(1)}$) is (2.0, 500.0). \n", + "\n", + "To access a value in a Numpy array, one indexes the array with the desired offset. For example the syntax to access location zero of `x_train` is `x_train[0]`.\n", + "Run the next code block below to get the $i^{th}$ training example." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(x^(0), y^(0)) = (1.0, 300.0)\n" + ] + } + ], + "source": [ + "i = 0 # Change this to 1 to see (x^1, y^1)\n", + "\n", + "x_i = x_train[i]\n", + "y_i = y_train[i]\n", + "print(f\"(x^({i}), y^({i})) = ({x_i}, {y_i})\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting the data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can plot these two points using the `scatter()` function in the `matplotlib` library, as shown in the cell below. \n", + "- The function arguments `marker` and `c` show the points as red crosses (the default is blue dots).\n", + "\n", + "You can use other functions in the `matplotlib` library to set the title and labels to display" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the data points\n", + "plt.scatter(x_train, y_train, marker='x', c='r')\n", + "# Set the title\n", + "plt.title(\"Housing Prices\")\n", + "# Set the y-axis label\n", + "plt.ylabel('Price (in 1000s of dollars)')\n", + "# Set the x-axis label\n", + "plt.xlabel('Size (1000 sqft)')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model function\n", + "\n", + " As described in lecture, the model function for linear regression (which is a function that maps from `x` to `y`) is represented as \n", + "\n", + "$$ f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{1}$$\n", + "\n", + "The formula above is how you can represent straight lines - different values of $w$ and $b$ give you different straight lines on the plot.




\n", + "\n", + "Let's try to get a better intuition for this through the code blocks below. Let's start with $w = 100$ and $b = 100$. \n", + "\n", + "**Note: You can come back to this cell to adjust the model's w and b parameters**" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w: 100\n", + "b: 100\n" + ] + } + ], + "source": [ + "w = 100\n", + "b = 100\n", + "print(f\"w: {w}\")\n", + "print(f\"b: {b}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's compute the value of $f_{w,b}(x^{(i)})$ for your two data points. You can explicitly write this out for each data point as - \n", + "\n", + "for $x^{(0)}$, `f_wb = w * x[0] + b`\n", + "\n", + "for $x^{(1)}$, `f_wb = w * x[1] + b`\n", + "\n", + "For a large number of data points, this can get unwieldy and repetitive. So instead, you can calculate the function output in a `for` loop as shown in the `compute_model_output` function below.\n", + "> **Note**: The argument description `(ndarray (m,))` describes a Numpy n-dimensional array of shape (m,). `(scalar)` describes an argument without dimensions, just a magnitude. \n", + "> **Note**: `np.zero(n)` will return a one-dimensional numpy array with $n$ entries \n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_model_output(x, w, b):\n", + " \"\"\"\n", + " Computes the prediction of a linear model\n", + " Args:\n", + " x (ndarray (m,)): Data, m examples \n", + " w,b (scalar) : model parameters \n", + " Returns\n", + " y (ndarray (m,)): target values\n", + " \"\"\"\n", + " m = x.shape[0]\n", + " f_wb = np.zeros(m)\n", + " for i in range(m):\n", + " f_wb[i] = w * x[i] + b\n", + " \n", + " return f_wb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's call the `compute_model_output` function and plot the output.." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "tmp_f_wb = compute_model_output(x_train, w, b,)\n", + "\n", + "# Plot our model prediction\n", + "plt.plot(x_train, tmp_f_wb, c='b',label='Our Prediction')\n", + "\n", + "# Plot the data points\n", + "plt.scatter(x_train, y_train, marker='x', c='r',label='Actual Values')\n", + "\n", + "# Set the title\n", + "plt.title(\"Housing Prices\")\n", + "# Set the y-axis label\n", + "plt.ylabel('Price (in 1000s of dollars)')\n", + "# Set the x-axis label\n", + "plt.xlabel('Size (1000 sqft)')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, setting $w = 100$ and $b = 100$ does *not* result in a line that fits our data. \n", + "\n", + "### Challenge\n", + "Try experimenting with different values of $w$ and $b$. What should the values be for a line that fits our data?\n", + "\n", + "#### Tip:\n", + "You can use your mouse to click on the green \"Hints\" below to reveal some hints for choosing b and w." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "\n", + " Hints\n", + "\n", + "

\n", + "

    \n", + "
  • Try $w = 200$ and $b = 100$
  • \n", + "
\n", + "

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Prediction\n", + "Now that we have a model, we can use it to make our original prediction. Let's predict the price of a house with 1200 sqft. Since the units of $x$ are in 1000's of sqft, $x$ is 1.2.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "$340 thousand dollars\n" + ] + } + ], + "source": [ + "w = 200 \n", + "b = 100 \n", + "x_i = 1.2\n", + "cost_1200sqft = w * x_i + b \n", + "\n", + "print(f\"${cost_1200sqft:.0f} thousand dollars\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Congratulations!\n", + "In this lab you have learned:\n", + " - Linear regression builds a model which establishes a relationship between features and targets\n", + " - In the example above, the feature was house size and the target was house price\n", + " - for simple linear regression, the model has two parameters $w$ and $b$ whose values are 'fit' using *training data*.\n", + " - once a model's parameters have been determined, the model can be used to make predictions on novel data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + }, + "toc-autonumbering": false + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/C1_W1_Lab03_Cost_function_Soln.ipynb b/week1/C1_W1_Lab03_Cost_function_Soln.ipynb new file mode 100644 index 0000000..c98b80a --- /dev/null +++ b/week1/C1_W1_Lab03_Cost_function_Soln.ipynb @@ -0,0 +1,352 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Cost Function \n", + "
\n", + "
\n", + "
\n", + "\n" + ], + "id": "39510563895119eb" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab you will:\n", + "- you will implement and explore the `cost` function for linear regression with one variable. \n" + ], + "id": "a160c6cc32746122" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tools\n", + "In this lab we will make use of: \n", + "- NumPy, a popular library for scientific computing\n", + "- Matplotlib, a popular library for plotting data\n", + "- local plotting routines in the lab_utils_uni.py file in the local directory" + ], + "id": "ab2b5e324c46a0ea" + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "%matplotlib widget\n", + "import matplotlib.pyplot as plt\n", + "from lab_utils_uni import plt_intuition, plt_stationary, plt_update_onclick, soup_bowl\n", + "plt.style.use('./deeplearning.mplstyle')" + ], + "id": "f025d8d8eea42714" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem Statement\n", + "\n", + "You would like a model which can predict housing prices given the size of the house. \n", + "Let's use the same two data points as before the previous lab- a house with 1000 square feet sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000.\n", + "\n", + "\n", + "| Size (1000 sqft) | Price (1000s of dollars) |\n", + "| -------------------| ------------------------ |\n", + "| 1 | 300 |\n", + "| 2 | 500 |\n" + ], + "id": "a0b38aaf53fecdb4" + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "x_train = np.array([1.0, 2.0]) #(size in 1000 square feet)\n", + "y_train = np.array([300.0, 500.0]) #(price in 1000s of dollars)" + ], + "id": "4a5bab31ff88bda5" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing Cost\n", + "The term 'cost' in this assignment might be a little confusing since the data is housing cost. Here, cost is a measure how well our model is predicting the target price of the house. The term 'price' is used for housing data.\n", + "\n", + "The equation for cost with one variable is:\n", + " $$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2 \\tag{1}$$ \n", + " \n", + "where \n", + " $$f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{2}$$\n", + " \n", + "- $f_{w,b}(x^{(i)})$ is our prediction for example $i$ using parameters $w,b$. \n", + "- $(f_{w,b}(x^{(i)}) -y^{(i)})^2$ is the squared difference between the target value and the prediction. \n", + "- These differences are summed over all the $m$ examples and divided by `2m` to produce the cost, $J(w,b)$. \n", + ">Note, in lecture summation ranges are typically from 1 to m, while code will be from 0 to m-1.\n" + ], + "id": "2fde323fe15bd227" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The code below calculates cost by looping over each example. In each loop:\n", + "- `f_wb`, a prediction is calculated\n", + "- the difference between the target and the prediction is calculated and squared.\n", + "- this is added to the total cost." + ], + "id": "23fa56cab00e1046" + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_cost(x, y, w, b): \n", + " \"\"\"\n", + " Computes the cost function for linear regression.\n", + " \n", + " Args:\n", + " x (ndarray (m,)): Data, m examples \n", + " y (ndarray (m,)): target values\n", + " w,b (scalar) : model parameters \n", + " \n", + " Returns\n", + " total_cost (float): The cost of using w,b as the parameters for linear regression\n", + " to fit the data points in x and y\n", + " \"\"\"\n", + " # number of training examples\n", + " m = x.shape[0] \n", + " \n", + " cost_sum = 0 \n", + " for i in range(m): \n", + " f_wb = w * x[i] + b \n", + " cost = (f_wb - y[i]) ** 2 \n", + " cost_sum = cost_sum + cost \n", + " total_cost = (1 / (2 * m)) * cost_sum \n", + "\n", + " return total_cost" + ], + "id": "1166da6c92b7cac0" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cost Function Intuition" + ], + "id": "efaf37cff0b92f69" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " Your goal is to find a model $f_{w,b}(x) = wx + b$, with parameters $w,b$, which will accurately predict house values given an input $x$. The cost is a measure of how accurate the model is on the training data.\n", + "\n", + "The cost equation (1) above shows that if $w$ and $b$ can be selected such that the predictions $f_{w,b}(x)$ match the target data $y$, the $(f_{w,b}(x^{(i)}) - y^{(i)})^2 $ term will be zero and the cost minimized. In this simple two point example, you can achieve this!\n", + "\n", + "In the previous lab, you determined that $b=100$ provided an optimal solution so let's set $b$ to 100 and focus on $w$.\n", + "\n", + "
\n", + "Below, use the slider control to select the value of $w$ that minimizes cost. It can take a few seconds for the plot to update." + ], + "id": "a4c0cec8b6d37318" + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "7d57d1ccadbf42d6bc17488114bbf179", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt_intuition(x_train,y_train)" + ], + "id": "7cd5334a6770f526" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot contains a few points that are worth mentioning.\n", + "- cost is minimized when $w = 200$, which matches results from the previous lab\n", + "- Because the difference between the target and pediction is squared in the cost equation, the cost increases rapidly when $w$ is either too large or too small.\n", + "- Using the `w` and `b` selected by minimizing cost results in a line which is a perfect fit to the data." + ], + "id": "30972f54ab8f1d94" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cost Function Visualization- 3D\n", + "\n", + "You can see how cost varies with respect to *both* `w` and `b` by plotting in 3D or using a contour plot. \n", + "It is worth noting that some of the plotting in this course can become quite involved. The plotting routines are provided and while it can be instructive to read through the code to become familiar with the methods, it is not needed to complete the course successfully. The routines are in lab_utils_uni.py in the local directory." + ], + "id": "6c6395d1ef2abecf" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Larger Data Set\n", + "It is instructive to view a scenario with a few more data points. This data set includes data points that do not fall on the same line. What does that mean for the cost equation? Can we find $w$, and $b$ that will give us a cost of 0? " + ], + "id": "e8329d184d8344fc" + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "x_train = np.array([1.0, 1.7, 2.0, 2.5, 3.0, 3.2])\n", + "y_train = np.array([250, 300, 480, 430, 630, 730,])" + ], + "id": "b0c0aed371b5ca39" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the contour plot, click on a point to select `w` and `b` to achieve the lowest cost. Use the contours to guide your selections. Note, it can take a few seconds to update the graph. " + ], + "id": "2bc747abba448d65" + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "d5cceda8ce34448290f1c2cac01ee091", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.close('all') \n", + "fig, ax, dyn_items = plt_stationary(x_train, y_train)\n", + "updater = plt_update_onclick(fig, ax, x_train, y_train, dyn_items)" + ], + "id": "9159d3905b017257" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above, note the dashed lines in the left plot. These represent the portion of the cost contributed by each example in your training set. In this case, values of approximately $w=209$ and $b=2.4$ provide low cost. Note that, because our training examples are not on a line, the minimum cost is not zero." + ], + "id": "5f4c1ac7bb9a78d" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Convex Cost surface\n", + "The fact that the cost function squares the loss ensures that the 'error surface' is convex like a soup bowl. It will always have a minimum that can be reached by following the gradient in all dimensions. In the previous plot, because the $w$ and $b$ dimensions scale differently, this is not easy to recognize. The following plot, where $w$ and $b$ are symmetric, was shown in lecture:" + ], + "id": "763c2e6ab47d9587" + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "b9ea89764a324a98893ec2d8d2689e77", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "soup_bowl()" + ], + "id": "13af7fc972d655b3" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Congratulations!\n", + "You have learned the following:\n", + " - The cost equation provides a measure of how well your predictions match your training data.\n", + " - Minimizing the cost can provide optimal values of $w$, $b$." + ], + "id": "850e586e9601ef7e" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [], + "id": "67ad1bd9bfe55fd" + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + }, + "toc-autonumbering": false + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/C1_W1_Lab04_Gradient_Descent_Soln.ipynb b/week1/C1_W1_Lab04_Gradient_Descent_Soln.ipynb new file mode 100644 index 0000000..2c615ff --- /dev/null +++ b/week1/C1_W1_Lab04_Gradient_Descent_Soln.ipynb @@ -0,0 +1,657 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Gradient Descent for Linear Regression\n", + "\n", + "
