{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [], "collapsed_sections": [], "toc_visible": true }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "code", "metadata": { "id": "S-YF9CRY1jj6" }, "source": [ "# Import packages for data loading\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn-white')\n", "\n", "# Dataset and utils\n", "from sklearn.datasets import load_boston\n", "from sklearn.model_selection import train_test_split\n", "\n", "# Additional packages\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn import linear_model\n", "from sklearn.metrics import mean_squared_error\n", "from mpl_toolkits import mplot3d\n", "from sklearn.pipeline import make_pipeline" ], "execution_count": 204, "outputs": [] }, { "cell_type": "markdown", "source": [ "# Importing Data:" ], "metadata": { "id": "pRfaXVjX-92U" } }, { "cell_type": "code", "metadata": { "id": "ipUzHulY28VA", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "53aed046-9135-4a2d-e14f-1de6d5531c2e" }, "source": [ "# Load dataset\n", "dataset = load_boston()" ], "execution_count": 205, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "/usr/local/lib/python3.7/dist-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n", "\n", " The Boston housing prices dataset has an ethical problem. You can refer to\n", " the documentation of this function for further details.\n", "\n", " The scikit-learn maintainers therefore strongly discourage the use of this\n", " dataset unless the purpose of the code is to study and educate about\n", " ethical issues in data science and machine learning.\n", "\n", " In this special case, you can fetch the dataset from the original\n", " source::\n", "\n", " import pandas as pd\n", " import numpy as np\n", "\n", "\n", " data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n", " raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n", " data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n", " target = raw_df.values[1::2, 2]\n", "\n", " Alternative datasets include the California housing dataset (i.e.\n", " :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n", " dataset. You can load the datasets as follows::\n", "\n", " from sklearn.datasets import fetch_california_housing\n", " housing = fetch_california_housing()\n", "\n", " for the California housing dataset and::\n", "\n", " from sklearn.datasets import fetch_openml\n", " housing = fetch_openml(name=\"house_prices\", as_frame=True)\n", "\n", " for the Ames housing dataset.\n", " \n", " warnings.warn(msg, category=FutureWarning)\n" ] } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "TlGxoDLnEhGy", "outputId": "ea6ce75c-f49b-4530-b34f-059d712b92c2" }, "source": [ "print(dataset.keys())" ], "execution_count": 206, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename', 'data_module'])\n" ] } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "MLaRy4vEEqSS", "outputId": "ccf0e0b4-3f1d-4f38-9f50-7ad7b75ae174" }, "source": [ "print(\"Feature names:\\n\")\n", "print(dataset.feature_names)" ], "execution_count": 207, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Feature names:\n", "\n", "['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'\n", " 'B' 'LSTAT']\n" ] } ] }, { "cell_type": "code", "metadata": { "id": "LE9Zg8EnZnrz", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "50f7faf0-c26e-40d2-ef85-3a2e32f78cdb" }, "source": [ "# defining X and y\n", "X = np.array(dataset.data) # Features\n", "y = np.array(dataset.target) # Prices\n", "\n", "print(f\"X shape: {X.shape}. Target variable: {y.shape}\")" ], "execution_count": 208, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "X shape: (506, 13). Target variable: (506,)\n" ] } ] }, { "cell_type": "markdown", "source": [ "# Preparing Data:\n", "\n", "I decided to choose Number of rooms as a feature. and price as an output." ], "metadata": { "id": "MA-IxEIl_C1b" } }, { "cell_type": "code", "metadata": { "id": "obu3r70VmObl", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "aa505a19-bc9c-4a4a-fc50-384e23bec2f3" }, "source": [ "# Select RM (Number of rooms) feature from X\n", "X_rm = X[:, 5].reshape(-1,1) \n", "y_price = y.reshape(-1,1)\n", "\n", "print(X_rm.shape)\n", "print(y_price.shape)" ], "execution_count": 209, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "(506, 1)\n", "(506, 1)\n" ] } ] }, { "cell_type": "markdown", "source": [ "The data points are as below:" ], "metadata": { "id": "orLraSgJtQJD" } }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10, 7))\n", "plt.scatter(X_rm, y_price)\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 425 }, "id": "QS_-89kjyExk", "outputId": "0594061f-d797-46a5-db92-43291c9a7710" }, "execution_count": 210, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [ "#Split dataset into training and test sets\n", "X_train, X_test, y_train, y_test = train_test_split(\n", "X_rm, y_price, test_size=0.2, random_state=5)" ], "metadata": { "id": "95ydfVHz_Jj1" }, "execution_count": 211, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "6Z7yJXYMysgI", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "d00ed68a-a275-4c1b-943a-3031196634fc" }, "source": [ "# Add intercept term to X_train\n", "print(f\"X_train shape: {X_train.shape} (without intercept term)\")\n", "X_train = np.hstack((np.ones((X_train.shape[0],1)), X_train))\n", "print(f\"X_train shape: {X_train.shape} (with intercept term)\")" ], "execution_count": 212, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "X_train shape: (404, 1) (without intercept term)\n", "X_train shape: (404, 2) (with intercept term)\n" ] } ] }, { "cell_type": "markdown", "source": [ "# Method 1: Linear Regression with one line code of python:" ], "metadata": { "id": "jHnot0pB-B5x" } }, { "cell_type": "code", "source": [ "#Linear Regression using ready python code\n", "\n", "reg = linear_model.LinearRegression()\n", "reg.fit(X_train, y_train)\n", "print('Coefficients: ', reg.coef_)\n", "print('intercept:' , reg.intercept_)" ], "metadata": { "id": "nSQ-azqTFKsw", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "b006a8ea-63ee-4951-a40f-8b52c9e9beb7" }, "execution_count": 213, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Coefficients: [[0. 8.82345634]]\n", "intercept: [-32.83912991]\n" ] } ] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10, 7)) \n", "plt.scatter(X_train[:,1], y_train)\n", "\n", "Line1 = reg.intercept_[0] + X_train[:,1] * reg.coef_[0,1]\n", "\n", "plt.plot(X_train[:,1], Line1, color='black', linewidth = 2, label='Python Regression')\n", "\n", "plt.ylabel('MEDV')\n", "plt.xlabel('Room Size')\n", "leg = plt.legend(loc='upper center')\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 439 }, "id": "sVRdGwH0g41u", "outputId": "91534c2e-4b1b-49f1-8c5e-a07749a0dd21" }, "execution_count": 214, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "The black line is the answer found by linear regression code that is available in python.\n", "\n", "In order to see the difference between this line with the one we studied in theory. I decided to use the closed form formula to calculate the coefficients:" ], "metadata": { "id": "bT8P9lZwtfaL" } }, { "cell_type": "markdown", "source": [ "# Method 2: Closed-form formula" ], "metadata": { "id": "_8EXFmJO-Pe6" } }, { "cell_type": "code", "source": [ "#Linear Regression easy mode (using closed-form)\n", "def normalEqn(X, y):\n", " theta_Normal = np.linalg.pinv(np.dot(X.T,X)).dot(X.T).dot(y)\n", " return theta_Normal" ], "metadata": { "id": "yq3bJ2iExQRk" }, "execution_count": 215, "outputs": [] }, { "cell_type": "code", "source": [ "theta_closedform = normalEqn(X_train, y_train)\n", "print(theta_closedform)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "GnHO8zoOCw3Y", "outputId": "da04bfeb-9693-4c84-f5d7-a839a31d2c0c" }, "execution_count": 216, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[-32.83912991]\n", " [ 8.82345634]]\n" ] } ] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10, 7)) \n", "plt.scatter(X_train[:,1], y_train)\n", "\n", "Line1 = reg.intercept_[0] + X_train[:,1] * reg.coef_[0,1]\n", "Line2 = theta_closedform[0] + X_train[:,1] * theta_closedform[1]\n", "\n", "plt.plot(X_train[:,1], Line1, color='black', linewidth = 2, label='Python Regression')\n", "plt.plot(X_train[:,1], Line2, color='red', linewidth = 2, label='Closed Form')\n", "\n", "plt.ylabel('MEDV')\n", "plt.xlabel('Room Size')\n", "leg = plt.legend(loc='upper center')\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 439 }, "id": "HHHHyj-3CrU-", "outputId": "11555c25-2e4e-4621-a9d8-bc16a6c68e26" }, "execution_count": 217, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "As we can see here, both lines are equal. so as a concolusion, python use the closed form for its function." ], "metadata": { "id": "7hnTd2QHushF" } }, { "cell_type": "markdown", "source": [ "# Method 3: Gradient Descent (Zero initial parameters)" ], "metadata": { "id": "2cGRXBBk-XZx" } }, { "cell_type": "markdown", "source": [ "Now, Lets build a linear regression using gradient descent algorithm.\n", "First I define 2 functions. first one to compute cost (SSE) and the other one the gradient decent function." ], "metadata": { "id": "PhMOdZrxsenJ" } }, { "cell_type": "code", "metadata": { "id": "E9fy8e-Y5fFx" }, "source": [ "# Loss function - Sum of Squared Errors (SSE)\n", "def compute_cost(X, y, theta):\n", " m = X.shape[0]\n", " h = np.dot(X,theta)\n", " J = np.sum(np.square(h - y)) / (2*m)\n", " return J" ], "execution_count": 218, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "0tUthCJ3z-t6" }, "source": [ "def gradient_descent(X, y, theta, learning_rate, num_iters):\n", "\n", " n_sample, n_feat = X.shape[0], theta.shape[0] - 1\n", " theta_history = np.zeros([(n_feat + 1), num_iters])\n", " J_history = np.zeros([num_iters,1])\n", " \n", " for i in range(num_iters):\n", " h = np.dot(X, theta)\n", " dtheta = np.dot((h-y).T,X).T / n_sample\n", " theta = theta - learning_rate*dtheta\n", " theta_history[:,i] = theta[:,0]\n", " J_history[i] = compute_cost(X,y,theta)\n", " #print(theta_history[0])\n", " return (theta, theta_history, J_history)" ], "execution_count": 219, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "ksJHgG7Y0CP9", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "959c0bf6-ed1a-49fc-bee9-c643b6351f0a" }, "source": [ "# Define and initialize parameters\n", "theta = np.zeros((X_train.shape[1], 1))\n", "print(f\"{theta}\")" ], "execution_count": 220, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[0.]\n", " [0.]]\n" ] } ] }, { "cell_type": "code", "metadata": { "id": "EBEeDfRr0Ew4", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "e174c66d-5cfc-4b6b-b953-20b81f10feab" }, "source": [ "num_iters = 500\n", "learning_rate = 0.0005\n", "initial_cost = compute_cost(X_train, y_train, theta)\n", "print(\"J (initial): \", initial_cost, \"\\n\")" ], "execution_count": 221, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "J (initial): 299.38922029702974 \n", "\n" ] } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "nlewVwj0UuYo", "outputId": "c18dcff2-0b30-4f3d-b740-c95edbb20cd5" }, "source": [ "# Apply gradient descent algorithm\n", "(theta, theta_history, J_history) = gradient_descent(X_train, y_train, theta, learning_rate, num_iters)\n", "print(f\"Optimal parameters: [{theta[0]}, {theta[1]}]\")\n", "print(f\"J (final): {J_history[-1]}\")" ], "execution_count": 222, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Optimal parameters: [[0.4643156], [3.58922423]]\n", "J (final): [30.94282509]\n" ] } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 345 }, "id": "cpkfjTQpUwW1", "outputId": "1deadb7c-6e34-4af2-9bc6-cea3fd00e66b" }, "source": [ "# Plot J history\n", "plt.figure(figsize=(5, 5)) \n", "plt.plot(range(len(J_history)), J_history)\n", "plt.title(\"Convergence Graph of Cost Function 'J'\")\n", "plt.xlabel(\"Number of Iterations\")\n", "plt.ylabel(\"Cost\")\n", "plt.grid()\n", "plt.show()" ], "execution_count": 223, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "code", "metadata": { "id": "YJdFABACYGfd", "colab": { "base_uri": "https://localhost:8080/", "height": 439 }, "outputId": "a6fceec5-6f26-408a-fd6e-c3a068eb8b77" }, "source": [ "plt.figure(figsize=(10, 7)) \n", "plt.scatter(X_train[:,1], y_train)\n", "\n", "Line1 = reg.intercept_[0] + X_train[:,1] * reg.coef_[0,1]\n", "Line2 = theta_closedform[0] + X_train[:,1] * theta_closedform[1]\n", "Line3 = theta[0] + X_train[:,1] * theta[1]\n", "\n", "plt.plot(X_train[:,1], Line1, color='black', linewidth = 2, label='Python Regression')\n", "plt.plot(X_train[:,1], Line2, color='red', linewidth = 2, label='Closed Form')\n", "plt.plot(X_train[:,1], Line3, color='green', linewidth = 2, label='Gradient Descent')\n", "\n", "plt.ylabel('MEDV')\n", "plt.xlabel('Room Size')\n", "leg = plt.legend(loc='upper center')\n", "plt.show()" ], "execution_count": 224, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "The Green line is the result we have got on the training data for gradient decent.