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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy import linalg\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Generate a dataset of 10k obs and 30 vars\n",
"n_obs = 10000\n",
"n_vars = 30\n",
"\n",
"# some of which are dependent of the others with the following added noises\n",
"noises_std = [1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9, 1e-10, 0, 0, 0]\n",
"\n",
"n_dep_vars = len(noises_std)\n",
"n_indep_vars = n_vars - n_dep_vars\n",
"\n",
"# We generate a random collinearity structure\n",
"dependence = np.random.normal(size=n_dep_vars*n_indep_vars).reshape((n_indep_vars, n_dep_vars))\n",
"\n",
"X = np.zeros(shape=(n_obs, n_vars))\n",
"\n",
"# Independent variables are N(0,1)\n",
"X[:, :n_indep_vars] = np.random.multivariate_normal(np.zeros(n_indep_vars), np.eye(n_indep_vars), size=n_obs)\n",
"\n",
"# Dependent variables are linear combinations of indep vars + N(0, noise_var)\n",
"X[:, -n_dep_vars:] = X[:, :n_indep_vars].dot(dependence) \\\n",
" + np.random.multivariate_normal(np.zeros(n_dep_vars), np.diag(noises_std)**2, size=n_obs)\n",
"\n",
"beta = np.random.normal(0, 1, size=n_indep_vars)\n",
"Y = X[:, :n_indep_vars].dot(beta) + np.random.normal(size=n_obs)\n",
"\n",
"U, S, Vh = np.linalg.svd(X)\n",
"V = Vh.T"
]
},
{
"cell_type": "code",
"execution_count": 258,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"def perm_to_mat(P):\n",
" Pi = np.zeros(shape=(len(P),len(P)))\n",
" \n",
" for i in range(len(P)):\n",
" Pi[P[i], i] = 1\n",
"\n",
" return Pi \n",
"\n",
"def inf(M):\n",
" S = np.linalg.svd(M, compute_uv=False)\n",
" return S[-1]\n",
"\n",
"def doit(X, Y, S, U, V, tol):\n",
" r = np.where(S > tol)[0][-1] + 1\n",
" \n",
" # Compute best rank-subset\n",
" delta = S[r-1]\n",
" eps = S[r]\n",
"\n",
" Veps12 = V[:, :r]\n",
"\n",
" R, perm = linalg.qr(Veps12.T, pivoting=True, mode='r')\n",
" P = perm_to_mat(perm)\n",
"\n",
" Xp = X.dot(P)\n",
" Vp = P.T.dot(V)\n",
" \n",
" AW = Xp[:, :r]\n",
" gammap = inf(AW)\n",
" \n",
" # Compute residuals\n",
" xw = np.linalg.solve(a=AW.T.dot(AW), b=AW.T.dot(Y))\n",
" rw = Y - AW.dot(xw)\n",
" \n",
" # Compute residuals for Ueps\n",
" Veps = V[:, :r]\n",
" Seps = np.diag(S[:r])\n",
" Ueps = U[:, :r]\n",
" \n",
" xeps = Veps.dot(np.linalg.inv(Seps)).dot(Ueps.T).dot(Y)\n",
" reps = Y - Ueps.dot(Seps).dot(Veps.T).dot(xeps)\n",
" \n",
" return (r, eps, 1.0/np.prod(S[:r])**2, eps / gammap, np.linalg.norm(reps), np.linalg.norm(reps - rw))\n",
"\n",
"tols = np.logspace(np.log10(S[-3]), np.log10(S[1]))\n",
"\n",
"res = np.zeros(shape=(len(tols), 6))\n",
"for i,tol in enumerate(tols):\n",
" res_i = doit(X, Y, S, U, V, tol)\n",
" for j in range(len(res_i)):\n",
" res[i, j] = res_i[j]\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 259,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f8c7cc9e050>"
]
},
"execution_count": 259,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"num_tol = np.sqrt(S.max() * n_obs * np.finfo(S.dtype).eps)\n",
"\n",
"plt.figure(figsize=(15,10))\n",
"plt.rc(\"font\", size=20)\n",
"\n",
"plt.scatter(list(range(len(S))), np.log10(S), label=r\"singular values\")\n",
"plt.plot([0, len(S)-1], [np.log10(num_tol), np.log10(num_tol)], c=\"red\", label=r\"$tol_{opt}$\")\n",
"plt.xlabel(\"i\")\n",
"plt.ylabel(r\"$\\sigma_i$\")\n",
"plt.title(r\"Singular values of $X$\")\n",
"plt.grid()\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 260,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f8c6d3d8310>"
]
},
"execution_count": 260,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"num_tol = np.sqrt(S.max() * n_obs * np.finfo(S.dtype).eps)\n",
"\n",
"plt.figure(figsize=(15,10))\n",
"plt.rc(\"font\", size=20)\n",
"\n",
"r_tol = res[np.argmin(np.abs(num_tol - tols)), 0]\n",
"\n",
"rs = range(1,n_vars)\n",
"dets = np.array([1/np.prod(S[:int(r)])**2 for r in xs])\n",
"\n",
"plt.plot(rs, dets, label=r\"lower bound on $[\\mathrm{det\\ }X_r^\\top X_r]^{-1}$\")\n",
"plt.plot([r_tol, r_tol], [dets.min(), dets.max()], c=\"red\", label=r\"rank for $tol = tol_{opt}$\")\n",
"\n",
"plt.title(r\"Investigating quantity: $[\\mathrm{det\\ } X^\\top X ]^{-1}$\")\n",
"plt.xlabel(\"rank\")\n",
"plt.yscale(\"log\")\n",
"plt.grid(b=True, which='both', linestyle='--')\n",
"plt.legend()\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 261,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f8c85998d50>"
]
},
"execution_count": 261,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"num_tol = np.sqrt(S.max() * n_obs * np.finfo(S.dtype).eps)\n",
"\n",
"plt.figure(figsize=(15,10))\n",
"plt.rc(\"font\", size=20)\n",
"\n",
"plt.loglog(tols, 1/res[:, 1], label=r\"$\\epsilon_{tol}^{-1}$\")\n",
"plt.loglog([num_tol, num_tol], [1/res[:, 1].max(), 1/res[:, 1].min()], c=\"red\", label=r\"$tol = tol_{opt}$\")\n",
"\n",
"plt.title(r\"For residual improvement $\\Delta$ over $r_{\\epsilon}$: $|| \\beta ||_2 \\geq \\Delta \\cdot \\epsilon_{tol}^{-1}$\")\n",
"plt.xlabel(r\"$\\log_{10}(tol)$\")\n",
"plt.grid(b=True, which='both', linestyle='--')\n",
"plt.legend()\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 265,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f8c4861a610>"
]
},
"execution_count": 265,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"num_tol = np.sqrt(S.max() * n_obs * np.finfo(S.dtype).eps)\n",
"\n",
"plt.figure(figsize=(15,10))\n",
"plt.rc(\"font\", size=20)\n",
"\n",
"bnorm = np.linalg.norm(Y)\n",
"plt.loglog(tols, res[:,3]*bnorm, label=r\"$|| y ||_2 * c_{tol}$\")\n",
"plt.loglog(tols, res[:,5], label=r\"$|| r_\\epsilon - r_W ||_2$\")\n",
"plt.loglog([num_tol, num_tol], [res[:, 5].min(), bnorm*res[:, 3].max()], c=\"red\", label=r\"$tol_{opt}$\")\n",
"\n",
"plt.title(r\"Quantifying the residual bias: $|| r_\\epsilon - r_W ||_2 \\leq || y ||_2 * c_{tol}$\")\n",
"plt.ylabel(r\"$\\log_{10}(error)$\")\n",
"plt.xlabel(r\"$\\log_{10}(tol)$\")\n",
"plt.grid(b=True, which='both', linestyle='--')\n",
"plt.legend(loc=\"upper left\")\n",
" "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.15"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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