\n", + "
\n", + "
" + ], + "id": "51d539b8933c08f0" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab, you will:\n", + "- automate the process of optimizing $w$ and $b$ using gradient descent." + ], + "id": "3c5af2ac34433447" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tools\n", + "In this lab, we will make use of: \n", + "- NumPy, a popular library for scientific computing\n", + "- Matplotlib, a popular library for plotting data\n", + "- plotting routines in the lab_utils.py file in the local directory" + ], + "id": "7a45aef1427d3296" + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math, copy\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('./deeplearning.mplstyle')\n", + "from lab_utils_uni import plt_house_x, plt_contour_wgrad, plt_divergence, plt_gradients" + ], + "id": "a1fce6f64e2718a1" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Problem Statement\n", + "\n", + "Let's use the same two data points as before - a house with 1000 square feet sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000.\n", + "\n", + "| Size (1000 sqft) | Price (1000s of dollars) |\n", + "| ----------------| ------------------------ |\n", + "| 1 | 300 |\n", + "| 2 | 500 |\n" + ], + "id": "1c0984e19ab9e6b4" + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Load our data set\n", + "x_train = np.array([1.0, 2.0]) #features\n", + "y_train = np.array([300.0, 500.0]) #target value" + ], + "id": "bf19c8fde61dfcfd" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Compute_Cost\n", + "This was developed in the last lab. We'll need it again here." + ], + "id": "b1780bff7ac8aa73" + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "#Function to calculate the cost\n", + "def compute_cost(x, y, w, b):\n", + " \n", + " m = x.shape[0] \n", + " cost = 0\n", + " \n", + " for i in range(m):\n", + " f_wb = w * x[i] + b\n", + " cost = cost + (f_wb - y[i])**2\n", + " total_cost = 1 / (2 * m) * cost\n", + "\n", + " return total_cost" + ], + "id": "fac0212ae8afd849" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Gradient descent summary\n", + "So far in this course, you have developed a linear model that predicts $f_{w,b}(x^{(i)})$:\n", + "$$f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{1}$$\n", + "In linear regression, you utilize input training data to fit the parameters $w$,$b$ by minimizing a measure of the error between our predictions $f_{w,b}(x^{(i)})$ and the actual data $y^{(i)}$. The measure is called the $cost$, $J(w,b)$. In training you measure the cost over all of our training samples $x^{(i)},y^{(i)}$\n", + "$$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2\\tag{2}$$ " + ], + "id": "ae55d8d0930866a3" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "In lecture, *gradient descent* was described as:\n", + "\n", + "$$\\begin{align*} \\text{repeat}&\\text{ until convergence:} \\; \\lbrace \\newline\n", + "\\; w &= w - \\alpha \\frac{\\partial J(w,b)}{\\partial w} \\tag{3} \\; \\newline \n", + " b &= b - \\alpha \\frac{\\partial J(w,b)}{\\partial b} \\newline \\rbrace\n", + "\\end{align*}$$\n", + "where, parameters $w$, $b$ are updated simultaneously. \n", + "The gradient is defined as:\n", + "$$\n", + "\\begin{align}\n", + "\\frac{\\partial J(w,b)}{\\partial w} &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})x^{(i)} \\tag{4}\\\\\n", + " \\frac{\\partial J(w,b)}{\\partial b} &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)}) \\tag{5}\\\\\n", + "\\end{align}\n", + "$$\n", + "\n", + "Here *simultaniously* means that you calculate the partial derivatives for all the parameters before updating any of the parameters." + ], + "id": "760cfdd6f3f8c687" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Implement Gradient Descent\n", + "You will implement gradient descent algorithm for one feature. You will need three functions. \n", + "- `compute_gradient` implementing equation (4) and (5) above\n", + "- `compute_cost` implementing equation (2) above (code from previous lab)\n", + "- `gradient_descent`, utilizing compute_gradient and compute_cost\n", + "\n", + "Conventions:\n", + "- The naming of python variables containing partial derivatives follows this pattern,$\\frac{\\partial J(w,b)}{\\partial b}$ will be `dj_db`.\n", + "- w.r.t is With Respect To, as in partial derivative of $J(wb)$ With Respect To $b$.\n" + ], + "id": "e3d4ec60b7ca63f6" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### compute_gradient\n", + "\n", + "`compute_gradient` implements (4) and (5) above and returns $\\frac{\\partial J(w,b)}{\\partial w}$,$\\frac{\\partial J(w,b)}{\\partial b}$. The embedded comments describe the operations." + ], + "id": "d2b095ba2d1b3f1a" + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_gradient(x, y, w, b): \n", + " \"\"\"\n", + " Computes the gradient for linear regression \n", + " Args:\n", + " x (ndarray (m,)): Data, m examples \n", + " y (ndarray (m,)): target values\n", + " w,b (scalar) : model parameters \n", + " Returns\n", + " dj_dw (scalar): The gradient of the cost w.r.t. the parameters w\n", + " dj_db (scalar): The gradient of the cost w.r.t. the parameter b \n", + " \"\"\"\n", + " \n", + " # Number of training examples\n", + " m = x.shape[0] \n", + " dj_dw = 0\n", + " dj_db = 0\n", + " \n", + " for i in range(m): \n", + " f_wb = w * x[i] + b \n", + " dj_dw_i = (f_wb - y[i]) * x[i] \n", + " dj_db_i = f_wb - y[i] \n", + " dj_db += dj_db_i\n", + " dj_dw += dj_dw_i \n", + " dj_dw = dj_dw / m \n", + " dj_db = dj_db / m \n", + " \n", + " return dj_dw, dj_db" + ], + "id": "c60c94ca2ba78bea" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
" + ], + "id": "4e7b10ba866408c9" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " The lectures described how gradient descent utilizes the partial derivative of the cost with respect to a parameter at a point to update that parameter. \n", + "Let's use our `compute_gradient` function to find and plot some partial derivatives of our cost function relative to one of the parameters, $w_0$.\n" + ], + "id": "6a7ec85f8dc84e49" + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt_gradients(x_train,y_train, compute_cost, compute_gradient)\n", + "plt.show()" + ], + "id": "92ccd2b1189c2e4f" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above, the left plot shows $\\frac{\\partial J(w,b)}{\\partial w}$ or the slope of the cost curve relative to $w$ at three points. On the right side of the plot, the derivative is positive, while on the left it is negative. Due to the 'bowl shape', the derivatives will always lead gradient descent toward the bottom where the gradient is zero.\n", + " \n", + "The left plot has fixed $b=100$. Gradient descent will utilize both $\\frac{\\partial J(w,b)}{\\partial w}$ and $\\frac{\\partial J(w,b)}{\\partial b}$ to update parameters. The 'quiver plot' on the right provides a means of viewing the gradient of both parameters. The arrow sizes reflect the magnitude of the gradient at that point. The direction and slope of the arrow reflects the ratio of $\\frac{\\partial J(w,b)}{\\partial w}$ and $\\frac{\\partial J(w,b)}{\\partial b}$ at that point.\n", + "Note that the gradient points *away* from the minimum. Review equation (3) above. The scaled gradient is *subtracted* from the current value of $w$ or $b$. This moves the parameter in a direction that will reduce cost." + ], + "id": "e2c8ab9d96d48ec0" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Gradient Descent\n", + "Now that gradients can be computed, gradient descent, described in equation (3) above can be implemented below in `gradient_descent`. The details of the implementation are described in the comments. Below, you will utilize this function to find optimal values of $w$ and $b$ on the training data." + ], + "id": "9a8470ca87962ea" + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function): \n", + " \"\"\"\n", + " Performs gradient descent to fit w,b. Updates w,b by taking \n", + " num_iters gradient steps with learning rate alpha\n", + " \n", + " Args:\n", + " x (ndarray (m,)) : Data, m examples \n", + " y (ndarray (m,)) : target values\n", + " w_in,b_in (scalar): initial values of model parameters \n", + " alpha (float): Learning rate\n", + " num_iters (int): number of iterations to run gradient descent\n", + " cost_function: function to call to produce cost\n", + " gradient_function: function to call to produce gradient\n", + " \n", + " Returns:\n", + " w (scalar): Updated value of parameter after running gradient descent\n", + " b (scalar): Updated value of parameter after running gradient descent\n", + " J_history (List): History of cost values\n", + " p_history (list): History of parameters [w,b] \n", + " \"\"\"\n", + " \n", + " # An array to store cost J and w's at each iteration primarily for graphing later\n", + " J_history = []\n", + " p_history = []\n", + " b = b_in\n", + " w = w_in\n", + " \n", + " for i in range(num_iters):\n", + " # Calculate the gradient and update the parameters using gradient_function\n", + " dj_dw, dj_db = gradient_function(x, y, w , b) \n", + "\n", + " # Update Parameters using equation (3) above\n", + " b = b - alpha * dj_db \n", + " w = w - alpha * dj_dw \n", + "\n", + " # Save cost J at each iteration\n", + " if i<100000: # prevent resource exhaustion \n", + " J_history.append( cost_function(x, y, w , b))\n", + " p_history.append([w,b])\n", + " # Print cost every at intervals 10 times or as many iterations if < 10\n", + " if i% math.ceil(num_iters/10) == 0:\n", + " print(f\"Iteration {i:4}: Cost {J_history[-1]:0.2e} \",\n", + " f\"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e} \",\n", + " f\"w: {w: 0.3e}, b:{b: 0.5e}\")\n", + " \n", + " return w, b, J_history, p_history #return w and J,w history for graphing" + ], + "id": "289c570d8e6d0b9f" + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0: Cost 7.93e+04 dj_dw: -6.500e+02, dj_db: -4.000e+02 w: 6.500e+00, b: 4.00000e+00\n", + "Iteration 1000: Cost 3.41e+00 dj_dw: -3.712e-01, dj_db: 6.007e-01 w: 1.949e+02, b: 1.08228e+02\n", + "Iteration 2000: Cost 7.93e-01 dj_dw: -1.789e-01, dj_db: 2.895e-01 w: 1.975e+02, b: 1.03966e+02\n", + "Iteration 3000: Cost 1.84e-01 dj_dw: -8.625e-02, dj_db: 1.396e-01 w: 1.988e+02, b: 1.01912e+02\n", + "Iteration 4000: Cost 4.28e-02 dj_dw: -4.158e-02, dj_db: 6.727e-02 w: 1.994e+02, b: 1.00922e+02\n", + "Iteration 5000: Cost 9.95e-03 dj_dw: -2.004e-02, dj_db: 3.243e-02 w: 1.997e+02, b: 1.00444e+02\n", + "Iteration 6000: Cost 2.31e-03 dj_dw: -9.660e-03, dj_db: 1.563e-02 w: 1.999e+02, b: 1.00214e+02\n", + "Iteration 7000: Cost 5.37e-04 dj_dw: -4.657e-03, dj_db: 7.535e-03 w: 1.999e+02, b: 1.00103e+02\n", + "Iteration 8000: Cost 1.25e-04 dj_dw: -2.245e-03, dj_db: 3.632e-03 w: 2.000e+02, b: 1.00050e+02\n", + "Iteration 9000: Cost 2.90e-05 dj_dw: -1.082e-03, dj_db: 1.751e-03 w: 2.000e+02, b: 1.00024e+02\n", + "(w,b) found by gradient descent: (199.9929,100.0116)\n" + ] + } + ], + "source": [ + "# initialize parameters\n", + "w_init = 0\n", + "b_init = 0\n", + "# some gradient descent settings\n", + "iterations = 10000\n", + "tmp_alpha = 1.0e-2\n", + "# run gradient descent\n", + "w_final, b_final, J_hist, p_hist = gradient_descent(x_train ,y_train, w_init, b_init, tmp_alpha, \n", + " iterations, compute_cost, compute_gradient)\n", + "print(f\"(w,b) found by gradient descent: ({w_final:8.4f},{b_final:8.4f})\")" + ], + "id": "b78236dad287b179" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " \n", + "Take a moment and note some characteristics of the gradient descent process printed above. \n", + "\n", + "- The cost starts large and rapidly declines as described in the slide from the lecture.\n", + "- The partial derivatives, `dj_dw`, and `dj_db` also get smaller, rapidly at first and then more slowly. As shown in the diagram from the lecture, as the process nears the 'bottom of the bowl' progress is slower due to the smaller value of the derivative at that point.\n", + "- progress slows though the learning rate, alpha, remains fixed" + ], + "id": "ac49cab25475792b" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cost versus iterations of gradient descent \n", + "A plot of cost versus iterations is a useful measure of progress in gradient descent. Cost should always decrease in successful runs. The change in cost is so rapid initially, it is useful to plot the initial decent on a different scale than the final descent. In the plots below, note the scale of cost on the axes and the iteration step." + ], + "id": "84928145fa5d834e" + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot cost versus iteration \n", + "fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True, figsize=(12,4))\n", + "ax1.plot(J_hist[:100])\n", + "ax2.plot(1000 + np.arange(len(J_hist[1000:])), J_hist[1000:])\n", + "ax1.set_title(\"Cost vs. iteration(start)\"); ax2.set_title(\"Cost vs. iteration (end)\")\n", + "ax1.set_ylabel('Cost') ; ax2.set_ylabel('Cost') \n", + "ax1.set_xlabel('iteration step') ; ax2.set_xlabel('iteration step') \n", + "plt.show()" + ], + "id": "3fb63a2e448607fa" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Predictions\n", + "Now that you have discovered the optimal values for the parameters $w$ and $b$, you can now use the model to predict housing values based on our learned parameters. As expected, the predicted values are nearly the same as the training values for the same housing. Further, the value not in the prediction is in line with the expected value." + ], + "id": "877b4268d61cbd1e" + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1000 sqft house prediction 300.0 Thousand dollars\n", + "1200 sqft house prediction 340.0 Thousand dollars\n", + "2000 sqft house prediction 500.0 Thousand dollars\n" + ] + } + ], + "source": [ + "print(f\"1000 sqft house prediction {w_final*1.0 + b_final:0.1f} Thousand dollars\")\n", + "print(f\"1200 sqft house prediction {w_final*1.2 + b_final:0.1f} Thousand dollars\")\n", + "print(f\"2000 sqft house prediction {w_final*2.0 + b_final:0.1f} Thousand dollars\")" + ], + "id": "e1840d7ee6522d2b" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Plotting\n", + "You can show the progress of gradient descent during its execution by plotting the cost over iterations on a contour plot of the cost(w,b). " + ], + "id": "622ef2db1d43a509" + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1,1, figsize=(12, 6))\n", + "plt_contour_wgrad(x_train, y_train, p_hist, ax)" + ], + "id": "9338e55a8dd87ceb" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above, the contour plot shows the $cost(w,b)$ over a range of $w$ and $b$. Cost levels are represented by the rings. Overlayed, using red arrows, is the path of gradient descent. Here are some things to note:\n", + "- The path makes steady (monotonic) progress toward its goal.\n", + "- initial steps are much larger than the steps near the goal." + ], + "id": "31e1cbcb0421b6e7" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Zooming in**, we can see that final steps of gradient descent. Note the distance between steps shrinks as the gradient approaches zero." + ], + "id": "90e4ccbd6599f90a" + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1,1, figsize=(12, 4))\n", + "plt_contour_wgrad(x_train, y_train, p_hist, ax, w_range=[180, 220, 0.5], b_range=[80, 120, 0.5],\n", + " contours=[1,5,10,20],resolution=0.5)" + ], + "id": "871c3cbed53e2e1d" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Increased Learning Rate\n", + "\n", + "
