Risk Convergence.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import sympy as smp\n",
    "\n",
    "from sklearn.base import BaseEstimator, RegressorMixin\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.ensemble import BaggingRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_problem(n, p, q, sigma, dist='identity', dist_params=None):\n",
    "    \n",
    "    if dist_params is None:\n",
    "        dist_params = {}\n",
    "        \n",
    "    if dist == 'identity':\n",
    "        Sig = np.eye(p)\n",
    "        X = np.random.randn(n, p + q)\n",
    "        X_test = np.random.randn(n, p + q)\n",
    "    elif dist == 'rho':\n",
    "        rho = dist_params['rho'] if 'rho' in dist_params else 0.5\n",
    "        Sig = (1 - rho) * np.eye(p) + rho * np.ones((p, p))\n",
    "        _, Q = np.linalg.eigh(Sig)\n",
    "        X = np.random.randn(n, p + q) @ Q.T\n",
    "        X_test = np.random.randn(n, p + q) @ Q.T\n",
    "    elif dist == 'logspace':\n",
    "        lowvar = dist_params['lowvar'] if 'lowvar' in dist_params else 1e-4\n",
    "        Q = dist_params['Q'] if 'Q' in dist_params else None\n",
    "        variances = np.random.permutation(np.logspace(0, np.log10(lowvar), p + q))\n",
    "        stds = np.sqrt(variances)\n",
    "        if Q is None:\n",
    "            Sig = np.diag(variances[:p])\n",
    "            X = np.random.randn(n, p + q) * stds[None, :]\n",
    "            X_test = np.random.randn(n, p + q) * stds[None, :]\n",
    "        else:\n",
    "            if Q == 'random':\n",
    "                A = np.random.randn(p, p)\n",
    "                _, Q = np.linalg.eigh(A + A.T)\n",
    "            Sig = Q @ (variances[:p, None] * Q.T)\n",
    "            X = (np.random.randn(n, p + q) * stds[None, :]) @ Q.T\n",
    "            X_test = (np.random.randn(n, p + q) * stds[None, :]) @ Q.T\n",
    "    \n",
    "    beta = np.random.randn(p) / np.sqrt(p)\n",
    "    y = X[:, :p] @ beta + sigma * np.random.randn(n)\n",
    "    \n",
    "    return X, y, beta, X_test, Sig\n",
    "\n",
    "\n",
    "def risk(beta, beta_hat, Sig=None, X_test=None):\n",
    "    \n",
    "    if Sig is None:\n",
    "        if X_test is None:\n",
    "            raise ValueError('Data covariance or test data must be provided.')\n",
    "        n, p = X_test.shape\n",
    "        Sig = X_test.T @ X_test / n\n",
    "    \n",
    "    beta_delta = beta - beta_hat\n",
    "    return beta_delta @ (Sig @ beta_delta)\n",
    "\n",
    "\n",
    "def ensemble_risk_ij(intersection_size, complement_intersection_size, gamma, sigma, eta=1):\n",
    "    \n",
    "    return complement_intersection_size * (1 + intersection_size * gamma / (eta - intersection_size * gamma)) + intersection_size * gamma * sigma**2 / (eta - intersection_size * gamma)\n",
    "\n",
    "\n",
    "def ensemble_risk(alpha, gamma, sigma, k=None, eta=1):\n",
    "    \n",
    "    if k is None:\n",
    "        return ensemble_risk_ij(alpha**2, (1 - alpha)**2, gamma, sigma, eta=1)\n",
    "    else:\n",
    "        return (1 - 1/k) * ensemble_risk_ij(alpha**2, (1 - alpha)**2, gamma, sigma, eta=1) + 1/k * ensemble_risk_ij(alpha, 1-alpha, gamma, sigma, eta=eta)\n",
    "\n",
    "\n",
    "def ensemble_optimal_alpha(gamma, sigma, k=None, eta=None):\n",
    "    \n",
    "    if k is None:\n",
    "    \n",
    "        a = 1\n",
    "        b = - (1 / gamma + 1 + sigma**2)\n",
    "        c = 1 / gamma\n",
    "        alpha = (-b - np.sqrt(b**2 - 4 * a * c)) / (2 * a)\n",
    "\n",
    "        return alpha\n",
    "\n",
    "    else:\n",
    "        if eta is None:\n",
    "            eta = 1\n",
    "            \n",
    "        alpha = smp.symbols('a', real=True)\n",
    "        r = ensemble_risk(alpha, gamma, sigma, k, eta)\n",
    "        drdalpha = smp.diff(r, alpha)\n",
    "        numerator, _ = smp.fraction(smp.simplify(drdalpha))\n",
    "        coeffs = smp.Poly(numerator).coeffs()\n",
    "        roots = [np.abs(r) for r in np.roots(coeffs) if np.angle(r) < 1e-2 and 0 <= np.abs(r) <= 1/gamma]\n",
    "        roots += [0, 1/gamma - 1e-6]\n",
    "        \n",
    "        return min(roots, key=lambda x: ensemble_risk(x, gamma, sigma, k, eta))\n",
    "\n",
    "\n",
    "def ridge_optimal_risk(gamma, sigma):\n",
    "    \n",
    "    dobriban = 1 / 2 * (1 + (gamma - 1) / gamma / sigma**2 + np.sqrt((1 - (gamma - 1) / gamma / sigma**2)**2 + 4 / sigma**2))\n",
    "    return (dobriban - 1) * sigma**2\n",
    "\n",
    "\n",
    "class EnsembleOLS(BaggingRegressor):\n",
    "    \n",
    "    def __init__(self, fit_intercept=False, *args, **kwargs):\n",
    "        \n",
    "        self.fit_intercept = fit_intercept\n",
    "        \n",
    "        kwargs.update({\n",
    "            'base_estimator': LinearRegression(fit_intercept=fit_intercept),\n",
    "            'bootstrap': False,\n",
    "            'bootstrap_features': False\n",
    "        })\n",
    "        super().__init__(*args, **kwargs)\n",
    "    \n",
    "    def get_coefs(self):\n",
    "        \n",
    "        p = self.n_features_\n",
    "        beta = np.zeros(p)\n",
    "        \n",
    "        for features, estimator in zip(self.estimators_features_, self.estimators_):\n",
    "            \n",
    "            beta[features] += estimator.coef_ / len(self.estimators_)\n",
    "        \n",
    "        return beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5..................................................\n",
      "1..................................................\n",
      "2..................................................\n"
     ]
    }
   ],
   "source": [
    "n = 200\n",
