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@ilanman
Last active November 18, 2023 13:31
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Gaussian Proccess
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"from numpy.random import multivariate_normal as mvn \n",
"import matplotlib.pyplot as plt\n",
"import matplotlib as mpl\n",
"import seaborn as sns\n",
"from matplotlib import animation, rcParams\n",
"rcParams.update({'figure.autolayout': True})\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def calc_covariance_matrix(X1,X2):\n",
" \"\"\"\n",
" Calculate the covariance matrix of a squared-exponential kernel\n",
" \"\"\"\n",
" \n",
" covariance = np.repeat(0, len(X1)*len(X2)).reshape(len(X1),len(X2)).astype(float)\n",
"\n",
" for i in range(len(X1)):\n",
" for j in range(len(X2)):\n",
" covariance[i,j] = np.exp(-0.5*(abs(X1[i]-X2[j]))**2)\n",
" #covariance[i,j] = np.minimum(X1[i],X2[j])\n",
" #covariance[i,j] = np.exp(-(np.sin(X1[i]-X2[j])/2))\n",
" \n",
" return covariance\n"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x_vals = np.linspace(-10,10,100)\n",
"sigma = calc_covariance_matrix(x_vals,x_vals)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_samples = 4\n",
"y_vals = np.repeat(0,len(x_vals)*n_samples).reshape(len(x_vals),n_samples).astype(float)\n",
"for i in range(n_samples):\n",
" # Each column represents a sample from a multivariate normal distribution\n",
" # with zero mean and covariance sigma\n",
" y_vals[:,i] = mvn(np.repeat(0,len(x_vals)),sigma)\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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EyEIIIYQQYfD7dQ6+don25n4UBVyjXloaemlp6B17jKLA6k3F7LlrBYqixLC3IhISIAsh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OAAAg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\nBgAAADwEZAAAAMDzX8xFEsNLRumSAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ed52610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pylab import rcParams\n",
"rcParams['figure.figsize'] = 10, 6\n",
"plt.plot(x_vals,y_vals,linewidth=2)\n",
"plt.title(\"Functions from a Gaussian Process with a Periodic Kernel\",size=16)\n",
"plt.ylabel(\"output, f(x)\")\n",
"plt.xlabel(\"intput, x\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def calculate_kernels(xs,x_vals):\n",
"\n",
" k_xx = calc_covariance_matrix(xs,xs)\n",
" k_xxs = calc_covariance_matrix(xs,x_vals)\n",
" k_xsx = calc_covariance_matrix(x_vals,xs)\n",
" k_xsxs = calc_covariance_matrix(x_vals,x_vals)\n",
" \n",
" return k_xx, k_xxs, k_xsx, k_xsxs"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def random_function(x):\n",
" return np.sin(x)*x + 4"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10f676cd0>"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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BbKcao08kKEEQ7F6loYHNB7IA+OHCEQ45hbstXT8xEr2nK5fyq0jLLlc7nAEj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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10fb15cd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_vals = np.linspace(0,10,50)\n",
"xs_ = np.linspace(0,10,20)\n",
"ys_ = random_function(xs_)\n",
"\n",
"xs = [1,5]\n",
"ys = random_function(xs)\n",
"\n",
"k_xx, k_xxs, k_xsx, k_xsxs = calculate_kernels(xs,x_vals)\n",
"\n",
"# mean and covariance function\n",
"f_star_bar = np.dot(np.dot(k_xsx,np.linalg.inv(k_xx)),ys)\n",
"cov_f_star = k_xsxs - np.dot(np.dot(k_xsx,np.linalg.inv(k_xx)),k_xxs)\n",
"\n",
"n_samples = len(x_vals)\n",
"values = np.repeat(0,len(x_vals)*n_samples).reshape(n_samples,len(x_vals)).astype(float)\n",
"for i in range(n_samples):\n",
" values[:,i] = mvn(f_star_bar, cov_f_star)\n",
"\n",
"fig = plt.figure(figsize=(6, 4))\n",
"std_1 = [2*np.std(i) for i in values]\n",
"#plt.fill_between(x_vals,f_star_bar - std_1,f_star_bar + std_1,color='red',alpha=0.2)\n",
"plt.scatter(xs, ys,color='darkred',s=100,alpha=0.4,label='Observed data')\n",
"plt.plot(x_vals,random_function(x_vals),linewidth=2,label='True function')\n",
"#plt.plot(x_vals,values)\n",
"plt.plot(x_vals,f_star_bar,linewidth=2,color='darkred',label='Prediction',linestyle='--')\n",
"plt.legend(loc='best')\n",
"plt.ylim(-5,15)\n",
"plt.xlim(0,10)\n",
"plt.title(\"Prediction based on 2 points - many Gaussians\",size=14)\n",
"plt.ylabel(\"output, f(x)\")\n",
"plt.xlabel(\"intput, x\")"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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jlzh8up5fvqP53SdnuH/+eO6aNZo4aeYTPvr9p2fpdbl55M4JA9b0RfDcMXUU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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10fb22fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mpl.rc('text', usetex = True)\n",
"mpl.rc('font', family = 'serif')\n",
"xs_ = np.linspace(0,10,100)\n",
"fig = plt.figure(figsize=(6, 4))\n",
"plt.plot(xs_,random_function(xs_))\n",
"plt.title(r\"Randomly chosen function: $\\bf{f(x) = 4 + sin(x)*x}$\",fontsize = 16)\n",
"plt.ylabel(\"output, f(x)\")\n",
"plt.xlabel(\"intput, x\")\n",
"plt.ylim(-5,15)\n",
"plt.xlim(0,10)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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ys7GoWgAgQmQXxEFJT9P0gqRyYC0A0HORAbxT0mJufldUIQAQIbQPWNJAKwuPjGzvVh2b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\nk9vTSDCAAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f69f090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(5, 4))\n",
"plt.scatter([1,5],random_function([1,5]),s=100)\n",
"plt.title(r\"2 points from $\\bf{f(x)}$\",fontsize = 14)\n",
"plt.ylabel(\"output, f(x)\")\n",
"plt.xlabel(\"intput, x\")\n",
"plt.ylim(-5,15)\n",
"plt.xlim(0,10)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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Xyy/y9qE22twwM9PGGZkyesHADxHXs3PNJO82G7OvXQHA3jWvdisnV1UwfVw6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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10faec6d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_vals = np.linspace(0,10,100)\n",
"xs_ = np.linspace(0,10,10)\n",
"np.random.shuffle(xs_)\n",
"ys_ = random_function(xs_)\n",
"\n",
"def animate(x):\n",
" fig.clear()\n",
" xs = xs_[:x+1]\n",
" ys = ys_[:x+1]\n",
"\n",
" k_xx, k_xxs, k_xsx, k_xsxs = calculate_kernels(xs,x_vals)\n",
"\n",
" # mean and covariance function\n",
" f_star_bar = np.dot(np.dot(k_xsx,np.linalg.inv(k_xx)),ys)\n",
" cov_f_star = k_xsxs - np.dot(np.dot(k_xsx,np.linalg.inv(k_xx)),k_xxs)\n",
"\n",
" n_samples = len(x_vals)\n",
" values = np.repeat(0,len(x_vals)*n_samples).reshape(n_samples,len(x_vals)).astype(float)\n",
" for i in range(n_samples):\n",
" values[:,i] = mvn(f_star_bar, cov_f_star)\n",
" \n",
" std_1 = [2*np.std(i) for i in values]\n",
" plt.fill_between(x_vals,f_star_bar - std_1,f_star_bar + std_1,color='red',alpha=0.2)\n",
" plt.plot(x_vals,f_star_bar,linewidth=2,color='darkred',label='Prediction',linestyle='--')\n",
" plt.scatter(xs, ys,color='darkred',s=100,alpha=0.6,label='Observed data')\n",
" plt.plot(x_vals,random_function(x_vals),linewidth=2,label='True function')\n",
" plt.legend(loc='upper left')\n",
" plt.ylim(-5,15)\n",
" plt.xlim(0,10)\n",
" plt.title(\"Approximating true function with more data\",size=16)\n",
" plt.ylabel(\"output, f(x)\")\n",
" plt.xlabel(\"intput, x\")\n",
"\n",
"fig = plt.figure(figsize=(5, 4))\n",
"anim = animation.FuncAnimation(fig, animate, frames=len(xs_), interval=1, blit=False)\n",
"#anim.save('GP.gif', writer='imagemagick', fps=2)\n",
"plt.show()"
]
}
],
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