\n", + " \n", + "
\n", + "In the lecture, there was a discussion related to the proper value of the learning rate, $\\alpha$ in equation(3). The larger $\\alpha$ is, the faster gradient descent will converge to a solution. But, if it is too large, gradient descent will diverge. Above you have an example of a solution which converges nicely.\n", + "\n", + "Let's try increasing the value of $\\alpha$ and see what happens:" + ], + "id": "fe6cbc15bef486f6" + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0: Cost 2.58e+05 dj_dw: -6.500e+02, dj_db: -4.000e+02 w: 5.200e+02, b: 3.20000e+02\n", + "Iteration 1: Cost 7.82e+05 dj_dw: 1.130e+03, dj_db: 7.000e+02 w: -3.840e+02, b:-2.40000e+02\n", + "Iteration 2: Cost 2.37e+06 dj_dw: -1.970e+03, dj_db: -1.216e+03 w: 1.192e+03, b: 7.32800e+02\n", + "Iteration 3: Cost 7.19e+06 dj_dw: 3.429e+03, dj_db: 2.121e+03 w: -1.551e+03, b:-9.63840e+02\n", + "Iteration 4: Cost 2.18e+07 dj_dw: -5.974e+03, dj_db: -3.691e+03 w: 3.228e+03, b: 1.98886e+03\n", + "Iteration 5: Cost 6.62e+07 dj_dw: 1.040e+04, dj_db: 6.431e+03 w: -5.095e+03, b:-3.15579e+03\n", + "Iteration 6: Cost 2.01e+08 dj_dw: -1.812e+04, dj_db: -1.120e+04 w: 9.402e+03, b: 5.80237e+03\n", + "Iteration 7: Cost 6.09e+08 dj_dw: 3.156e+04, dj_db: 1.950e+04 w: -1.584e+04, b:-9.80139e+03\n", + "Iteration 8: Cost 1.85e+09 dj_dw: -5.496e+04, dj_db: -3.397e+04 w: 2.813e+04, b: 1.73730e+04\n", + "Iteration 9: Cost 5.60e+09 dj_dw: 9.572e+04, dj_db: 5.916e+04 w: -4.845e+04, b:-2.99567e+04\n" + ] + } + ], + "source": [ + "# initialize parameters\n", + "w_init = 0\n", + "b_init = 0\n", + "# set alpha to a large value\n", + "iterations = 10\n", + "tmp_alpha = 8.0e-1\n", + "# run gradient descent\n", + "w_final, b_final, J_hist, p_hist = gradient_descent(x_train ,y_train, w_init, b_init, tmp_alpha, \n", + " iterations, compute_cost, compute_gradient)" + ], + "id": "904051e5b17f7611" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above, $w$ and $b$ are bouncing back and forth between positive and negative with the absolute value increasing with each iteration. Further, each iteration $\\frac{\\partial J(w,b)}{\\partial w}$ changes sign and cost is increasing rather than decreasing. This is a clear sign that the *learning rate is too large* and the solution is diverging. \n", + "Let's visualize this with a plot." + ], + "id": "3e128d8848ed786d" + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt_divergence(p_hist, J_hist,x_train, y_train)\n", + "plt.show()" + ], + "id": "525859aea07d903" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above, the left graph shows $w$'s progression over the first few steps of gradient descent. $w$ oscillates from positive to negative and cost grows rapidly. Gradient Descent is operating on both $w$ and $b$ simultaneously, so one needs the 3-D plot on the right for the complete picture." + ], + "id": "f188bcb1dbebb9d" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Congratulations!\n", + "In this lab you:\n", + "- delved into the details of gradient descent for a single variable.\n", + "- developed a routine to compute the gradient\n", + "- visualized what the gradient is\n", + "- completed a gradient descent routine\n", + "- utilized gradient descent to find parameters\n", + "- examined the impact of sizing the learning rate" + ], + "id": "1d1832515c0982de" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [], + "id": "2b544fe91032e577" + } + ], + "metadata": { + "dl_toc_settings": { + "rndtag": "40291" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + }, + "toc-autonumbering": false + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/betaversion/C1_W1_Lab01_Python_Jupyter_Soln.ipynb b/week1/betaversion/C1_W1_Lab01_Python_Jupyter_Soln.ipynb new file mode 100644 index 0000000..2b26925 --- /dev/null +++ b/week1/betaversion/C1_W1_Lab01_Python_Jupyter_Soln.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Brief Introduction to Python and Jupyter Notebooks\n", + "Welcome to the first optional lab! \n", + "Optional labs are available to:\n", + "- provide information - like this notebook\n", + "- reinforce lecture material with hands-on examples\n", + "- provide working examples of routines used in the graded labs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab, you will:\n", + "- Get a brief introduction to Jupyter notebooks\n", + "- Take a tour of Jupyter notebooks\n", + "- Learn the difference between markdown cells and code cells\n", + "- Practice some basic python\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The easiest way to become familiar with Jupyter notebooks is to take the tour available above in the Help menu:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "
missing
\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Jupyter notebooks have two types of cells that are used in this course. Cells such as this which contain documentation called `Markdown Cells`. The name is derived from the simple formatting language used in the cells. You will not be required to produce markdown cells. Its useful to understand the `cell pulldown` shown in graphic below. Occasionally, a cell will end up in the wrong mode and you may need to restore it to the right state:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + " missing\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The other type of cell is the `code cell` where you will write your code:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "This is code cell\n" + ] + } + ], + "source": [ + "#This is a 'Code' Cell\n", + "print(\"This is code cell\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Python\n", + "You can write your code in the code cells. \n", + "To run the code, select the cell and either\n", + "- hold the shift-key down and hit 'enter' or 'return'\n", + "- click the 'run' arrow above\n", + "
\n", + " \n", + "
\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Print statement\n", + "Print statements will generally use the python f-string style. \n", + "Try creating your own print in the following cell. \n", + "Try both methods of running the cell." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "f strings allow you to embed variables right in the strings!\n" + ] + } + ], + "source": [ + "# print statements\n", + "variable = \"right in the strings!\"\n", + "print(f\"f strings allow you to embed variables {variable}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Congratulations!\n", + "You now know how to find your way around a Jupyter Notebook." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/betaversion/C1_W1_Lab02_Course_Preview_Soln.ipynb b/week1/betaversion/C1_W1_Lab02_Course_Preview_Soln.ipynb new file mode 100644 index 0000000..81a0133 --- /dev/null +++ b/week1/betaversion/C1_W1_Lab02_Course_Preview_Soln.ipynb @@ -0,0 +1,33 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ungraded Lab - Examples of Material that will be covered in this course\n", + "Work in Progress" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/betaversion/C1_W1_Lab03_Model_Representation_Soln.ipynb b/week1/betaversion/C1_W1_Lab03_Model_Representation_Soln.ipynb new file mode 100644 index 0000000..69cbf77 --- /dev/null +++ b/week1/betaversion/C1_W1_Lab03_Model_Representation_Soln.ipynb @@ -0,0 +1,398 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Model Representation\n", + "\n", + "
\n", + " \n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab you will:\n", + "- Learn to implement the model $f_{w,b}$ for linear regression with one variable" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notation\n", + "Here is a summary of some of the notation you will encounter. \n", + "\n", + "|General
Notation | Description| Python (if applicable) |\n", + "|: ------------|: ------------------------------------------------------------||\n", + "| $a$ | scalar, non bold ||\n", + "| $\\mathbf{a}$ | vector, bold ||\n", + "| **Regression** | | | |\n", + "| $\\mathbf{x}$ | Training Example feature values (in this lab - Size (1000 sqft)) | `x_train` | \n", + "| $\\mathbf{y}$ | Training Example targets (in this lab Price (1000s of dollars)).) | `y_train` \n", + "| $x^{(i)}$, $y^{(i)}$ | $i_{th}$Training Example | `x_i`, `y_i`|\n", + "| m | Number of training examples | `m`|\n", + "| $w$ | parameter: weight, | `w` |\n", + "| $b$ | parameter: bias | `b` | \n", + "| $f_{w,b}(x^{(i)})$ | The result of the model evaluation at $x^{(i)}$ parameterized by $w,b$: $f_{w,b}(x^{(i)}) = wx^{(i)}+b$ | `f_wb` | \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tools\n", + "In this lab you will make use of: \n", + "- NumPy, a popular library for scientific computing\n", + "- Matplotlib, a popular library for plotting data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('./deeplearning.mplstyle')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Statement\n", + " \n", + "\n", + "As in the lecture, you will use the motivating example of housing price prediction. \n", + "This lab will use a simple data set with only two data points - a house with 1000 square feet(sqft) sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000. These two points will constitute our *data or training set*. In this lab, the units of size are 1000 sqft and the units of price are $1000's of dollars.\n", + "\n", + "| Size (1000 sqft) | Price (1000s of dollars) |\n", + "| -------------------| ------------------------ |\n", + "| 1.0 | 300 |\n", + "| 2.0 | 500 |\n", + "\n", + "You would like to fit a linear regression model (shown above as the blue straight line) through these two points, so you can then predict price for other houses - say, a house with 1200 sqft.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Please run the following code cell to create your `x_train` and `y_train` variables. The data is stored in one-dimensional NumPy arrays." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# x_train is the input variable (size in 1000 square feet)\n", + "# y_train in the target (price in 1000s of dollars)\n", + "x_train = np.array([1.0, 2.0])\n", + "y_train = np.array([300.0, 500.0])\n", + "print(f\"x_train = {x_train}\")\n", + "print(f\"y_train = {y_train}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ">**Note**: The course will frequently utilize the python 'f-string' output formatting described [here](https://docs.python.org/3/tutorial/inputoutput.html) when printing. The content between the curly braces is evaluated when producing the output." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Number of training examples `m`\n", + "You will use `m` to denote the number of training examples. Numpy arrays have a `.shape` parameter. `x_train.shape` returns a python tuple with an entry for each dimension. `x_train.shape[0]` is the length of the array and number of examples as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# m is the number of training examples\n", + "print(f\"x_train.shape: {x_train.shape}\")\n", + "m = x_train.shape[0]\n", + "print(f\"Number of training examples is: {m}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One can also use the Python `len()` function as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# m is the number of training examples\n", + "m = len(x_train)\n", + "print(f\"Number of training examples is: {m}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Training example `x_i, y_i`\n", + "\n", + "You will use (x$^{(i)}$, y$^{(i)}$) to denote the $i^{th}$ training example. Since Python is zero indexed, (x$^{(0)}$, y$^{(0)}$) is (1.0, 300.0) and (x$^{(1)}$, y$^{(1)}$) is (2.0, 500.0). \n", + "\n", + "To access a value in a Numpy array, one indexes the array with the desired offset. For example the syntax to access location zero of `x_train` is `x_train[0]`.\n", + "Run the next code block below to get the $i^{th}$ training example." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "i = 0 # Change this to 1 to see (x^1, y^1)\n", + "\n", + "x_i = x_train[i]\n", + "y_i = y_train[i]\n", + "print(f\"(x^({i}), y^({i})) = ({x_i}, {y_i})\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting the data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can plot these two points using the `scatter()` function in the `matplotlib` library, as shown in the cell below. \n", + "- The function arguments `marker` and `c` show the points as red crosses (the default is blue dots).\n", + "\n", + "You can also use other functions in the `matplotlib` library to display the title and labels for the axes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Plot the data points\n", + "plt.scatter(x_train, y_train, marker='x', c='r')\n", + "# Set the title\n", + "plt.title(\"Housing Prices\")\n", + "# Set the y-axis label\n", + "plt.ylabel('Price (in 1000s of dollars)')\n", + "# Set the x-axis label\n", + "plt.xlabel('Size (1000 sqft)')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model function\n", + "\n", + " As described in lecture, the model function for linear regression (which is a function that maps from `x` to `y`) is represented as \n", + "\n", + "$$ f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{1}$$\n", + "\n", + "The formula above is how you can represent straight lines - different values of $w$ and $b$ give you different straight lines on the plot.