\n", "\n", "As we can see, the result for gradient descent is not according to what we expected. at the begining I thought maybe the number iteration and learning rate is wrong. which then I fixed them according to below figure and based on my J plot:\n", "\n", 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], "metadata": { "id": "d-B0i6qRvBhs" } }, { "cell_type": "markdown", "source": [ "Then I remembered that the problem with gradent descent is local minima. So as now I know the correct theta. I want to change the start point to lead the process to total minima. so let's change the initial parameters for theta and do it again:" ], "metadata": { "id": "1Dojfvn8ZJll" } }, { "cell_type": "markdown", "source": [ "# Method 4: Gradient Descent (Smart initial parameters)" ], "metadata": { "id": "H5efLTf2-kwY" } }, { "cell_type": "code", "source": [ "print(theta.shape)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "54KxfDuXWukM", "outputId": "21a5ba91-6e59-4e2c-ea3f-2d5135092e3a" }, "execution_count": 225, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "(2, 1)\n" ] } ] }, { "cell_type": "code", "source": [ "theta_New = np.zeros((X_train.shape[1], 1))\n", "theta_New[0] = -30\n", "theta_New[1] = 7\n", "print(f\"{theta_New}\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "h4Hyy80hzoWW", "outputId": "5f9c9f0f-ef33-4247-f012-0f5375ed8cc6" }, "execution_count": 226, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[-30.]\n", " [ 7.]]\n" ] } ] }, { "cell_type": "code", "source": [ "num_iters = 500\n", "learning_rate = 0.0005\n", "initial_cost = compute_cost(X_train, y_train, theta_New)\n", "print(\"J (initial): \", initial_cost, \"\\n\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "KCUUg506XKbe", "outputId": "a75b2b61-deea-4cb3-c27f-58340e953e1c" }, "execution_count": 227, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "J (initial): 62.320291678217814 \n", "\n" ] } ] }, { "cell_type": "code", "source": [ "# Apply gradient descent algorithm\n", "(theta_New, theta_history, J_history) = gradient_descent(X_train, y_train, theta_New, learning_rate, num_iters)\n", "print(f\"Optimal parameters: [{theta[0]}, {theta[1]}]\")\n", "print(f\"J (final): {J_history[-1]}\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "W3HFVnOXXW8O", "outputId": "67bf6adb-1f22-4bcc-d30b-1746a171c8b0" }, "execution_count": 228, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Optimal parameters: [[0.4643156], [3.58922423]]\n", "J (final): [24.36167573]\n" ] } ] }, { "cell_type": "code", "source": [ "# Plot J history\n", "plt.figure(figsize=(5, 5)) \n", "plt.plot(range(len(J_history)), J_history)\n", "plt.title(\"Convergence Graph of Cost Function 'J'\")\n", "plt.xlabel(\"Number of Iterations\")\n", "plt.ylabel(\"Cost\")\n", "plt.grid()\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 345 }, "id": "BE2qqO18z2xs", "outputId": "09546528-9c90-4dab-ea77-6dc62adfd8a0" }, "execution_count": 229, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10, 7)) \n", "plt.scatter(X_train[:,1], y_train)\n", "\n", "Line1 = reg.intercept_[0] + X_train[:,1] * reg.coef_[0,1]\n", "Line2 = theta_closedform[0] + X_train[:,1] * theta_closedform[1]\n", "Line3 = theta[0] + X_train[:,1] * theta[1]\n", "Line4 = theta_New[0] + + X_train[:,1] * theta_New[1]\n", "\n", "plt.plot(X_train[:,1], Line1, color='black', linewidth = 2, label='Python Regression')\n", "plt.plot(X_train[:,1], Line2, color='red', linewidth = 2, label='Closed Form')\n", "plt.plot(X_train[:,1], Line3, color='green', linewidth = 2, label='Gradient Descent')\n", "plt.plot(X_train[:,1], Line4, color='Yellow', linewidth = 2, label='Gradient Descent with better initial parameters')\n", "\n", "plt.ylabel('MEDV')\n", "plt.xlabel('Room Size')\n", "leg = plt.legend(loc='upper