{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear regression\n", "\n", "we want to solve linear regression \n", "$${\\rm minimize}_w \\|{\\bf X}w-{\\bf y}\\|_2^2$$\n", "- first generate (input, output) paired data examples\n", "\n", "- there is a subtlety (in notations mainly) in how we handle constant offset\n", "\n", "- given data $x=(x[1],x[2],x[3],\\cdots,x[d])$ in $d$-dimensions, \n", "one option is to use **linear predictor** of the form \n", "$$f(x) = w^Tx = w_1x[1] + w_2x[2] + \\cdots, w_dx[d]$$\n", "\n", "- another option is to use **affine predictor**, by appending a one to the data, i.e. $x=(1,x[1],x[2],x[3],\\cdots,x[d])$\n", "$$f(x) = w^Tx = w_0 + w_1x[1] + \\cdots + w_d x[d]$$\n", "\n", "- We will use these notations interchangeably, as it should be clear from the context which one we are using\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# generate training data\n", "import numpy as np\n", "n = 100 # sample size\n", "x = np.random.uniform(-1,1,n) #sample input data\n", "x = np.sort(x)\n", "x[0]=-1\n", "x[n-1]=1\n", "\n", "# ground truth is 5-th order polynomial and we add Gaussian noise to it\n", "y = (x-.99)*(x-.4)*(x-.25)*(x+.6)*(x+.8) + .03*np.random.randn(n)\n", "\n", "# plot the samples and grounstruth\n", "t = np.linspace(-1,1,100)\n", "y0 = (t-.99)*(t-.4)*(t-.25)*(t+.6)*(t+.8)\n", "import matplotlib.pyplot as plt\n", "plt.plot(x,y,'o')\n", "#plt.plot(t,y0,'k-')\n", "plt.title('Train set = 100 paired samples from noisy degree-5 polynomial')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "# generate test data\n", "n_ = 100\n", "x_ = np.random.uniform(-1,1,n_)\n", "y_ = (x_-.99)*(x_-.4)*(x_-.25)*(x_+.6)*(x_+.8) + .03*np.random.randn(n_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "next, create **data matrix** ${\\bf X}$\n", "$${\\bf X} = \\begin{bmatrix} (x_1)^T\\\\ (x_2)^T\\\\ \\vdots \\\\ (x_n)^T \\end{bmatrix}$$\n", "- the $i$-th row od ${\\bf X}$ is input raw data of $i$-th sample, transposed\n", "- the $j$-th column of ${\\bf X}$ gives values of $j$-th data entry across $n$ data points \n", "- $X_{ij}$ is the value of $j$-th entry for $i$-th sample data point" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constant fit example\n", "we are going to ignore any input data and try to fit a constanf function $f(x)=w_1$\n", "\n", "we create a data matrix with $x_i=1$\n", "\n", "data matrix is " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# create a data matrix X\n", "X = np.vstack([np.ones(len(x))]).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that the least squares solution is \n", "\\begin{eqnarray} \n", "\\hat{w}_{\\rm LS} &=& (X^TX)^{-1}X^T y\\\\ \n", "&=& n^{-1} 1^T y \\\\\n", "&=& \\frac{1}{n}\\sum_{i=1}^n y_i\n", "\\end{eqnarray}\n", "\n", "\n", "which is just the average of the sample outcome data, \n", "and the prediction is \n", "$\\hat{w}_{\\rm LS} = \\frac{1}{n}\\sum_{i=1}^n y_i$ for all data point $x$, \n", "\n", "\n", "$$ \\hat{y} = \\begin{bmatrix} \\hat{y}_1\\\\ \\vdots\\\\ \\hat{y}_n \\end{bmatrix} = \\begin{bmatrix} \\hat{w}_{\\rm LS}^Tx_1 \\\\ \\vdots \\\\ \\hat{w}_{\\rm LS}^T x_n\\end{bmatrix} = \\hat{w}_{\\rm LS} \\begin{bmatrix}1\\\\ \\vdots\\\\ 1\\end{bmatrix}$$\n", "\n", "hence, **the average is the best constant fit** for suqared loss\n", "\n", "and the MSE is the variance of the outcome:\n", "\n", "$$ \\frac1n \\sum_{i=1}^n ({\\rm ave}(y)-y_i)^2$$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "0.2709858277792123" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# linear regression with constant feature\n", "w = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh = w*X\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(x, yh, 'g',label='degree-0')\n", "plt.legend()\n", "plt.title('degree-0 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh)**2)\n", "display(MSE_train)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_))]).T\n", "yh_ = w*X_\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "for **affine** fit, we use $(1,x_i)$ as the input data, and the data matrix ${\\bf X}$ is" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# create a data matrix X\n", "X = np.vstack([np.ones(len(x)),x]).