\n", + "\n", + "Let's try to get a better intuition for this through the code blocks below. Let's start with $w = 100$ and $b = 100$. \n", + "\n", + "**Note: You can come back to this cell to adjust the model's w and b parameters**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "w = 100\n", + "b = 100\n", + "print(f\"w: {w}\")\n", + "print(f\"b: {b}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's compute the value of $f_{w,b}(x^{(i)})$ for your two data points. You can explicitly write this out for each data point as - \n", + "\n", + "for $x^{(0)}$, `f_wb = w * x[0] + b`\n", + "\n", + "for $x^{(1)}$, `f_wb = w * x[1] + b`\n", + "\n", + "For a large number of data points, this can get unwieldy and repetitive. So instead, you can calculate the function output in a `for` loop as shown in the `compute_model_output` function below.\n", + "> **Note**: The argument description `(ndarray (m,))` describes a Numpy n-dimensional array of shape (m,). `(scalar)` describes an argument without dimensions, just a magnitude. \n", + "> **Note**: `np.zero(n)` will return a one-dimensional numpy array with $n$ entries \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_model_output(x, w, b):\n", + " \"\"\"\n", + " Computes the prediction of a linear model\n", + " Args:\n", + " x (ndarray (m,)): Data, m examples \n", + " w,b (scalar) : model parameters \n", + " Returns\n", + " y (ndarray (m,)): target values\n", + " \"\"\"\n", + " m = x.shape[0]\n", + " f_wb = np.zeros(m)\n", + " for i in range(m):\n", + " f_wb[i] = w * x[i] + b\n", + " \n", + " return f_wb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's call the `compute_model_output` function and plot the output.." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "tmp_f_wb = compute_model_output(x_train, w, b,)\n", + "\n", + "# Plot our model prediction\n", + "plt.plot(x_train, tmp_f_wb, c='b',label='Our Prediction')\n", + "\n", + "# Plot the data points\n", + "plt.scatter(x_train, y_train, marker='x', c='r',label='Actual Values')\n", + "\n", + "# Set the title\n", + "plt.title(\"Housing Prices\")\n", + "# Set the y-axis label\n", + "plt.ylabel('Price (in 1000s of dollars)')\n", + "# Set the x-axis label\n", + "plt.xlabel('Size (1000 sqft)')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, setting $w = 100$ and $b = 100$ does *not* result in a line that fits our data. \n", + "\n", + "### Challenge\n", + "Try experimenting with different values of $w$ and $b$. What should the values be for a line that fits our data?\n", + "\n", + "#### Tip:\n", + "You can use your mouse to click on the triangle to the left of the green \"Hints\" below to reveal some hints for choosing b and w." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "\n", + " Hints\n", + "\n", + "

\n", + "

    \n", + "
  • Try $w = 200$ and $b = 100$
  • \n", + "
\n", + "

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Prediction\n", + "Now that we have a model, we can use it to make our original prediction. Let's predict the price of a house with 1200 sqft. Since the units of $x$ are in 1000's of sqft, $x$ is 1.2.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "w = 200 \n", + "b = 100 \n", + "x_i = 1.2\n", + "cost_1200sqft = w * x_i + b \n", + "\n", + "print(f\"${cost_1200sqft:.0f} thousand dollars\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Congratulations!\n", + "In this lab you have learned:\n", + " - Linear regression builds a model which establishes a relationship between features and targets\n", + " - In the example above, the feature was house size and the target was house price\n", + " - for simple linear regression, the model has two parameters $w$ and $b$ whose values are 'fit' using *training data*.\n", + " - once a model's parameters have been determined, the model can be used to make predictions on novel data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + }, + "toc-autonumbering": false + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/betaversion/C1_W1_Lab04_Cost_function_Soln.ipynb b/week1/betaversion/C1_W1_Lab04_Cost_function_Soln.ipynb new file mode 100644 index 0000000..a18c5da --- /dev/null +++ b/week1/betaversion/C1_W1_Lab04_Cost_function_Soln.ipynb @@ -0,0 +1,307 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Cost Function \n", + "
\n", + "
\n", + "
\n", + "\n" + ], + "id": "7d3391ce25e5ba89" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab you will:\n", + "- you will implement and explore the `cost` function for linear regression with one variable. \n" + ], + "id": "1e010f719c5d086f" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tools\n", + "In this lab we will make use of: \n", + "- NumPy, a popular library for scientific computing\n", + "- Matplotlib, a popular library for plotting data\n", + "- local plotting routines in the lab_utils_uni.py file in the local directory" + ], + "id": "13698dcbd73ca0d9" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "%matplotlib widget\n", + "import matplotlib.pyplot as plt\n", + "from lab_utils_uni import plt_intuition, plt_stationary, plt_update_onclick, soup_bowl\n", + "plt.style.use('./deeplearning.mplstyle')" + ], + "id": "32c06d217d8bb153" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem Statement\n", + "\n", + "You would like a model which can predict housing prices given the size of the house. \n", + "Let's use the same two data points as before the previous lab- a house with 1000 square feet sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000.\n", + "\n", + "\n", + "| Size (1000 sqft) | Price (1000s of dollars) |\n", + "| -------------------| ------------------------ |\n", + "| 1 | 300 |\n", + "| 2 | 500 |\n" + ], + "id": "68e608da30aff630" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x_train = np.array([1.0, 2.0]) #(size in 1000 square feet)\n", + "y_train = np.array([300.0, 500.0]) #(price in 1000s of dollars)" + ], + "id": "8f289b3bf82b01f0" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing Cost\n", + "The term 'cost' in this assignment might be a little confusing since the data is housing cost. Here, cost is a measure how well our model is predicting the target price of the house. The term 'price' is used for housing data.\n", + "\n", + "The equation for cost with one variable is:\n", + " $$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2 \\tag{1}$$ \n", + " \n", + "where \n", + " $$f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{2}$$\n", + " \n", + "- $f_{w,b}(x^{(i)})$ is our prediction for example $i$ using parameters $w,b$. \n", + "- $(f_{w,b}(x^{(i)}) -y^{(i)})^2$ is the squared difference between the target value and the prediction. \n", + "- These differences are summed over all the $m$ examples and divided by `2m` to produce the cost, $J(w,b)$. \n", + ">Note, in lecture summation ranges are typically from 1 to m, while code will be from 0 to m-1.\n" + ], + "id": "ab44dcb0c92cfdc" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The code below calculates cost by looping over each example. In each loop:\n", + "- `f_wb`, a prediction is calculated\n", + "- the difference between the target and the prediction is calculated and squared.\n", + "- this is added to the total cost." + ], + "id": "a63a74f54bb59b2d" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_cost(x, y, w, b): \n", + " \"\"\"\n", + " Computes the cost function for linear regression.\n", + " \n", + " Args:\n", + " x (ndarray (m,)): Data, m examples \n", + " y (ndarray (m,)): target values\n", + " w,b (scalar) : model parameters \n", + " \n", + " Returns\n", + " total_cost (float): The cost of using w,b as the parameters for linear regression\n", + " to fit the data points in x and y\n", + " \"\"\"\n", + " # number of training examples\n", + " m = x.shape[0] \n", + " \n", + " cost_sum = 0 \n", + " for i in range(m): \n", + " f_wb = w * x[i] + b \n", + " cost = (f_wb - y[i]) ** 2 \n", + " cost_sum = cost_sum + cost \n", + " total_cost = (1 / (2 * m)) * cost_sum \n", + "\n", + " return total_cost" + ], + "id": "60ea841f910b8fb8" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cost Function Intuition" + ], + "id": "b1c901ba1558365" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " Your goal is to find a model $f_{w,b}(x) = wx + b$, with parameters $w,b$, which will accurately predict house values given an input $x$. The cost is a measure of how accurate the model is on the training data.\n", + "\n", + "The cost equation (1) above shows that if $w$ and $b$ can be selected such that the predictions $f_{w,b}(x)$ match the target data $y$, the $(f_{w,b}(x^{(i)}) - y^{(i)})^2 $ term will be zero and the cost minimized. In this simple two point example, you can achieve this!\n", + "\n", + "In the previous lab, you determined that $b=100$ provided an optimal solution so let's set $b$ to 100 and focus on $w$.\n", + "\n", + "
\n", + "Below, use the slider control to select the value of $w$ that minimizes cost. It can take a few seconds for the plot to update." + ], + "id": "954affed3a8238a1" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt_intuition(x_train,y_train)" + ], + "id": "1b2e52672dee209" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot contains a few points that are worth mentioning.\n", + "- cost is minimized when $w = 200$, which matches results from the previous lab\n", + "- Because the difference between the target and pediction is squared in the cost equation, the cost increases rapidly when $w$ is either too large or too small.\n", + "- Using the `w` and `b` selected by minimizing cost results in a line which is a perfect fit to the data." + ], + "id": "63966209b0e61188" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cost Function Visualization- 3D\n", + "\n", + "You can see how cost varies with respect to *both* `w` and `b` by plotting in 3D or using a contour plot. \n", + "It is worth noting that some of the plotting in this course can become quite involved. The plotting routines are provided and while it can be instructive to read through the code to become familiar with the methods, it is not needed to complete the course successfully. The routines are in lab_utils_uni.py in the local directory." + ], + "id": "8e2feee1b673a863" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Larger Data Set\n", + "It's use instructive to view a scenario with a few more data points. This data set includes data points that do not fall on the same line. What does that mean for the cost equation? Can we find $w$, and $b$ that will give us a cost of 0? " + ], + "id": "454fc752f58e3ee" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x_train = np.array([1.0, 1.7, 2.0, 2.5, 3.0, 3.2])\n", + "y_train = np.array([250, 300, 480, 430, 630, 730,])" + ], + "id": "dc3d7ddc773fc308" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the contour plot, click on a point to select `w` and `b` to achieve the lowest cost. Use the contours to guide your selections. Note, it can take a few seconds to update the graph. " + ], + "id": "7685a3371c85960d" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.close('all') \n", + "fig, ax, dyn_items = plt_stationary(x_train, y_train)\n", + "updater = plt_update_onclick(fig, ax, x_train, y_train, dyn_items)" + ], + "id": "9132ad0f6d362e2f" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above, note the dashed lines in the left plot. These represent the portion of the cost contributed by each example in your training set. In this case, values of approximately $w=209$ and $b=2.4$ provide low cost. Note that, because our training examples are not on a line, the minimum cost is not zero." + ], + "id": "78bf73a9e76b7764" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Convex Cost surface\n", + "The fact that the cost function squares the loss ensures that the 'error surface' is convex like a soup bowl. It will always have a minimum that can be reached by following the gradient in all dimensions. In the previous plot, because the $w$ and $b$ dimensions scale differently, this is not easy to recognize. The following plot, where $w$ and $b$ are symmetric, was shown in lecture:" + ], + "id": "136c6383bf6097f5" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "soup_bowl()" + ], + "id": "2a02853e7204d759" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Congratulations!