    "gammas = [0.5, 1, 2]\n",
    "sigma = 1\n",
    "dist = 'identity'\n",
    "dist_params = None\n",
    "n_trials = 50\n",
    "ks = np.unique(np.logspace(0, 3, dtype=int))\n",
    "\n",
    "risks_ridge = np.zeros(len(gammas))\n",
    "risks_ensemble = np.zeros((len(gammas), n_trials, len(ks)))\n",
    "risks_ensemble_eta = np.zeros((len(gammas), n_trials, len(ks)))\n",
    "\n",
    "for t, gamma in enumerate(gammas):\n",
    "    \n",
    "    print(gamma, end='')\n",
    "\n",
    "    p = int(gamma*n)\n",
    "\n",
    "    alpha = ensemble_optimal_alpha(gamma, sigma)\n",
    "    risks_ridge[t] = ridge_optimal_risk(gamma, sigma)\n",
    "    r_ensemble = ensemble_risk(alpha, gamma, sigma)\n",
    "\n",
    "    eta = min(1.0, 1.1*alpha*gamma)\n",
    "\n",
    "\n",
    "    for i in range(n_trials):\n",
    "        print('.', end='')\n",
    "\n",
    "        X, y, beta, X_test, Sig = generate_problem(n, p, 0, sigma, dist, dist_params)\n",
    "\n",
    "        ens_ols = EnsembleOLS(n_estimators=1, warm_start=True, max_samples=1.0, max_features=alpha, n_jobs=-1)\n",
    "        ens_ols_eta = EnsembleOLS(n_estimators=1, warm_start=True, max_samples=eta, max_features=alpha, n_jobs=-1)\n",
    "\n",
    "        for j, k in enumerate(ks):\n",
    "            ens_ols.n_estimators = k\n",
    "            ens_ols.fit(X, y)\n",
    "            beta_hat = ens_ols.get_coefs()\n",
    "            risks_ensemble[t, i, j] = risk(beta, beta_hat, Sig)\n",
    "\n",
    "            ens_ols_eta.n_estimators = k\n",
    "            ens_ols_eta.fit(X, y)\n",
    "            beta_hat = ens_ols_eta.get_coefs()\n",
    "            risks_ensemble_eta[t, i, j] = risk(beta, beta_hat, Sig)\n",
    "    \n",
    "    print('')\n",
    "\n",
    "np.savez('risk_versus_k.npz', gammas=gammas, ks=ks, risks_ensemble=risks_ensemble, risks_ensemble_eta=risks_ensemble_eta, risks_ridge=risks_ridge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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GEGygYYAnbev44uKkoWGNfDYIMejhx3vh2glQzdBpYp4mZtXM5A2TOZZ4DL1Rz5thb9oh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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
    "\n",
    "plt.figure(dpi=100)\n",
    "\n",
    "for t, gamma in enumerate(gammas):\n",
    "    plt.loglog(ks, risks_ensemble[t, :, :].mean(0), color=colors[t], label=r'$\\gamma=%g$' % gamma)\n",
    "    plt.plot(ks, risks_ensemble_eta[t, :, :].mean(0), ':', color=colors[t])\n",
    "    plt.plot(ks, [risks_ridge[t]] * len(ks), '--', color=colors[t])\n",
    "\n",
    "plt.legend() \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1....................................................................................................\n",
      "0.12589254117941673....................................................................................................\n",
      "0.15848931924611134....................................................................................................\n",
      "0.19952623149688797....................................................................................................\n",
      "0.251188643150958....................................................................................................\n",
      "0.31622776601683794....................................................................................................\n",
      "0.3981071705534973....................................................................................................\n",
      "0.5011872336272724....................................................................................................\n",
      "0.6309573444801934....................................................................................................\n",
      "0.7943282347242815....................................................................................................\n",
      "1.0....................................................................................................\n",
      "1.2589254117941675....................................................................................................\n",
      "1.584893192461114....................................................................................................\n",
      "1.9952623149688797....................................................................................................\n",
      "2.511886431509581....................................................................................................\n",
      "3.1622776601683795....................................................................................................\n",
      "3.981071705534973....................................................................................................\n",
      "5.011872336272725....................................................................................................\n",
      "6.309573444801933....................................................................................................\n",
      "7.943282347242818....................................................................................................\n",
      "10.0....................................................................................................\n"
     ]
    }
   ],
   "source": [
    "n = 200\n",
    "gamma = 2\n",
    "p = int(gamma*n)\n",
    "sigmas = np.logspace(-1, 1, 21)\n",
    "dist = 'identity'\n",
    "dist_params = None\n",
    "ks = [20, 100, 500]\n",
    "n_trials = 100\n",
    "\n",
    "risks_ridge = np.zeros(len(sigmas))\n",
    "risks_ensemble = np.zeros((len(sigmas), n_trials, len(ks)))\n",
    "\n",
    "for t, sigma in enumerate(sigmas):\n",
    "    \n",
    "    print(sigma, end='')\n",
    "\n",
    "    alpha = ensemble_optimal_alpha(gamma, sigma)\n",
    "    risks_ridge[t] = ridge_optimal_risk(gamma, sigma)\n",
    "\n",
    "    for i in range(n_trials):\n",
    "        \n",
    "        print('.', end='')\n",
    "\n",
    "        for j, k in enumerate(ks):\n",
    "            X, y, beta, X_test, Sig = generate_problem(n, p, 0, sigma, dist, dist_params)\n",
    "            ens_ols = EnsembleOLS(n_estimators=k, warm_start=False, max_samples=1.0, max_features=alpha, n_jobs=-1)\n",
    "            ens_ols.fit(X, y)\n",
    "            beta_hat = ens_ols.get_coefs()\n",
    "            risks_ensemble[t, i, j] = risk(beta, beta_hat, Sig)\n",
    "    \n",
    "    print('')\n",
    "\n",
    "np.savez('risk_versus_sigma.npz', sigmas=sigmas, ks=ks, risks_ensemble=risks_ensemble, risks_ridge=risks_ridge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TaNUCTYPFTmFNM9uzKjlUXMfpv9YHRQQzvn9vJgzozbhEE72DvRdWJJycg6Io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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
    "\n",
    "plt.figure(dpi=100)\n",
    "\n",
    "for j, k in enumerate(ks):\n",
    "    plt.loglog(sigmas, risks_ensemble[:, :, j].mean(1), color=colors[j], label='$k=%d$' % k)\n",
    "plt.plot(sigmas, risks_ridge, '--', color='black')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20\n",
      "0.1....................................................................................................\n",
      "0.12589254117941673....................................................................................................\n",
      "0.15848931924611134....................................................................................................\n",
      "0.19952623149688797....................................................................................................\n",
      "0.251188643150958....................................................................................................\n",
      "0.31622776601683794....................................................................................................\n",
      "0.3981071705534973....................................................................................................\n",
      "0.5011872336272724....................................................................................................\n",
      "0.6309573444801934....................................................................................................\n",
      "0.7943282347242815....................................................................................................\n",
      "1.0....................................................................................................\n",
      "1.2589254117941675....................................................................................................\n",
      "1.584893192461114....................................................................................................\n",
      "1.9952623149688797....................................................................................................\n",
      "2.511886431509581....................................................................................................\n",
      "3.1622776601683795....................................................................................................\n",
      "3.981071705534973....................................................................................................\n",
      "5.011872336272725....................................................................................................\n",
      "6.309573444801933....................................................................................................\n",
      "7.943282347242818....................................................................................................\n",
      "10.0....................................................................................................\n",
      "100\n",
      "0.1....................................................................................................\n",
      "0.12589254117941673....................................................................................................\n",
      "0.15848931924611134....................................................................................................\n",
      "0.19952623149688797....................................................................................................\n",
      "0.251188643150958....................................................................................................\n",
      "0.31622776601683794....................................................................................................\n",
      "0.3981071705534973....................................................................................................\n",
      "0.5011872336272724....................................................................................................\n",
      "0.6309573444801934....................................................................................................\n",
      "0.7943282347242815....................................................................................................\n",
      "1.0....................................................................................................\n",
      "1.2589254117941675....................................................................................................\n",
      "1.584893192461114....................................................................................................\n",
      "1.9952623149688797....................................................................................................\n",
      "2.511886431509581....................................................................................................\n",
      "3.1622776601683795....................................................................................................\n",
      "3.981071705534973....................................................................................................\n",
      "5.011872336272725....................................................................................................\n",
      "6.309573444801933....................................................................................................\n",
      "7.943282347242818....................................................................................................\n",
      "10.0....................................................................................................\n",
      "500\n",
      "0.1....................................................................................................\n",
      "0.12589254117941673....................................................................................................\n",
      "0.15848931924611134....................................................................................................\n",
      "0.19952623149688797....................................................................................................\n",
      "0.251188643150958....................................................................................................\n",
      "0.31622776601683794....................................................................................................\n",
      "0.3981071705534973....................................................................................................\n",
      "0.5011872336272724....................................................................................................\n",
      "0.6309573444801934....................................................................................................\n",
      "0.7943282347242815....................................................................................................\n",
      "1.0....................................................................................................\n",
      "1.2589254117941675....................................................................................................\n",
      "1.584893192461114....................................................................................................\n",
      "1.9952623149688797....................................................................................................\n",
      "2.511886431509581....................................................................................................\n",
      "3.1622776601683795....................................................................................................\n",
      "3.981071705534973....................................................................................................\n",
      "5.011872336272725....................................................................................................\n",
      "6.309573444801933....................................................................................................\n",
      "7.943282347242818....................................................................................................\n",
      "10.0....................................................................................................\n"
     ]
    }
   ],
   "source": [
    "n = 200\n",
    "gamma = 2\n",
    "p = int(gamma*n)\n",
    "sigmas = np.logspace(-1, 1, 21)\n",
    "dist = 'identity'\n",
    "dist_params = None\n",
    "ks = [20, 100, 500]\n",
    "n_trials = 100\n",
    "\n",
    "risks_ridge = np.zeros(len(sigmas))\n",
    "risks_ensemble = np.zeros((len(sigmas), n_trials, len(ks)))\n",
    "\n",
    "for j, k in enumerate(ks):\n",
    "    print(k)\n",
    "    \n",
    "    for t, sigma in enumerate(sigmas):\n",
    "\n",
    "        print(sigma, end='')\n",
    "\n",
    "        alpha = ensemble_optimal_alpha(gamma, sigma, k)\n",
    "        if alpha*p < 1:\n",
    "            alpha = 1\n",
    "        risks_ridge[t] = ridge_optimal_risk(gamma, sigma)\n",
    "\n",
    "        for i in range(n_trials):\n",
    "\n",
    "            print('.', end='')\n",
    "\n",
    "            X, y, beta, X_test, Sig = generate_problem(n, p, 0, sigma, dist, dist_params)\n",
    "\n",
    "            ens_ols = EnsembleOLS(n_estimators=k, warm_start=False, max_samples=1.0, max_features=alpha, n_jobs=-1)\n",
    "\n",
    "            ens_ols.fit(X, y)\n",
    "            beta_hat = ens_ols.get_coefs()\n",
    "            risks_ensemble[t, i, j] = risk(beta, beta_hat, Sig)\n",
    "\n",
    "        print('')\n",
    "\n",
    "np.savez('risk_versus_sigma_optimal_alpha.npz', sigmas=sigmas, ks=ks, risks_ensemble=risks_ensemble, risks_ridge=risks_ridge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Nb8T5zPOlp3k7ejPithGMvm003k6yErO4OSScCCHETRKVmkfoQnMwaenpxPuj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\nYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
    "\n",
    "plt.figure(dpi=100)\n",
    "\n",
    "for j, k in enumerate(ks):\n",
    "    plt.loglog(sigmas, risks_ensemble[:, :, j].mean(1), color=colors[j], label='$k=%d$' % k)\n",
    "plt.plot(sigmas, risks_ridge, '--', color='black')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}