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week2/C1_W2_Lab06_Sklearn_Normal_Soln.ipynb
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week2/C1_W2_Lab06_Sklearn_Normal_Soln.ipynb
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Optional Lab: Linear Regression using Scikit-Learn"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"There is an open-source, commercially usable machine learning toolkit called [scikit-learn](https://scikit-learn.org/stable/index.html). This toolkit contains implementations of many of the algorithms that you will work with in this course.\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Goals\n",
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"In this lab you will:\n",
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"- Utilize scikit-learn to implement linear regression using a close form solution based on the normal equation"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Tools\n",
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"You will utilize functions from scikit-learn as well as matplotlib and NumPy. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from sklearn.linear_model import LinearRegression\n",
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"from lab_utils_multi import load_house_data\n",
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"plt.style.use('./deeplearning.mplstyle')\n",
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"np.set_printoptions(precision=2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<a name=\"toc_40291_2\"></a>\n",
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"# Linear Regression, closed-form solution\n",
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"Scikit-learn has the [linear regression model](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression) which implements a closed-form linear regression.\n",
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"\n",
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"Let's use the data from the early labs - a house with 1000 square feet sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000.\n",
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"\n",
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"| Size (1000 sqft) | Price (1000s of dollars) |\n",
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"| ----------------| ------------------------ |\n",
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"| 1 | 300 |\n",
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"| 2 | 500 |\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Load the data set"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"X_train = np.array([1.0, 2.0]) #features\n",
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"y_train = np.array([300, 500]) #target value"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Create and fit the model\n",
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"The code below performs regression using scikit-learn. \n",
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"The first step creates a regression object. \n",
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"The second step utilizes one of the methods associated with the object, `fit`. This performs regression, fitting the parameters to the input data. The toolkit expects a two-dimensional X matrix."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"linear_model = LinearRegression()\n",
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"#X must be a 2-D Matrix\n",
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"linear_model.fit(X_train.reshape(-1, 1), y_train) "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### View Parameters \n",
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"The $\\mathbf{w}$ and $\\mathbf{b}$ parameters are referred to as 'coefficients' and 'intercept' in scikit-learn."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"b = linear_model.intercept_\n",
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"w = linear_model.coef_\n",
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"print(f\"w = {w:}, b = {b:0.2f}\")\n",
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"print(f\"'manual' prediction: f_wb = wx+b : {1200*w + b}\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Make Predictions\n",
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"\n",
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"Calling the `predict` function generates predictions."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"y_pred = linear_model.predict(X_train.reshape(-1, 1))\n",
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"\n",
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"print(\"Prediction on training set:\", y_pred)\n",
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"\n",
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"X_test = np.array([[1200]])\n",
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"print(f\"Prediction for 1200 sqft house: ${linear_model.predict(X_test)[0]:0.2f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Second Example\n",
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"The second example is from an earlier lab with multiple features. The final parameter values and predictions are very close to the results from the un-normalized 'long-run' from that lab. That un-normalized run took hours to produce results, while this is nearly instantaneous. The closed-form solution work well on smaller data sets such as these but can be computationally demanding on larger data sets. \n",
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">The closed-form solution does not require normalization."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# load the dataset\n",
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"X_train, y_train = load_house_data()\n",
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"X_features = ['size(sqft)','bedrooms','floors','age']"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"linear_model = LinearRegression()\n",
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"linear_model.fit(X_train, y_train) "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"b = linear_model.intercept_\n",
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"w = linear_model.coef_\n",
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"print(f\"w = {w:}, b = {b:0.2f}\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"print(f\"Prediction on training set:\\n {linear_model.predict(X_train)[:4]}\" )\n",
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"print(f\"prediction using w,b:\\n {(X_train @ w + b)[:4]}\")\n",
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"print(f\"Target values \\n {y_train[:4]}\")\n",
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"\n",
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"x_house = np.array([1200, 3,1, 40]).reshape(-1,4)\n",
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"x_house_predict = linear_model.predict(x_house)[0]\n",
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"print(f\" predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = ${x_house_predict*1000:0.2f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Congratulations!\n",
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"In this lab you:\n",
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"- utilized an open-source machine learning toolkit, scikit-learn\n",
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"- implemented linear regression using a close-form solution from that toolkit"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.10"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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