\n", + "You have learned the following:\n", + " - The cost equation provides a measure of how well your predictions match your training data.\n", + " - Minimizing the cost can provide optimal values of $w$, $b$." + ], + "id": "1f57a3241189a2cc" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [], + "id": "9b162b4e8ebec360" + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + }, + "toc-autonumbering": false + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/week1/betaversion/C1_W1_Lab05_Gradient_Descent_Soln.ipynb b/week1/betaversion/C1_W1_Lab05_Gradient_Descent_Soln.ipynb new file mode 100644 index 0000000..16db021 --- /dev/null +++ b/week1/betaversion/C1_W1_Lab05_Gradient_Descent_Soln.ipynb @@ -0,0 +1,558 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optional Lab: Gradient Descent for Linear Regression\n", + "\n", + "
\n", + "
\n", + "
" + ], + "id": "5c7e9de1670dfc91" + }, + { + "cell_type": "markdown", + "id": "da452e68", + "metadata": {}, + "source": [ + "## Goals\n", + "In this lab, you will:\n", + "- automate the process of optimizing $w$ and $b$ using gradient descent." + ] + }, + { + "cell_type": "markdown", + "id": "6f6d4021", + "metadata": {}, + "source": [ + "## Tools\n", + "In this lab, we will make use of: \n", + "- NumPy, a popular library for scientific computing\n", + "- Matplotlib, a popular library for plotting data\n", + "- plotting routines in the lab_utils.py file in the local directory" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ef4d610a", + "metadata": {}, + "outputs": [], + "source": [ + "import math, copy\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('./deeplearning.mplstyle')\n", + "from lab_utils_uni import plt_house_x, plt_contour_wgrad, plt_divergence, plt_gradients" + ] + }, + { + "cell_type": "markdown", + "id": "c571a7b4", + "metadata": {}, + "source": [ + "\n", + "# Problem Statement\n", + "\n", + "Let's use the same two data points as before - a house with 1000 square feet sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000.\n", + "\n", + "| Size (1000 sqft) | Price (1000s of dollars) |\n", + "| ----------------| ------------------------ |\n", + "| 1 | 300 |\n", + "| 2 | 500 |\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "26dd9666", + "metadata": {}, + "outputs": [], + "source": [ + "# Load our data set\n", + "x_train = np.array([1.0, 2.0]) #features\n", + "y_train = np.array([300.0, 500.0]) #target value" + ] + }, + { + "cell_type": "markdown", + "id": "2b7851bd", + "metadata": {}, + "source": [ + "\n", + "### Compute_Cost\n", + "This was developed in the last lab. We'll need it again here." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9c6ffb7d", + "metadata": {}, + "outputs": [], + "source": [ + "#Function to calculate the cost\n", + "def compute_cost(x, y, w, b):\n", + " \n", + " m = x.shape[0] \n", + " cost = 0\n", + " \n", + " for i in range(m):\n", + " f_wb = w * x[i] + b\n", + " cost = cost + (f_wb - y[i])**2\n", + " total_cost = 1 / (2 * m) * cost\n", + "\n", + " return total_cost" + ] + }, + { + "cell_type": "markdown", + "id": "fd4be849", + "metadata": {}, + "source": [ + "\n", + "## Gradient descent summary\n", + "So far in this course, you have developed a linear model that predicts $f_{w,b}(x^{(i)})$:\n", + "$$f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{1}$$\n", + "In linear regression, you utilize input training data to fit the parameters $w$,$b$ by minimizing a measure of the error between our predictions $f_{w,b}(x^{(i)})$ and the actual data $y^{(i)}$. The measure is called the $cost$, $J(w,b)$. In training you measure the cost over all of our training samples $x^{(i)},y^{(i)}$\n", + "$$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2\\tag{2}$$ " + ] + }, + { + "cell_type": "markdown", + "id": "6061233c", + "metadata": {}, + "source": [ + "\n", + "In lecture, *gradient descent* was described as:\n", + "\n", + "$$\\begin{align*} \\text{repeat}&\\text{ until convergence:} \\; \\lbrace \\newline\n", + "\\; w &= w - \\alpha \\frac{\\partial J(w,b)}{\\partial w} \\tag{3} \\; \\newline \n", + " b &= b - \\alpha \\frac{\\partial J(w,b)}{\\partial b} \\newline \\rbrace\n", + "\\end{align*}$$\n", + "where, parameters $w$, $b$ are updated simultaneously. \n", + "The gradient is defined as:\n", + "$$\n", + "\\begin{align}\n", + "\\frac{\\partial J(w,b)}{\\partial w} &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})x^{(i)} \\tag{4}\\\\\n", + " \\frac{\\partial J(w,b)}{\\partial b} &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)}) \\tag{5}\\\\\n", + "\\end{align}\n", + "$$\n", + "\n", + "Here *simultaniously* means that you calculate the partial derivatives for all the parameters before updating any of the parameters." + ] + }, + { + "cell_type": "markdown", + "id": "6cfb9401", + "metadata": {}, + "source": [ + "\n", + "## Implement Gradient Descent\n", + "You will implement batch gradient descent algorithm for one feature. You will need three functions. \n", + "- `compute_gradient` implementing equation (4) and (5) above\n", + "- `compute_cost` implementing equation (2) above (code from previous lab)\n", + "- `gradient_descent`, utilizing compute_gradient and compute_cost\n", + "\n", + "Conventions:\n", + "- The naming of python variables containing partial derivatives follows this pattern,$\\frac{\\partial J(w,b)}{\\partial b}$ will be `dj_db`.\n", + "- w.r.t is With Respect To, as in partial derivative of $J(wb)$ With Respect To $b$.\n" + ] + }, + { + "cell_type": "markdown", + "id": "f9b6ad38", + "metadata": {}, + "source": [ + "\n", + "### compute_gradient\n", + "\n", + "`compute_gradient` implements (4) and (5) above and returns $\\frac{\\partial J(w,b)}{\\partial w}$,$\\frac{\\partial J(w,b)}{\\partial b}$. The embedded comments describe the operations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "857066af", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_gradient(x, y, w, b): \n", + " \"\"\"\n", + " Computes the gradient for linear regression \n", + " Args:\n", + " x (ndarray (m,)): Data, m examples \n", + " y (ndarray (m,)): target values\n", + " w,b (scalar) : model parameters \n", + " Returns\n", + " dj_dw (scalar): The gradient of the cost w.r.t. the parameters w\n", + " dj_db (scalar): The gradient of the cost w.r.t. the parameter b \n", + " \"\"\"\n", + " \n", + " # Number of training examples\n", + " m = x.shape[0] \n", + " dj_dw = 0\n", + " dj_db = 0\n", + " \n", + " for i in range(m): \n", + " f_wb = w * x[i] + b \n", + " dj_dw_i = (f_wb - y[i]) * x[i] \n", + " dj_db_i = f_wb - y[i] \n", + " dj_db += dj_db_i\n", + " dj_dw += dj_dw_i \n", + " dj_dw = dj_dw / m \n", + " dj_db = dj_db / m \n", + " \n", + " return dj_dw, dj_db" + ] + }, + { + "cell_type": "markdown", + "id": "dccbb458", + "metadata": {}, + "source": [ + "
" + ] + }, + { + "cell_type": "markdown", + "id": "42358679", + "metadata": {}, + "source": [ + " The lectures described how gradient descent utilizes the partial derivative of the cost with respect to a parameter at a point to update that parameter. \n", + "Let's use our `compute_gradient` function to find and plot some partial derivatives of our cost function relative to one of the parameters, $w_0$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "01d52fb1", + "metadata": {}, + "outputs": [], + "source": [ + "plt_gradients(x_train,y_train, compute_cost, compute_gradient)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "20269810", + "metadata": {}, + "source": [ + "Above, the left plot shows $\\frac{\\partial J(w,b)}{\\partial w}$ or the slope of the cost curve relative to $w$ at three points. On the right side of the plot, the derivative is positive, while on the left it is negative. Due to the 'bowl shape', the derivatives will always lead gradient descent toward the bottom where the gradient is zero.\n", + " \n", + "The left plot has fixed $b=100$. Gradient descent will utilize both $\\frac{\\partial J(w,b)}{\\partial w}$ and $\\frac{\\partial J(w,b)}{\\partial b}$ to update parameters. The 'quiver plot' on the right provides a means of viewing the gradient of both parameters. The arrow sizes reflect the magnitude of the gradient at that point. The direction and slope of the arrow reflects the ratio of $\\frac{\\partial J(w,b)}{\\partial w}$ and $\\frac{\\partial J(w,b)}{\\partial b}$ at that point.\n", + "Note that the gradient points *away* from the minimum. Review equation (3) above. The scaled gradient is *subtracted* from the current value of $w$ or $b$. This moves the parameter in a direction that will reduce cost." + ] + }, + { + "cell_type": "markdown", + "id": "09cde02a", + "metadata": {}, + "source": [ + "\n", + "### Gradient Descent\n", + "Now that gradients can be computed, gradient descent, described in equation (3) above can be implemented. The details of the implementation are described in the comments. Below, you will utilize this function to find optimal values of $w$ and $b$ on the training data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ca792dcb", + "metadata": {}, + "outputs": [], + "source": [ + "def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function): \n", + " \"\"\"\n", + " Performs batch gradient descent to fit w,b. Updates w,b by taking \n", + " num_iters gradient steps with learning rate alpha\n", + " \n", + " Args:\n", + " x (ndarray (m,)) : Data, m examples \n", + " y (ndarray (m,)) : target values\n", + " w_in,b_in (scalar): initial values of model parameters \n", + " alpha (float): Learning rate\n", + " num_iters (int): number of iterations to run gradient descent\n", + " cost_function: function to call to produce cost\n", + " gradient_function: function to call to produce gradient\n", + " \n", + " Returns:\n", + " w (scalar): Updated value of parameter after running gradient descent\n", + " b (scalar): Updated value of parameter after running gradient descent\n", + " J_history (List): History of cost values\n", + " p_history (list): History of parameters [w,b] \n", + " \"\"\"\n", + " \n", + " w = copy.deepcopy(w_in) # avoid modifying global w_in\n", + " # An array to store cost J and w's at each iteration primarily for graphing later\n", + " J_history = []\n", + " p_history = []\n", + " b = b_in\n", + " w = w_in\n", + " \n", + " for i in range(num_iters):\n", + " # Calculate the gradient and update the parameters using gradient_function\n", + " dj_dw, dj_db = gradient_function(x, y, w , b) \n", + "\n", + " # Update Parameters using equation (3) above\n", + " b = b - alpha * dj_db \n", + " w = w - alpha * dj_dw \n", + "\n", + " # Save cost J at each iteration\n", + " if i<100000: # prevent resource exhaustion \n", + " J_history.append( cost_function(x, y, w , b))\n", + " p_history.append([w,b])\n", + " # Print cost every at intervals 10 times or as many iterations if < 10\n", + " if i% math.ceil(num_iters/10) == 0:\n", + " print(f\"Iteration {i:4}: Cost {J_history[-1]:0.2e} \",\n", + " f\"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e} \",\n", + " f\"w: {w: 0.3e}, b:{b: 0.5e}\")\n", + " \n", + " return w, b, J_history, p_history #return w and J,w history for graphing" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "af449437", + "metadata": {}, + "outputs": [], + "source": [ + "# initialize parameters\n", + "w_init = 0\n", + "b_init = 0\n", + "# some gradient descent settings\n", + "iterations = 10000\n", + "tmp_alpha = 1.0e-2\n", + "# run gradient descent\n", + "w_final, b_final, J_hist, p_hist = gradient_descent(x_train ,y_train, w_init, b_init, tmp_alpha, \n", + " iterations, compute_cost, compute_gradient)\n", + "print(f\"(w,b) found by gradient descent: ({w_final:8.4f},{b_final:8.4f})\")" + ] + }, + { + "cell_type": "markdown", + "id": "f659147c", + "metadata": {}, + "source": [ + " \n", + "Take a moment and note some characteristics of the gradient descent process printed above. \n", + "\n", + "- The cost starts large and rapidly declines as described in the slide from the lecture.