center')\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 439 }, "id": "A-jP9ZYxXfwT", "outputId": "9bbf1b81-129c-472c-8fbc-099e0c17feb6" }, "execution_count": 230, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "Now as we can see the result of gradient descent is very close to the right answer. :)))" ], "metadata": { "id": "wUlK9UOSbJmj" } }, { "cell_type": "markdown", "source": [ "# Test Data and predictions:" ], "metadata": { "id": "gqa1FRJF-wit" } }, { "cell_type": "markdown", "source": [ "Now I want to see how they work on Test data:" ], "metadata": { "id": "9FYROXbabnKb" } }, { "cell_type": "code", "source": [ "X_test = np.hstack((np.ones((X_test.shape[0],1)), X_test))" ], "metadata": { "id": "Tb60ZCXSzFVQ" }, "execution_count": 231, "outputs": [] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10, 7)) \n", "plt.scatter(X_test[:,1], y_test)\n", "\n", "plt.ylabel('MEDV')\n", "plt.xlabel('Room Size')\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 439 }, "id": "DHJgRH9wqQEx", "outputId": "a903dc11-9403-4e91-db97-24b5ac3a058d" }, "execution_count": 232, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [ "# Answers for Line1/Line2:\n", "y_pred1 = reg.predict(X_test)" ], "metadata": { "id": "z1nustwcbtWD" }, "execution_count": 233, "outputs": [] }, { "cell_type": "code", "source": [ "# Answers for Line3:\n", "y_pred3 = np.dot(X_test, theta)" ], "metadata": { "id": "tFzEaBc25cf5" }, "execution_count": 234, "outputs": [] }, { "cell_type": "code", "source": [ "# Answers for Line4:\n", "y_pred4 = np.dot(X_test, theta_New)" ], "metadata": { "id": "FPWcrCY68gQP" }, "execution_count": 235, "outputs": [] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10, 7)) \n", "plt.scatter(X_test[:,1], y_test)\n", "\n", "for i in range(X_test.shape[0]):\n", " plt.plot(X_test[i,1], y_pred1[i,0], 'bo', color='black', linestyle=\"--\")\n", " plt.plot(X_test[i,1], y_pred3[i,0], 'bo', color='red', linestyle=\"--\")\n", " plt.plot(X_test[i,1], y_pred4[i,0], 'bo', color='yellow', linestyle=\"--\")\n", "\n", "plt.ylabel('MEDV')\n", "plt.xlabel('Room Size')\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 439 }, "id": "NvxtDWZD0iuB", "outputId": "4c8c2088-1a8e-4deb-9f06-807c705cf527" }, "execution_count": 236, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "# Evaluation:" ], "metadata": { "id": "DDWVBpQT-3Ev" } }, { "cell_type": "code", "source": [ "#Evaluation function\n", "def compute_cost_test(X, y_real, y_predicted):\n", " m = X.shape[0]\n", " cost = np.sum(np.square(y_predicted - y_real)) / (2*m)\n", " return cost" ], "metadata": { "id": "_3VFvdmn3Xeu" }, "execution_count": 237, "outputs": [] }, { "cell_type": "code", "source": [ "#Cost for test data with Line1/2:\n", "compute_cost_test(X_test, y_test, y_pred1)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "_xlpTFCL5JZQ", "outputId": "cf2f86c8-497b-4049-9609-7a49b932a9a7" }, "execution_count": 238, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "11.985227763995649" ] }, "metadata": {}, "execution_count": 238 } ] }, { "cell_type": "code", "source": [ "#Cost for test data with Line3:\n", "compute_cost_test(X_test, y_test, y_pred3)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "Q7hN3ei68TR7", "outputId": "cd71cade-1fd0-43a4-db13-16df5a078c1d" }, "execution_count": 239, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "23.32169292335092" ] }, "metadata": {}, "execution_count": 239 } ] }, { "cell_type": "code", "source": [ "#Cost for test data with Line4:\n", "compute_cost_test(X_test, y_test, y_pred4)" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "40OtwnRb9Efv", "outputId": "abdf6982-39ce-422d-b6ac-33e6ce04e126" }, "execution_count": 240, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "12.389038810925268" ] }, "metadata": {}, "execution_count": 240 } ] }, { "cell_type": "markdown", "source": [ "# **Concolution:**\n", "\n", "The best way to find the solution is the closed form of the calculating coefficients of the line or hyperplane. But as we cannot always use this method, Gradient Descent is another method which we try to find the parameters, but the start point is very important in it." ], "metadata": { "id": "m9Kv_W9v9cAf" } } ] }