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "the prediction has the form \n", "$$\\hat{y} = w_1+w_2x$$\n", "this is called **straight-line fit** and if $x$ is time, it is called **trend line**\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# linear regression\n", "p=1\n", "w1 = np.array(2)\n", "w1 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh1= np.matmul(X,w1)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(x, yh1, 'g',label='degree-1')\n", "plt.plot(x, yh, 'g-.',label='degree-0')\n", "plt.legend()\n", "plt.title('degree-1 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh1)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_]).T\n", "yh_= np.matmul(X_,w1)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.array([[1,MSE_train,MSE_test]]) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Polynomial features\n", "\n", "polynomial functions are useful features, as any smooth function can be represented by polynomials of large enough degree using Taylor expansion. \n", "\n", "for degere 2 polynomial, we use $(1,x,x^2)$ as feature vector" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=2\n", "X = np.vstack([np.ones(len(x)),x,x**2]).T\n", "\n", "# degree-2 polynomial linear regression\n", "w2 = np.array(3)\n", "w2 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh2= np.matmul(X,w2)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(x, yh2, 'g',label='degree-2')\n", "plt.plot(x, yh1, 'g',label='degree-1')\n", "plt.plot(x, yh, 'g-.',label='degree-0')\n", "plt.legend()\n", "plt.title('degree-2 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh2)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2]).T\n", "yh_= np.matmul(X_,w2)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "for p=3 degree polynomial, we use feature vector $(1,x,x^2,x^3)$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=3\n", "X = np.vstack([np.ones(len(x)),x,x**2,x**3]).T\n", "\n", "# degree-p polynomial linear regression\n", "w3 = np.array(p+1)\n", "w3 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh3= np.matmul(X,w3)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(x, yh3, 'g',label='degree-3')\n", "plt.legend()\n", "plt.title('degree-3 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh3)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2,x_**3]).T\n", "yh_= np.matmul(X_,w3)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=4\n", "X = np.vstack([np.ones(len(x)),x,x**2,x**3,x**4]).T\n", "\n", "# degree-p polynomial linear regression\n", "w4 = np.array(p+1)\n", "w4 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh4= np.matmul(X,w4)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(t, np.matmul(np.vstack([np.ones(len(t)),t,t**2,t**3,t**4]).T,w4), 'g',label='degree-4')\n", "plt.legend()\n", "plt.title('degree-4 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh4)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2,x_**3,x_**4]).T\n", "yh_= np.matmul(X_,w4)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=5\n", "X = np.vstack([np.ones(len(x)),x,x**2,x**3,x**4,x**5]).T\n", "\n", "# degree-p polynomial linear regression\n", "w5 = np.array(p+1)\n", "w5 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh5= np.matmul(X,w5)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(t, np.matmul(np.vstack([np.ones(len(t)),t,t**2,t**3,t**4,t**5]).T,w5), 'g',label='degree-5')\n", "plt.legend()\n", "plt.title('degree-5 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh5)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2,x_**3,x_**4,x_**5]).T\n", "yh_= np.matmul(X_,w5)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=10\n", "X = np.vstack([np.ones(len(x)),x,x**2,x**3,x**4,x**5,x**6,x**7,x**8,x**9,x**10]).T\n", "\n", "# degree-p polynomial linear regression\n", "w10 = np.array(p+1)\n", "w10 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh10= np.matmul(X,w10)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(t, np.matmul(np.vstack([np.ones(len(t)),t,t**2,t**3,t**4,t**5,t**6,t**7,t**8,t**9,t**10]).T,w10), 'g',label='degree-10')\n", "plt.legend()\n", "plt.title('degree-10 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh10)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2,x_**3,x_**4,x_**5,x_**6,x_**7,x_**8,x_**9,x_**10]).T\n", "yh_= np.matmul(X_,w10)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=15\n", "X = np.vstack([np.ones(len(x)),x,x**2,x**3,x**4,x**5,x**6,x**7,x**8,x**9,x**10,x**11,x**12,x**13,x**14,x**15]).T\n", "\n", "# degree-p polynomial linear regression\n", "w15 = np.array(p+1)\n", "w15 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh15= np.matmul(X,w15)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(t, np.matmul(np.vstack([np.ones(len(t)),t,t**2,t**3,t**4,t**5,t**6,t**7,t**8,t**9,t**10,t**11,t**12,t**13,t**14,t**15]).T,w15), 'g',label='degree-15')\n", "plt.legend()\n", "plt.title('degree-15 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh15)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2,x_**3,x_**4,x_**5,x_**6,x_**7,x_**8,x_**9,x_**10,x_**11,x_**12,x_**13,x_**14,x_**15]).T\n", "yh_= np.matmul(X_,w15)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a data matrix X\n", "p=20\n", "X = np.vstack([np.ones(len(x)),x,x**2,x**3,x**4,x**5,x**6,x**7,x**8,x**9,x**10,x**11,x**12,x**13,x**14,x**15,x**16,x**17,x**18,x**19,x**20]).T\n", "\n", "# degree-p polynomial linear regression\n", "w20 = np.array(p+1)\n", "w20 = np.matmul(np.matmul(np.linalg.inv(np.matmul(X.T,X)),X.T),y)\n", "yh20= np.matmul(X,w20)\n", "\n", "plt.plot(x,y,'o')\n", "plt.plot(t,y0,'k-',label='ground truth')\n", "plt.plot(t, np.matmul(np.vstack([np.ones(len(t)),t,t**2,t**3,t**4,t**5,t**6,t**7,t**8,t**9,t**10,t**11,t**12,t**13,t**14,t**15,t**16,t**17,t**18,t**19,t**20]).T,w20), 'g',label='degree-20')\n", "plt.legend()\n", "plt.title('degree-20 polynomial regression')\n", "plt.xlabel(\"input x\")\n", "plt.ylabel(\"response y\")\n", "plt.show()\n", "\n", "MSE_train = (1/float(n))*np.sum((y - yh20)**2)\n", "\n", "# MSE on fresh data not used in training\n", "X_ = np.vstack([np.ones(len(x_)),x_,x_**2,x_**3,x_**4,x_**5,x_**6,x_**7,x_**8,x_**9,x_**10,x_**11,x_**12,x_**13,x_**14,x_**15,x_**16,x_**17,x_**18,x_**19,x_**20]).T\n", "yh_= np.matmul(X_,w20)\n", "MSE_test = (1/float(n_))*np.sum((y_ - yh_)**2) \n", "MSE = np.append(MSE,[[p,MSE_train,MSE_test]],axis=0) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "feature engineering requires domain knowledge about what are good features for the application\n", "\n" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(MSE.T[0],MSE.T[1],'o-',label='train error')\n", "plt.plot(MSE.T[0],MSE.T[2],'o-',label='test error')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- the **training error** always decrease as we increase the complexity of the model (which in this example is increasing the degree of the polynomial)\n", "- on the other hand, the **test error** that we compute, which is the average error over fresh drawn samples, has a sweet spot where the test error is minimum\n", "- this corresponds usually to the true complexity of the model, which in this case is degree-5 polynomial\n", "-although we did not know (just frmo the samples) that the ground truth is a degree-5 polynomial, we could use the test error to guess the degree of the model we need to use to fit this data (and this process is known as hyper parameter tuning using test error)\n", "- we will learn much more about it in next couple of weeks" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.9" } }, "nbformat": 4, "nbformat_minor": 4 }