{ "cells": [ { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Read the dataset\n", "To read the dataset we are going to use the function `read_csv` from the [pandas library](https://pandas.pydata.org/). In the following box the dataset is first loaded as a \"dataframe\" (similar to those from R), each column correspond to a variable (dimension) and each row to a point.\n", "\n", "This dataset consist of $n=9$ __physiological and medical variables (columns)__ measured for $m=768$ __patients (rows)__\n", "\n", "Each column represents the following variables:\n", "\n", "+ column 0: *Pregnancies*: Number of times pregnant\n", "+ column 1: *Glucose*: Plasma glucose concentration a 2 hours in an oral glucose tolerance test\n", "+ column 2: *BloodPressure*: Diastolic blood pressure (mm Hg)\n", "+ column 3: *SkinThickness*: Triceps skin fold thickness (mm)\n", "+ column 4: *Insulin*: 2-Hour serum insulin (mu U/ml)\n", "+ column 5: *BMI*: Body mass index (weight in kg/(height in m)^2)\n", "+ column 6: *DiabetesPedigreeFunction*: Diabetes pedigree function\n", "+ column 7: *Age*: Age (years)\n", "+ column 8: *Outcome*: The person is diabetic or not (1 or 0)\n" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "dataset = pd.read_csv('diabetes.csv',header=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see the first 3 lines of the dataset we use the `head` method with a parameter `3`" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Pregnancies Glucose BloodPressure SkinThickness Insulin BMI \\\n", "0 6 148 72 35 0 33.6 \n", "1 1 85 66 29 0 26.6 \n", "2 8 183 64 0 0 23.3 \n", "\n", " DiabetesPedigreeFunction Age Outcome \n", "0 0.627 50 1 \n", "1 0.351 31 0 \n", "2 0.672 32 1 " ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dataset.head(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Description of the regression problem \n", "\n", "For this project, we will consider a reduced dataset with the following 5 columns as the __conditions__:\n", "+ Pregancies\n", "+ BloodPressure\n", "+ SkinThinkness\n", "+ BMI\n", "+ Age\n", "\n", "Let $X$ be a $m\\times 5$ matrix corresponding to the values of each one of these condition variable for each patient. \n", "\n", "And We are going to consider the following column as our __observation__:\n", "+ Glucose\n", "\n", "Let $y$ be the vector of observations for each patient\n", "\n", "### Goal (Least Squares):\n", "Our goal is to find $c$ a vector of __parameters__ such that:\n", "$$X\\cdot c +r = y \\quad \\text{and}\\quad ||r||_2 \\text{ is minimized }$$\n", "\n", "### Construction of $X$ and $y$\n", "In the following box we construct our matrix $X$ and vector $y$ as `np.array`, so you do not need to bother understanding the structure of the dataframe. \n" ] }, { "cell_type": "code", "execution_count": 208, "metadata": {}, "outputs": [], "source": [ "# Get only the requiered variables\n", "dataset_X = dataset[[\"Pregnancies\",\n", " \"BloodPressure\",\n", " \"SkinThickness\",\n", " \"BMI\",\n", " \"Age\"]]\n", "# Get only the observation variable\n", "dataset_y = dataset[\"Glucose\"]\n", "# Get only np.array out of the dataset\n", "X = dataset_X.values\n", "y = dataset_y.values" ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "type of X: \n", "shape of X: (768, 5)\n", "type of y: \n", "shape of y: (768,)\n" ] } ], "source": [ "print(\"type of X: \",type(X))\n", "print(\"shape of X: \",X.shape)\n", "print(\"type of y: \",type(y))\n", "print(\"shape of y: \",y.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Questions\n", "+ 1) Plot $y$ as a function of the values of each column of $X$\n", "+ 2) Compute a $QR$ factorization of $X$\n", "+ 3) Use the factorization to compute the vector $c$\n", "+ 4) Plot $y$ and the regression $X\\cdot c$, as a function of the values of each column of $X$\n", "+ 5) Apply the SVD to $X = \\hat U \\Sigma V^*$\n", "+ 6) Represent the points in the plane defined by the two first column vectors of $V$.\n", "+ 7) Represent the projection of the canonical axis in this plane" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1) Plot the data" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Glucose')" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(1,figsize=(13,13))\n", "# Plot Glucose vs Pregnancies\n", "plt.subplot(321)\n", "plt.plot(X[:,0], y, \"o\")\n", "plt.xlabel(\"Pregnancies\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs BloodPressure\n", "plt.subplot(322)\n", "plt.plot(X[:,1], y, \"o\")\n", "plt.xlabel(\"BloodPressure\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs BloodPressure\n", "plt.subplot(323)\n", "plt.plot(X[:,2], y, \"o\")\n", "plt.xlabel(\"SkinThickness\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs Glucose\n", "plt.subplot(324)\n", "plt.plot(X[:,3], y, \"o\")\n", "plt.xlabel(\"BMI\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs Age\n", "plt.subplot(325)\n", "plt.plot(X[:,4], y, \"o\")\n", "plt.xlabel(\"Age\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2) Compute QR factorization" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [], "source": [ "Q,R = np.linalg.qr(X)" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((768, 5), (5, 5))" ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q.shape,R.