\n", + "- The partial derivatives, `dj_dw`, and `dj_db` also get smaller, rapidly at first and then more slowly. As shown in the diagram from the lecture, as the process nears the 'bottom of the bowl' progress is slower due to the smaller value of the derivative at that point.\n", + "- progress slows though the learning rate, alpha, remains fixed" + ] + }, + { + "cell_type": "markdown", + "id": "a2366fd8", + "metadata": {}, + "source": [ + "### Cost versus iterations of gradient descent \n", + "A plot of cost versus iterations is a useful measure of progress in gradient descent. Cost should always decrease in successful runs. The change in cost is so rapid initially, it is also helpful in this case to view a plot that does not include the initial iterations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ceb161ee", + "metadata": {}, + "outputs": [], + "source": [ + "# plot cost versus iteration \n", + "fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True, figsize=(12,4))\n", + "ax1.plot(J_hist)\n", + "ax2.plot(1000 + np.arange(len(J_hist[1000:])), J_hist[1000:])\n", + "ax1.set_title(\"Cost vs. iteration\"); ax2.set_title(\"Cost vs. iteration (tail)\")\n", + "ax1.set_ylabel('Cost') ; ax2.set_ylabel('Cost') \n", + "ax1.set_xlabel('iteration step') ; ax2.set_xlabel('iteration step') \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "205bd40f", + "metadata": {}, + "source": [ + "### Predictions\n", + "Now that you have discovered the optimal values for the parameters $w$ and $b$, you can now use the model to predict housing values based on our learned parameters. As expected, the predicted values are nearly the same as the training values for the same housing. Further, the value not in the prediction is in line with the expected value." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "54271146", + "metadata": {}, + "outputs": [], + "source": [ + "print(f\"1000 sqft house prediction {w_final*1.0 + b_final:0.1f} Thousand dollars\")\n", + "print(f\"1200 sqft house prediction {w_final*1.2 + b_final:0.1f} Thousand dollars\")\n", + "print(f\"2000 sqft house prediction {w_final*2.0 + b_final:0.1f} Thousand dollars\")" + ] + }, + { + "cell_type": "markdown", + "id": "b7081853", + "metadata": {}, + "source": [ + "\n", + "## Plotting\n", + "You can show the progress of gradient descent during its execution by plotting the cost over iterations on a contour plot of the cost(w,b). " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e6c9e24f", + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,1, figsize=(12, 6))\n", + "plt_contour_wgrad(x_train, y_train, p_hist, ax)" + ] + }, + { + "cell_type": "markdown", + "id": "1d3bda0a", + "metadata": {}, + "source": [ + "Above, the contour plot shows the $cost(w,b)$ over a range of $w$ and $b$. Cost levels are represented by the rings. Overlayed, using red arrows, is the path of gradient descent. Here are some things to note:\n", + "- The path makes steady (monotonic) progress toward its goal.\n", + "- initial steps are much larger than the steps near the goal." + ] + }, + { + "cell_type": "markdown", + "id": "9d2f0d6b", + "metadata": {}, + "source": [ + "**Zooming in**, we can see that final steps of gradient descent. Note the distance between steps shrinks as the gradient approaches zero." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5e58742e", + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,1, figsize=(12, 4))\n", + "plt_contour_wgrad(x_train, y_train, p_hist, ax, w_range=[180, 220, 0.5], b_range=[80, 120, 0.5],\n", + " contours=[1,5,10,20],resolution=0.5)" + ] + }, + { + "cell_type": "markdown", + "id": "66a68a52", + "metadata": {}, + "source": [ + "\n", + "### Increased Learning Rate\n", + "\n", + "
\n", + " \n", + "
\n", + "In the lecture, there was a discussion related to the proper value of the learning rate, $\\alpha$ in equation(3). The larger $\\alpha$ is, the faster gradient descent will converge to a solution. But, if it is too large, gradient descent will diverge. Above you have an example of a solution which converges nicely.\n", + "\n", + "Let's try increasing the value of $\\alpha$ and see what happens:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "01c2c046", + "metadata": {}, + "outputs": [], + "source": [ + "# initialize parameters\n", + "w_init = 0\n", + "b_init = 0\n", + "# set alpha to a large value\n", + "iterations = 10\n", + "tmp_alpha = 8.0e-1\n", + "# run gradient descent\n", + "w_final, b_final, J_hist, p_hist = gradient_descent(x_train ,y_train, w_init, b_init, tmp_alpha, \n", + " iterations, compute_cost, compute_gradient)" + ] + }, + { + "cell_type": "markdown", + "id": "84d9cb5e", + "metadata": {}, + "source": [ + "Above, $w$ and $b$ are bouncing back and forth between positive and negative with the absolute value increasing with each iteration. Further, each iteration $\\frac{\\partial J(w,b)}{\\partial w}$ changes sign and cost is increasing rather than decreasing. This is a clear sign that the *learning rate is too large* and the solution is diverging. \n", + "Let's visualize this with a plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cd87463e", + "metadata": {}, + "outputs": [], + "source": [ + "plt_divergence(p_hist, J_hist,x_train, y_train)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "1af14beb", + "metadata": {}, + "source": [ + "Above, the left graph shows $w$'s progression over the first few steps of gradient descent. $w$ oscillates from positive to negative and cost grows rapidly. Gradient Descent is operating on both $w$ and $b$ simultaneously, so one needs the 3-D plot on the right for the complete picture." + ] + }, + { + "cell_type": "markdown", + "id": "17283374", + "metadata": {}, + "source": [ + "\n", + "## Congratulations!\n", + "In this lab you:\n", + "- delved into the details of gradient descent for a single variable.\n", + "- developed a routine to compute the gradient\n", + "- visualized what the gradient is\n", + "- completed a gradient descent routine\n", + "- utilized gradient descent to find parameters\n", + "- examined the impact of sizing the learning rate" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "852c45c0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "dl_toc_settings": { + "rndtag": "40291" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + 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ax.text(0.15,0.02,cstr, transform=ax.transAxes, color=dlpurple) + +########## +# Cost lab +########## + + +def plt_intuition(x_train, y_train): + + w_range = np.array([200-200,200+200]) + tmp_b = 100 + + w_array = np.arange(*w_range, 5) + cost = np.zeros_like(w_array) + for i in range(len(w_array)): + tmp_w = w_array[i] + cost[i] = compute_cost(x_train, y_train, tmp_w, tmp_b) + + @interact(w=(*w_range,10),continuous_update=False) + def func( w=150): + f_wb = np.dot(x_train, w) + tmp_b + + fig, ax = plt.subplots(1, 2, constrained_layout=True, figsize=(8,4)) + fig.canvas.toolbar_position = 'bottom' + + mk_cost_lines(x_train, y_train, w, tmp_b, ax[0]) + plt_house_x(x_train, y_train, f_wb=f_wb, ax=ax[0]) + + ax[1].plot(w_array, cost) + cur_cost = compute_cost(x_train, y_train, w, tmp_b) + ax[1].scatter(w,cur_cost, s=100, color=dldarkred, zorder= 10, label= f"cost at w={w}") + ax[1].hlines(cur_cost, ax[1].get_xlim()[0],w, lw=4, color=dlpurple, ls='dotted') + ax[1].vlines(w, ax[1].get_ylim()[0],cur_cost, lw=4, color=dlpurple, ls='dotted') + ax[1].set_title("Cost vs. w, (b fixed at 100)") + ax[1].set_ylabel('Cost') + ax[1].set_xlabel('w') + ax[1].legend(loc='upper center') + fig.suptitle(f"Minimize Cost: Current Cost = {cur_cost:0.0f}", fontsize=12) + plt.show() + +# this is the 2D cost curve with interactive slider +def plt_stationary(x_train, y_train): + # setup figure + fig = plt.figure( figsize=(9,8)) + #fig = plt.figure(constrained_layout=True, figsize=(12,10)) + fig.set_facecolor('#ffffff') #white + fig.canvas.toolbar_position = 'top' + #gs = GridSpec(2, 2, figure=fig, wspace = 0.01) + gs = GridSpec(2, 2, figure=fig) + ax0 = fig.add_subplot(gs[0, 0]) + ax1 = fig.add_subplot(gs[0, 1]) + ax2 = fig.add_subplot(gs[1, :], projection='3d') + ax = np.array([ax0,ax1,ax2]) + + #setup useful ranges and common linspaces + w_range = np.array([200-300.,200+300]) + b_range = np.array([50-300., 50+300]) + b_space = np.linspace(*b_range, 100) + w_space = np.linspace(*w_range, 100) + + # get cost for w,b ranges for contour and 3D + tmp_b,tmp_w = np.meshgrid(b_space,w_space) + z=np.zeros_like(tmp_b) + for i in range(tmp_w.shape[0]): + for j in range(tmp_w.shape[1]): + z[i,j] = compute_cost(x_train, y_train, tmp_w[i][j], tmp_b[i][j] ) + if z[i,j] == 0: z[i,j] = 1e-6 + + w0=200;b=-100 #initial point + ### plot model w cost ### + f_wb = np.dot(x_train,w0) + b + mk_cost_lines(x_train,y_train,w0,b,ax[0]) + plt_house_x(x_train, y_train, f_wb=f_wb, ax=ax[0]) + + ### plot contour ### + CS = ax[1].contour(tmp_w, tmp_b, np.log(z),levels=12, linewidths=2, alpha=0.7,colors=dlcolors) + ax[1].set_title('Cost(w,b)') + ax[1].set_xlabel('w', fontsize=10) + ax[1].set_ylabel('b', fontsize=10) + ax[1].set_xlim(w_range) ; ax[1].set_ylim(b_range) + cscat = ax[1].scatter(w0,b, s=100, color=dlblue, zorder= 10, label="cost with \ncurrent w,b") + chline = ax[1].hlines(b, ax[1].get_xlim()[0],w0, lw=4, color=dlpurple, ls='dotted') + cvline = ax[1].vlines(w0, ax[1].get_ylim()[0],b, lw=4, color=dlpurple, ls='dotted') + ax[1].text(0.5,0.95,"Click to choose w,b", bbox=dict(facecolor='white', ec = 'black'), fontsize = 10, + transform=ax[1].transAxes, verticalalignment = 'center', horizontalalignment= 'center') + + #Surface plot of the cost function J(w,b) + ax[2].plot_surface(tmp_w, tmp_b, z, cmap = dlcm, alpha=0.3, antialiased=True) + ax[2].plot_wireframe(tmp_w, tmp_b, z, color='k', alpha=0.1) + plt.xlabel("$w$") + plt.ylabel("$b$") + ax[2].zaxis.set_rotate_label(False) + ax[2].xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax[2].yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax[2].zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax[2].set_zlabel("J(w, b)\n\n", rotation=90) + plt.title("Cost(w,b) \n [You can rotate this figure]", size=12) + ax[2].view_init(30, -120) + + return fig,ax, [cscat, chline, cvline] + + +#https://matplotlib.org/stable/users/event_handling.html +class plt_update_onclick: + def __init__(self, fig, ax, x_train,y_train, dyn_items): + self.fig = fig + self.ax = ax + self.x_train = x_train + self.y_train = y_train + self.dyn_items = dyn_items + self.cid = fig.canvas.mpl_connect('button_press_event', self) + + def __call__(self, event): + if event.inaxes == self.ax[1]: + ws = event.xdata + bs = event.ydata + cst = compute_cost(self.x_train, self.y_train, ws, bs) + + # clear and redraw line plot + self.ax[0].clear() + f_wb = np.dot(self.x_train,ws) + bs + mk_cost_lines(self.x_train,self.y_train,ws,bs,self.ax[0]) + plt_house_x(self.x_train, self.y_train, f_wb=f_wb, ax=self.ax[0]) + + # remove lines and re-add on countour plot and 3d plot + for artist in self.dyn_items: + artist.remove() + + a = self.ax[1].scatter(ws,bs, s=100, color=dlblue, zorder= 10, label="cost with \ncurrent w,b") + b = self.ax[1].hlines(bs, self.ax[1].get_xlim()[0],ws, lw=4, color=dlpurple, ls='dotted') + c = self.ax[1].vlines(ws, self.ax[1].get_ylim()[0],bs, lw=4, color=dlpurple, ls='dotted') + d = self.ax[1].annotate(f"Cost: {cst:.0f}", xy= (ws, bs), xytext = (4,4), textcoords = 'offset points', + bbox=dict(facecolor='white'), size = 10) + + #Add point in 3D surface plot + e = self.ax[2].scatter3D(ws, bs,cst , marker='X', s=100) + + self.dyn_items = [a,b,c,d,e] + self.fig.canvas.draw() + + +def soup_bowl(): + """ Create figure and plot with a 3D projection""" + fig = plt.figure(figsize=(8,8)) + + #Plot configuration + ax = fig.add_subplot(111, projection='3d') + ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax.zaxis.set_rotate_label(False) + ax.view_init(45, -120) + + #Useful linearspaces to give values to the parameters w and b + w = np.linspace(-20, 20, 100) + b = np.linspace(-20, 20, 100) + + #Get the z value for a bowl-shaped cost function + z=np.zeros((len(w), len(b))) + j=0 + for x in w: + i=0 + for y in b: + z[i,j] = x**2 + y**2 + i+=1 + j+=1 + + #Meshgrid used for plotting 3D functions + W, B = np.meshgrid(w, b) + + #Create the 3D surface plot of the bowl-shaped cost function + ax.plot_surface(W, B, z, cmap = "Spectral_r", alpha=0.7, antialiased=False) + ax.plot_wireframe(W, B, z, color='k', alpha=0.1) + ax.set_xlabel("$w$") + ax.set_ylabel("$b$") + ax.set_zlabel("$J(w,b)$", rotation=90) + ax.set_title("$J(w,b)$\n [You can rotate this figure]", size=15) + + plt.show() + +def inbounds(a,b,xlim,ylim): + xlow,xhigh = xlim + ylow,yhigh = ylim + ax, ay = a + bx, by = b + if (ax > xlow and ax < xhigh) and (bx > xlow and bx < xhigh) \ + and (ay > ylow and ay < yhigh) and (by > ylow and by < yhigh): + return True + return False + +def plt_contour_wgrad(x, y, hist, ax, w_range=[-100, 500, 5], b_range=[-500, 500, 5], + contours = [0.1,50,1000,5000,10000,25000,50000], + resolution=5, w_final=200, b_final=100,step=10 ): + b0,w0 = np.meshgrid(np.arange(*b_range),np.arange(*w_range)) + z=np.zeros_like(b0) + for i in range(w0.shape[0]): + for j in range(w0.shape[1]): + z[i][j] = compute_cost(x, y, w0[i][j], b0[i][j] ) + + CS = ax.contour(w0, b0, z, contours, linewidths=2, + colors=[dlblue, dlorange, dldarkred, dlmagenta, dlpurple]) + ax.clabel(CS, inline=1, fmt='%1.0f', fontsize=10) + ax.set_xlabel("w"); ax.set_ylabel("b") + ax.set_title('Contour plot of cost J(w,b), vs b,w with path of gradient descent') + w = w_final; b=b_final + ax.hlines(b, ax.get_xlim()[0],w, lw=2, color=dlpurple, ls='dotted') + ax.vlines(w, ax.get_ylim()[0],b, lw=2, color=dlpurple, ls='dotted') + + base = hist[0] + for point in hist[0::step]: + edist = np.sqrt((base[0] - point[0])**2 + (base[1] - point[1])**2) + if(edist > resolution or point==hist[-1]): + if inbounds(point,base, ax.get_xlim(),ax.get_ylim()): + plt.annotate('', xy=point, xytext=base,xycoords='data', + arrowprops={'arrowstyle': '->', 'color': 'r', 'lw': 3}, + va='center', ha='center') + base=point + return + + +def plt_divergence(p_hist, J_hist, x_train,y_train): + + x=np.zeros(len(p_hist)) + y=np.zeros(len(p_hist)) + v=np.zeros(len(p_hist)) + for i in range(len(p_hist)): + x[i] = p_hist[i][0] + y[i] = p_hist[i][1] + v[i] = J_hist[i] + + fig = plt.figure(figsize=(12,5)) + plt.subplots_adjust( wspace=0 ) + gs = fig.add_gridspec(1, 5) + fig.suptitle(f"Cost escalates when learning rate is too large") + #=============== + # First subplot + #=============== + ax = fig.add_subplot(gs[:2], ) + + # Print w vs cost to see minimum + fix_b = 100 + w_array = np.arange(-70000, 70000, 1000) + cost = np.zeros_like(w_array) + + for i in range(len(w_array)): + tmp_w = w_array[i] + cost[i] = compute_cost(x_train, y_train, tmp_w, fix_b) + + ax.plot(w_array, cost) + ax.plot(x,v, c=dlmagenta) + ax.set_title("Cost vs w, b set to 100") + ax.set_ylabel('Cost') + ax.set_xlabel('w') + ax.xaxis.set_major_locator(MaxNLocator(2)) + + #=============== + # Second Subplot + #=============== + + tmp_b,tmp_w = np.meshgrid(np.arange(-35000, 35000, 500),np.arange(-70000, 70000, 500)) + z=np.zeros_like(tmp_b) + for i in range(tmp_w.shape[0]): + for j in range(tmp_w.shape[1]): + z[i][j] = compute_cost(x_train, y_train, tmp_w[i][j], tmp_b[i][j] ) + + ax = fig.add_subplot(gs[2:], projection='3d') + ax.plot_surface(tmp_w, tmp_b, z, alpha=0.3, color=dlblue) + ax.xaxis.set_major_locator(MaxNLocator(2)) + ax.yaxis.set_major_locator(MaxNLocator(2)) + + ax.set_xlabel('w', fontsize=16) + ax.set_ylabel('b', fontsize=16) + ax.set_zlabel('\ncost', fontsize=16) + plt.title('Cost vs (b, w)') + # Customize the view angle + ax.view_init(elev=20., azim=-65) + ax.plot(x, y, v,c=dlmagenta) + + return + +# draw derivative line +# y = m*(x - x1) + y1 +def add_line(dj_dx, x1, y1, d, ax): + x = np.linspace(x1-d, x1+d,50) + y = dj_dx*(x - x1) + y1 + ax.scatter(x1, y1, color=dlblue, s=50) + ax.plot(x, y, '--', c=dldarkred,zorder=10, linewidth = 1) + xoff = 30 if x1 == 200 else 10 + ax.annotate(r"$\frac{\partial J}{\partial w}$ =%d" % dj_dx, fontsize=14, + xy=(x1, y1), xycoords='data', + xytext=(xoff, 10), textcoords='offset points', + arrowprops=dict(arrowstyle="->"), + horizontalalignment='left', verticalalignment='top') + +def plt_gradients(x_train,y_train, f_compute_cost, f_compute_gradient): + #=============== + # First subplot + #=============== + fig,ax = plt.subplots(1,2,figsize=(12,4)) + + # Print w vs cost to see minimum + fix_b = 100 + w_array = np.linspace(-100, 500, 50) + w_array = np.linspace(0, 400, 50) + cost = np.zeros_like(w_array) + + for i in range(len(w_array)): + tmp_w = w_array[i] + cost[i] = f_compute_cost(x_train, y_train, tmp_w, fix_b) + ax[0].plot(w_array, cost,linewidth=1) + ax[0].set_title("Cost vs w, with gradient; b set to 100") + ax[0].set_ylabel('Cost') + ax[0].set_xlabel('w') + + # plot lines for fixed b=100 + for tmp_w in [100,200,300]: + fix_b = 100 + dj_dw,dj_db = f_compute_gradient(x_train, y_train, tmp_w, fix_b ) + j = f_compute_cost(x_train, y_train, tmp_w, fix_b) + add_line(dj_dw, tmp_w, j, 30, ax[0]) + + #=============== + # Second Subplot + #=============== + + tmp_b,tmp_w = np.meshgrid(np.linspace(-200, 200, 10), np.linspace(-100, 600, 10)) + U = np.zeros_like(tmp_w) + V = np.zeros_like(tmp_b) + for i in range(tmp_w.shape[0]): + for j in range(tmp_w.shape[1]): + U[i][j], V[i][j] = f_compute_gradient(x_train, y_train, tmp_w[i][j], tmp_b[i][j] ) + X = tmp_w + Y = tmp_b + n=-2 + color_array = np.sqrt(((V-n)/2)**2 + ((U-n)/2)**2) + + ax[1].set_title('Gradient shown in quiver plot') + Q = ax[1].quiver(X, Y, U, V, color_array, units='width', ) + ax[1].quiverkey(Q, 0.9, 0.9, 2, r'$2 \frac{m}{s}$', labelpos='E',coordinates='figure') + ax[1].set_xlabel("w"); ax[1].set_ylabel("b") diff --git a/week1/data.txt b/week1/data.txt new file mode 100644 index 0000000..d1b6bc3 --- /dev/null +++ b/week1/data.txt @@ -0,0 +1,47 @@ +2104,3,399900 +1600,3,329900 +2400,3,369000 +1416,2,232000 +3000,4,539900 +1985,4,299900 +1534,3,314900 +1427,3,198999 +1380,3,212000 +1494,3,242500 +1940,4,239999 +2000,3,347000 +1890,3,329999 +4478,5,699900 +1268,3,259900 +2300,4,449900 +1320,2,299900 +1236,3,199900 +2609,4,499998 +3031,4,599000 +1767,3,252900 +1888,2,255000 +1604,3,242900 +1962,4,259900 +3890,3,573900 +1100,3,249900 +1458,3,464500 +2526,3,469000 +2200,3,475000 +2637,3,299900 +1839,2,349900 +1000,1,169900 +2040,4,314900 +3137,3,579900 +1811,4,285900 +1437,3,249900 +1239,3,229900 +2132,4,345000 +4215,4,549000 +2162,4,287000 +1664,2,368500 +2238,3,329900 +2567,4,314000 +1200,3,299000 +852,2,179900 +1852,4,299900 +1203,3,239500 \ No newline at end of file diff --git a/week1/deeplearning.mplstyle b/week1/deeplearning.mplstyle new file mode 100644 index 0000000..e01280f --- /dev/null +++ b/week1/deeplearning.mplstyle @@ -0,0 +1,124 @@ +# see https://matplotlib.org/stable/tutorials/introductory/customizing.html +lines.linewidth: 4 +lines.solid_capstyle: butt + +legend.fancybox: true + +# Verdana" for non-math text, +# Cambria Math + +#Blue (Crayon-Aqua) 0096FF +#Dark Red C00000 +#Orange (Apple Orange) FF9300 +#Black 000000 +#Magenta FF40FF +#Purple 7030A0 + +axes.prop_cycle: cycler('color', ['0096FF', 'FF9300', 'FF40FF', '7030A0', 'C00000']) +#axes.facecolor: f0f0f0 # grey +axes.facecolor: ffffff # white +axes.labelsize: large +axes.axisbelow: true +axes.grid: False +axes.edgecolor: f0f0f0 +axes.linewidth: 3.0 +axes.titlesize: x-large + +patch.edgecolor: f0f0f0 +patch.linewidth: 0.5 + +svg.fonttype: path + +grid.linestyle: - +grid.linewidth: 1.0 +grid.color: cbcbcb + +xtick.major.size: 0 +xtick.minor.size: 0 +ytick.major.size: 0 +ytick.minor.size: 0 + +savefig.edgecolor: f0f0f0 +savefig.facecolor: f0f0f0 + +#figure.subplot.left: 0.08 +#figure.subplot.right: 0.95 +#figure.subplot.bottom: 0.07 + +#figure.facecolor: f0f0f0 # grey +figure.facecolor: ffffff # white + +## *************************************************************************** +## * FONT * +## *************************************************************************** +## The font properties used by `text.Text`. +## See https://matplotlib.org/api/font_manager_api.html for more information +## on font properties. The 6 font properties used for font matching are +## given below with their default values. +## +## The font.family property can take either a concrete font name (not supported +## when rendering text with usetex), or one of the following five generic +## values: +## - 'serif' (e.g., Times), +## - 'sans-serif' (e.g., Helvetica), +## - 'cursive' (e.g., Zapf-Chancery), +## - 'fantasy' (e.g., Western), and +## - 'monospace' (e.g., Courier). +## Each of these values has a corresponding default list of font names +## (font.serif, etc.); the first available font in the list is used. Note that +## for font.serif, font.sans-serif, and font.monospace, the first element of +## the list (a DejaVu font) will always be used because DejaVu is shipped with +## Matplotlib and is thus guaranteed to be available; the other entries are +## left as examples of other possible values. +## +## The font.style property has three values: normal (or roman), italic +## or oblique. 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ax.text(0.15,0.02,cstr, transform=ax.transAxes, color=dlpurple) + +########## +# Cost lab +########## + + +def plt_intuition(x_train, y_train): + + w_range = np.array([200-200,200+200]) + tmp_b = 100 + + w_array = np.arange(*w_range, 5) + cost = np.zeros_like(w_array) + for i in range(len(w_array)): + tmp_w = w_array[i] + cost[i] = compute_cost(x_train, y_train, tmp_w, tmp_b) + + @interact(w=(*w_range,10),continuous_update=False) + def func( w=150): + f_wb = np.dot(x_train, w) + tmp_b + + fig, ax = plt.subplots(1, 2, constrained_layout=True, figsize=(8,4)) + fig.canvas.toolbar_position = 'bottom' + + mk_cost_lines(x_train, y_train, w, tmp_b, ax[0]) + plt_house_x(x_train, y_train, f_wb=f_wb, ax=ax[0]) + + ax[1].plot(w_array, cost) + cur_cost = compute_cost(x_train, y_train, w, tmp_b) + ax[1].scatter(w,cur_cost, s=100, color=dldarkred, zorder= 10, label= f"cost at w={w}") + ax[1].hlines(cur_cost, ax[1].get_xlim()[0],w, lw=4, color=dlpurple, ls='dotted') + ax[1].vlines(w, ax[1].get_ylim()[0],cur_cost, lw=4, color=dlpurple, ls='dotted') + ax[1].set_title("Cost vs. w, (b fixed at 100)") + ax[1].set_ylabel('Cost') + ax[1].set_xlabel('w') + ax[1].legend(loc='upper center') + fig.suptitle(f"Minimize Cost: Current Cost = {cur_cost:0.0f}", fontsize=12) + plt.show() + +# this is the 2D cost curve with interactive slider +def plt_stationary(x_train, y_train): + # setup figure + fig = plt.figure( figsize=(9,8)) + #fig = plt.figure(constrained_layout=True, figsize=(12,10)) + fig.set_facecolor('#ffffff') #white + fig.canvas.toolbar_position = 'top' + #gs = GridSpec(2, 2, figure=fig, wspace = 0.01) + gs = GridSpec(2, 2, figure=fig) + ax0 = fig.add_subplot(gs[0, 0]) + ax1 = fig.add_subplot(gs[0, 1]) + ax2 = fig.add_subplot(gs[1, :], projection='3d') + ax = np.array([ax0,ax1,ax2]) + + #setup useful ranges and common linspaces + w_range = np.array([200-300.,200+300]) + b_range = np.array([50-300., 50+300]) + b_space = np.linspace(*b_range, 100) + w_space = np.linspace(*w_range, 100) + + # get cost for w,b ranges for contour and 3D + tmp_b,tmp_w = np.meshgrid(b_space,w_space) + z=np.zeros_like(tmp_b) + for i in range(tmp_w.shape[0]): + for j in range(tmp_w.shape[1]): + z[i,j] = compute_cost(x_train, y_train, tmp_w[i][j], tmp_b[i][j] ) + if z[i,j] == 0: z[i,j] = 1e-6 + + w0=200;b=-100 #initial point + ### plot model w cost ### + f_wb = np.dot(x_train,w0) + b + mk_cost_lines(x_train,y_train,w0,b,ax[0]) + plt_house_x(x_train, y_train, f_wb=f_wb, ax=ax[0]) + + ### plot contour ### + CS = ax[1].contour(tmp_w, tmp_b, np.log(z),levels=12, linewidths=2, alpha=0.7,colors=dlcolors) + ax[1].set_title('Cost(w,b)') + ax[1].set_xlabel('w', fontsize=10) + ax[1].set_ylabel('b', fontsize=10) + ax[1].set_xlim(w_range) ; ax[1].set_ylim(b_range) + cscat = ax[1].scatter(w0,b, s=100, color=dlblue, zorder= 10, label="cost with \ncurrent w,b") + chline = ax[1].hlines(b, ax[1].get_xlim()[0],w0, lw=4, color=dlpurple, ls='dotted') + cvline = ax[1].vlines(w0, ax[1].get_ylim()[0],b, lw=4, color=dlpurple, ls='dotted') + ax[1].text(0.5,0.95,"Click to choose w,b", bbox=dict(facecolor='white', ec = 'black'), fontsize = 10, + transform=ax[1].transAxes, verticalalignment = 'center', horizontalalignment= 'center') + + #Surface plot of the cost function J(w,b) + ax[2].plot_surface(tmp_w, tmp_b, z, cmap = dlcm, alpha=0.3, antialiased=True) + ax[2].plot_wireframe(tmp_w, tmp_b, z, color='k', alpha=0.1) + plt.xlabel("$w$") + plt.ylabel("$b$") + ax[2].zaxis.set_rotate_label(False) + ax[2].xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax[2].yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax[2].zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax[2].set_zlabel("J(w, b)\n\n", rotation=90) + plt.title("Cost(w,b) \n [You can rotate this figure]", size=12) + ax[2].view_init(30, -120) + + return fig,ax, [cscat, chline, cvline] + + +#https://matplotlib.org/stable/users/event_handling.html +class plt_update_onclick: + def __init__(self, fig, ax, x_train,y_train, dyn_items): + self.fig = fig + self.ax = ax + self.x_train = x_train + self.y_train = y_train + self.dyn_items = dyn_items + self.cid = fig.canvas.mpl_connect('button_press_event', self) + + def __call__(self, event): + if event.inaxes == self.ax[1]: + ws = event.xdata + bs = event.ydata + cst = compute_cost(self.x_train, self.y_train, ws, bs) + + # clear and redraw line plot + self.ax[0].clear() + f_wb = np.dot(self.x_train,ws) + bs + mk_cost_lines(self.x_train,self.y_train,ws,bs,self.ax[0]) + plt_house_x(self.x_train, self.y_train, f_wb=f_wb, ax=self.ax[0]) + + # remove lines and re-add on countour plot and 3d plot + for artist in self.dyn_items: + artist.remove() + + a = self.ax[1].scatter(ws,bs, s=100, color=dlblue, zorder= 10, label="cost with \ncurrent w,b") + b = self.ax[1].hlines(bs, self.ax[1].get_xlim()[0],ws, lw=4, color=dlpurple, ls='dotted') + c = self.ax[1].vlines(ws, self.ax[1].get_ylim()[0],bs, lw=4, color=dlpurple, ls='dotted') + d = self.ax[1].annotate(f"Cost: {cst:.0f}", xy= (ws, bs), xytext = (4,4), textcoords = 'offset points', + bbox=dict(facecolor='white'), size = 10) + + #Add point in 3D surface plot + e = self.ax[2].scatter3D(ws, bs,cst , marker='X', s=100) + + self.dyn_items = [a,b,c,d,e] + self.fig.canvas.draw() + + +def soup_bowl(): + """ Create figure and plot with a 3D projection""" + fig = plt.figure(figsize=(8,8)) + + #Plot configuration + ax = fig.add_subplot(111, projection='3d') + ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) + ax.zaxis.set_rotate_label(False) + ax.view_init(45, -120) + + #Useful linearspaces to give values to the parameters w and b + w = np.linspace(-20, 20, 100) + b = np.linspace(-20, 20, 100) + + #Get the z value for a bowl-shaped cost function + z=np.zeros((len(w), len(b))) + j=0 + for x in w: + i=0 + for y in b: + z[i,j] = x**2 + y**2 + i+=1 + j+=1 + + #Meshgrid used for plotting 3D functions + W, B = np.meshgrid(w, b) + + #Create the 3D surface plot of the bowl-shaped cost function + ax.plot_surface(W, B, z, cmap = "Spectral_r", alpha=0.7, antialiased=False) + ax.plot_wireframe(W, B, z, color='k', alpha=0.1) + ax.set_xlabel("$w$") + ax.set_ylabel("$b$") + ax.set_zlabel("$J(w,b)$", rotation=90) + ax.set_title("$J(w,b)$\n [You can rotate this figure]", size=15) + + plt.show() + +def inbounds(a,b,xlim,ylim): + xlow,xhigh = xlim + ylow,yhigh = ylim + ax, ay = a + bx, by = b + if (ax > xlow and ax < xhigh) and (bx > xlow and bx < xhigh) \ + and (ay > ylow and ay < yhigh) and (by > ylow and by < yhigh): + return True + return False + +def plt_contour_wgrad(x, y, hist, ax, w_range=[-100, 500, 5], b_range=[-500, 500, 5], + contours = [0.1,50,1000,5000,10000,25000,50000], + resolution=5, w_final=200, b_final=100,step=10 ): + b0,w0 = np.meshgrid(np.arange(*b_range),np.arange(*w_range)) + z=np.zeros_like(b0) + for i in range(w0.shape[0]): + for j in range(w0.shape[1]): + z[i][j] = compute_cost(x, y, w0[i][j], b0[i][j] ) + + CS = ax.contour(w0, b0, z, contours, linewidths=2, + colors=[dlblue, dlorange, dldarkred, dlmagenta, dlpurple]) + ax.clabel(CS, inline=1, fmt='%1.0f', fontsize=10) + ax.set_xlabel("w"); ax.set_ylabel("b") + ax.set_title('Contour plot of cost J(w,b), vs b,w with path of gradient descent') + w = w_final; b=b_final + ax.hlines(b, ax.get_xlim()[0],w, lw=2, color=dlpurple, ls='dotted') + ax.vlines(w, ax.get_ylim()[0],b, lw=2, color=dlpurple, ls='dotted') + + base = hist[0] + for point in hist[0::step]: + edist = np.sqrt((base[0] - point[0])**2 + (base[1] - point[1])**2) + if(edist > resolution or point==hist[-1]): + if inbounds(point,base, ax.get_xlim(),ax.get_ylim()): + plt.annotate('', xy=point, xytext=base,xycoords='data', + arrowprops={'arrowstyle': '->', 'color': 'r', 'lw': 3}, + va='center', ha='center') + base=point + return + + +def plt_divergence(p_hist, J_hist, x_train,y_train): + + x=np.zeros(len(p_hist)) + y=np.zeros(len(p_hist)) + v=np.zeros(len(p_hist)) + for i in range(len(p_hist)): + x[i] = p_hist[i][0] + y[i] = p_hist[i][1] + v[i] = J_hist[i] + + fig = plt.figure(figsize=(12,5)) + plt.subplots_adjust( wspace=0 ) + gs = fig.add_gridspec(1, 5) + fig.suptitle(f"Cost escalates when learning rate is too large") + #=============== + # First subplot + #=============== + ax = fig.add_subplot(gs[:2], ) + + # Print w vs cost to see minimum + fix_b = 100 + w_array = np.arange(-70000, 70000, 1000) + cost = np.zeros_like(w_array) + + for i in range(len(w_array)): + tmp_w = w_array[i] + cost[i] = compute_cost(x_train, y_train, tmp_w, fix_b) + + ax.plot(w_array, cost) + ax.plot(x,v, c=dlmagenta) + ax.set_title("Cost vs w, b set to 100") + ax.set_ylabel('Cost') + ax.set_xlabel('w') + ax.xaxis.set_major_locator(MaxNLocator(2)) + + #=============== + # Second Subplot + #=============== + + tmp_b,tmp_w = np.meshgrid(np.arange(-35000, 35000, 500),np.arange(-70000, 70000, 500)) + z=np.zeros_like(tmp_b) + for i in range(tmp_w.shape[0]): + for j in range(tmp_w.shape[1]): + z[i][j] = compute_cost(x_train, y_train, tmp_w[i][j], tmp_b[i][j] ) + + ax = fig.add_subplot(gs[2:], projection='3d') + ax.plot_surface(tmp_w, tmp_b, z, alpha=0.3, color=dlblue) + ax.xaxis.set_major_locator(MaxNLocator(2)) + ax.yaxis.set_major_locator(MaxNLocator(2)) + + ax.set_xlabel('w', fontsize=16) + ax.set_ylabel('b', fontsize=16) + ax.set_zlabel('\ncost', fontsize=16) + plt.title('Cost vs (b, w)') + # Customize the view angle + ax.view_init(elev=20., azim=-65) + ax.plot(x, y, v,c=dlmagenta) + + return + +# draw derivative line +# y = m*(x - x1) + y1 +def add_line(dj_dx, x1, y1, d, ax): + x = np.linspace(x1-d, x1+d,50) + y = dj_dx*(x - x1) + y1 + ax.scatter(x1, y1, color=dlblue, s=50) + ax.plot(x, y, '--', c=dldarkred,zorder=10, linewidth = 1) + xoff = 30 if x1 == 200 else 10 + ax.annotate(r"$\frac{\partial J}{\partial w}$ =%d" % dj_dx, fontsize=14, + xy=(x1, y1), xycoords='data', + xytext=(xoff, 10), textcoords='offset points', + arrowprops=dict(arrowstyle="->"), + horizontalalignment='left', verticalalignment='top') + +def plt_gradients(x_train,y_train, f_compute_cost, f_compute_gradient): + #=============== + # First subplot + #=============== + fig,ax = plt.subplots(1,2,figsize=(12,4)) + + # Print w vs cost to see minimum + fix_b = 100 + w_array = np.linspace(-100, 500, 50) + w_array = np.linspace(0, 400, 50) + cost = np.zeros_like(w_array) + + for i in range(len(w_array)): + tmp_w = w_array[i] + cost[i] = f_compute_cost(x_train, y_train, tmp_w, fix_b) + ax[0].plot(w_array, cost,linewidth=1) + ax[0].set_title("Cost vs w, with gradient; b set to 100") + ax[0].set_ylabel('Cost') + ax[0].set_xlabel('w') + + # plot lines for fixed b=100 + for tmp_w in [100,200,300]: + fix_b = 100 + dj_dw,dj_db = f_compute_gradient(x_train, y_train, tmp_w, fix_b ) + j = f_compute_cost(x_train, y_train, tmp_w, fix_b) + add_line(dj_dw, tmp_w, j, 30, ax[0]) + + #=============== + # Second Subplot + #=============== + + tmp_b,tmp_w = np.meshgrid(np.linspace(-200, 200, 10), np.linspace(-100, 600, 10)) + U = np.zeros_like(tmp_w) + V = np.zeros_like(tmp_b) + for i in range(tmp_w.shape[0]): + for j in range(tmp_w.shape[1]): + U[i][j], V[i][j] = f_compute_gradient(x_train, y_train, tmp_w[i][j], tmp_b[i][j] ) + X = tmp_w + Y = tmp_b + n=-2 + color_array = np.sqrt(((V-n)/2)**2 + ((U-n)/2)**2) + + ax[1].set_title('Gradient shown in quiver plot') + Q = ax[1].quiver(X, Y, U, V, color_array, units='width', ) + ax[1].quiverkey(Q, 0.9, 0.9, 2, r'$2 \frac{m}{s}$', labelpos='E',coordinates='figure') + ax[1].set_xlabel("w"); ax[1].set_ylabel("b")

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