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@jcboyd
Created June 4, 2024 07:47
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NumPy implementation of Gaussian processes
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{
"cells": [
{
"cell_type": "markdown",
"id": "c19f8259",
"metadata": {},
"source": [
"# Noise-free Gaussian processes"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "01facc86",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x1151e5210>"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 500x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"mu = np.array([1, 0])\n",
"cov = np.eye(2)\n",
"\n",
"def sample_mvn(mu, cov, n_samples=50):\n",
"\n",
" d = mu.shape[0]\n",
"\n",
" z = np.random.randn(d, n_samples)\n",
" L = np.linalg.cholesky(cov)\n",
"\n",
" return mu + L.dot(z).T\n",
"\n",
"fig, ax = plt.subplots(figsize=(5, 5))\n",
"ax.axis('equal')\n",
"\n",
"s = sample_mvn(mu, cov, n_samples=100)\n",
"\n",
"plt.scatter(s[:, 0], s[:, 1])"
]
},
{
"cell_type": "markdown",
"id": "fa962b93",
"metadata": {},
"source": [
"## Sample prior"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "0f6a27fb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x10e11fb10>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# https://github.com/probml/pmtk3/blob/dfe84aabf65d4e5133a62ac1f4722bf3834a3327/toolbox/BasicModels/gauss/gaussSample.m\n",
"# https://github.com/probml/pmtk3/blob/dfe84aabf65d4e5133a62ac1f4722bf3834a3327/demos/gprDemoNoiseFree.m\n",
"\n",
"n_samples = 100\n",
"\n",
"def k(x, y, L=1, sig=1):\n",
" return sig * np.exp(-(x - y[:, None]) ** 2 / (2 * L ** 2))\n",
"\n",
"def k_eps(x):\n",
" return 1e-5 * np.eye(x.shape[0])\n",
"\n",
"def mu(x, r=0):\n",
" return r * x ** 2\n",
"\n",
"xs = np.linspace(-5, 5, num=n_samples)\n",
"\n",
"mu_r = 0\n",
"\n",
"K = k(xs, xs) + k_eps(xs)\n",
"M = mu(xs, r=mu_r)\n",
"\n",
"fs = sample_mvn(M, K, n_samples=3)\n",
"\n",
"fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10, 5))\n",
"\n",
"ax1.plot(xs, fs[0])\n",
"ax1.plot(xs, fs[1])\n",
"ax1.plot(xs, fs[2])\n",
"ax1.set_xlim([xs.min(), xs.max()])\n",
"\n",
"asp = np.diff(ax1.get_xlim()) / np.diff(ax1.get_ylim())\n",
"ax1.set_aspect(asp)\n",
"\n",
"ax2.imshow(K)"
]
},
{
"cell_type": "markdown",
"id": "632b25a2",
"metadata": {},
"source": [
"## Sample posterior"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1e373722",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x1153f5890>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_tr = np.array([-4, -3, -2, -1, 4])\n",
"\n",
"f = lambda x : np.sin(x)\n",
"f_tr = f(x_tr)\n",
"\n",
"def sample_posteriors(x_tr, xs, k, n_samples=1):\n",
"\n",
" x_all = np.hstack([x_tr, xs])\n",
" K_all = k(x_all, x_all) + k_eps(x_all)\n",
"\n",
" K = K_all[:x_tr.shape[0], :x_tr.shape[0]]\n",
" Ks = K_all[:x_tr.shape[0], x_tr.shape[0]:]\n",
" Kss = K_all[x_tr.shape[0]:, x_tr.shape[0]:]\n",
"\n",
" Kinv = np.linalg.inv(K)\n",
"\n",
" M_tr = mu(x_tr, r=mu_r)\n",
"\n",
" M_p = M + Ks.T.dot(Kinv).dot(f_tr - M_tr)\n",
" K_p = Kss - Ks.T.dot(Kinv).dot(Ks) + k_eps(xs)\n",
"\n",
" fs = sample_mvn(M_p, K_p, n_samples=n_samples)\n",
"\n",
" return fs, M_p, K_p\n",
"\n",
"L = 1\n",
"\n",
"fs, M_p, K_p = sample_posteriors(x_tr, xs, lambda x, y : k(x, y, L=L))\n",
"\n",
"fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10, 5))\n",
"\n",
"ax1.scatter(x_tr, f_tr, color='black', label='Tr. data')\n",
"\n",
"for i, s in enumerate(fs):\n",
" ax1.plot(xs, s, label='$L = %0.1f$' % L)\n",
" \n",
"ax1.plot(xs, M_p, color='red', linestyle='--', label='$\\mu(x)$')\n",
"\n",
"ax1.set_xlim([xs.min(), xs.max()])\n",
"\n",
"ax1.fill_between(y1=M_p - 2 * np.sqrt(np.diag(K_p)),\n",
" y2=M_p + 2 * np.sqrt(np.diag(K_p)), x=xs,\n",
" color='gray', alpha=0.25, edgecolor='black', label='95% CI')\n",
"\n",
"asp = np.diff(ax1.get_xlim()) / np.diff(ax1.get_ylim())\n",
"ax1.set_aspect(asp)\n",
"ax1.set_xlabel('$x$')\n",
"ax1.set_ylabel('$f(x)$')\n",
"\n",
"ax1.legend(fontsize='small', loc='upper right')\n",
"\n",
"ax2.imshow(K_p)"
]
}
],
"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": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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