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "R is upper triangular matrix" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 215, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Q is a orthonormal matrix" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(Q.T.dot(Q))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3) Compute parameter vector $c$ solving the least-squares equation\n", "$X^* X c = X^* y$ (normal equation) and $X = QR$ (QR factorization)\n", "\n", "Then: $(QR)^*(QR) c = (QR)^* y$\n", "\n", "$R^* Q^* Q R c = R^* Q^* y$\n", "\n", "$R^* R c = R^* Q^* y$\n", "\n", "If $X$ is full rank then $R$ is invertible\n", "\n", "$Rc = Q^* y$\n", "\n", "$c = R^{-1} Q^* y$" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [], "source": [ "c = np.linalg.inv(R).dot(Q.T).dot(y)" ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.60676759 0.3219836 -0.04742801 1.86698339 1.19918515]\n" ] } ], "source": [ "print(c)" ] }, { "cell_type": "code", "execution_count": 219, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(c,\"o\")\n", "plt.hlines(0,xmin=0,xmax=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Some Interpretation \n", "##### Recall of the variables:\n", "+ 0: Pregancies\n", "+ 1: BloodPressure\n", "+ 2: SkinThinkness\n", "+ 3: BMI\n", "+ 4: Age\n", "\n", "What happens if an individual increases his BMI of one unit? The regression tells you that his glucose level should increase by 1.866\n", "\n", "What happens if an individual get 1 year older? The regression tells you that his glucose level should increase by 1.199\n", "\n", "If the skin thickness increases, then the impact in the glucose level is very low (-0.047)\n", "\n", "...\n", "\n", "Keep in mind that this is not reality, this is just a regression model, and we did not even checked the statistical validity of these results (out of the scope of this lecture)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the regression $X\\cdot c$" ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [], "source": [ "Xc = X.dot(c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4) Plot $y$ and $Xc$ as a function of each variable in $X$" ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Glucose')" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(1,figsize=(13,13))\n", "# Plot Glucose vs Pregnancies\n", "plt.subplot(321)\n", "plt.plot(X[:,0], y, \"o\")\n", "plt.plot(X[:,0], Xc, \"o\")\n", "plt.xlabel(\"Pregnancies\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs BloodPressure\n", "plt.subplot(322)\n", "plt.plot(X[:,1], y, \"o\")\n", "plt.plot(X[:,1], Xc, \"o\")\n", "plt.xlabel(\"BloodPressure\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs BloodPressure\n", "plt.subplot(323)\n", "plt.plot(X[:,2], y, \"o\")\n", "plt.plot(X[:,2], Xc, \"o\")\n", "plt.xlabel(\"SkinThickness\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs Glucose\n", "plt.subplot(324)\n", "plt.plot(X[:,3], y, \"o\")\n", "plt.plot(X[:,3], Xc, \"o\")\n", "plt.xlabel(\"BMI\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n", "# Plot Glucose vs Age\n", "plt.subplot(325)\n", "plt.plot(X[:,4], y, \"o\")\n", "plt.plot(X[:,4], Xc, \"o\")\n", "plt.xlabel(\"Age\", fontsize=20)\n", "plt.ylabel(\"Glucose\", fontsize=20)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5) Apply SVD to $X$" ] }, { "cell_type": "code", "execution_count": 250, "metadata": {}, "outputs": [], "source": [ "U,s,Vt = np.linalg.svd(X,full_matrices=False)\n", "V = Vt" ] }, { "cell_type": "code", "execution_count": 251, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-6.47630098e-17, 1.50342701e-17, 1.00613962e-16, 2.59052039e-16,\n", " 1.93132547e-16])" ] }, "execution_count": 251, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_.mean(axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the STD along each principal axis" ] }, { "cell_type": "code", "execution_count": 252, "metadata": {}, "outputs": [], "source": [ "variances = s/(X.shape[0]-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the % of STD carried by each principal axis" ] }, { "cell_type": "code", "execution_count": 253, "metadata": {}, "outputs": [], "source": [ "variances_percent = variances / sum(variances)" ] }, { "cell_type": "code", "execution_count": 254, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([69.64783151, 12.55796676, 9.28703089, 6.28474808, 2.22242276])" ] }, "execution_count": 254, "metadata": {}, "output_type": "execute_result" } ], "source": [ "variances_percent*100" ] }, { "cell_type": "code", "execution_count": 255, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 255, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(variances_percent*100,\"o\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6) Represent the points in the plane defined by the two first vector columns of $V$ \n" ] }, { "cell_type": "code", "execution_count": 256, "metadata": {}, "outputs": [], "source": [ "X_principal = X.dot(V[:,:2])" ] }, { "cell_type": "code", "execution_count": 257, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 257, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(X_principal[:,0],X_principal[:,1],\"o\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7) Represent the canonical axis in the plane defined by the two first vector columns of $V$" ] }, { "cell_type": "code", "execution_count": 258, "metadata": {}, "outputs": [], "source": [ "map_cannonical = np.eye(5).dot(V).T[:,:2]" ] }, { "cell_type": "code", "execution_count": 259, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-1, 1)" ] }, "execution_count": 259, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.arrow(0,0,*map_cannonical[0,:],head_width=0.05)\n", "plt.arrow(0,0,*map_cannonical[1,:],head_width=0.05)\n", "plt.arrow(0,0,*map_cannonical[2,:],head_width=0.05)\n", "plt.arrow(0,0,*map_cannonical[3,:],head_width=0.05)\n", "plt.arrow(0,0,*map_cannonical[4,:],head_width=0.05)\n", "plt.text(x=map_cannonical[0,0],y=map_cannonical[0,1],s = \"Pregnancies\")\n", "plt.text(x=map_cannonical[1,0],y=map_cannonical[1,1],s = \"BloodPressure\")\n", "plt.text(x=map_cannonical[2,0],y=map_cannonical[2,1],s = \"SkinThickness\")\n", "plt.text(x=map_cannonical[3,0],y=map_cannonical[3,1],s = \"BMI\")\n", "plt.text(x=map_cannonical[4,0],y=map_cannonical[4,1],s = \"Age\")\n", "plt.xlim([-1,1])\n", "plt.ylim([-1,1])\n" ] }, { "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }