unbounded_treatment-paper-figures.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from off_pol_eval_functions import * \n",
    "from matplotlib import cm\n",
    "from scipy import interpolate\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "n = 5000\n",
    "m = 10\n",
    "d= 1\n",
    "t_lo = -0.5\n",
    "t_hi = 1.3\n",
    "test_val = 0.4\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation & configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x230.4 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/az/anaconda2/lib/python2.7/site-packages/sklearn/model_selection/_split.py:2053: FutureWarning: You should specify a value for 'cv' instead of relying on the default value. The default value will change from 3 to 5 in version 0.22.\n",
      "  warnings.warn(CV_WARNING, FutureWarning)\n",
      "/Users/az/anaconda2/lib/python2.7/site-packages/sklearn/model_selection/_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'float' object has no attribute 'log1p'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m          Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-746a060d4bf1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     51\u001b[0m \u001b[0msub_params\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'spline'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msplined_f_tck\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 53\u001b[0;31m \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbandwidth_selection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m200\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0msub_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     54\u001b[0m \u001b[0;32mprint\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/Box Sync/clean-code/continuous-policy-learning/off_pol_eval_functions.pyc\u001b[0m in \u001b[0;36mbandwidth_selection\u001b[0;34m(n_samp, h_sub, **params)\u001b[0m\n\u001b[1;32m    984\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    985\u001b[0m     \u001b[0mcond_dens_hess\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mHessian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscores_cond_f_y_given_tau_x_caller\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 986\u001b[0;31m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mest_h\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mh_sub\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mregr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcond_dens_hess\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0msamp_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    987\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/Box Sync/clean-code/continuous-policy-learning/off_pol_eval_functions.pyc\u001b[0m in \u001b[0;36mest_h\u001b[0;34m(h_sub, regr, hess, **samp_params)\u001b[0m\n\u001b[1;32m    899\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mh_sub\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    900\u001b[0m         \u001b[0;32mprint\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 901\u001b[0;31m         \u001b[0mbias\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mbias_integrand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msamp_params\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'tau'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msamp_params\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'x_samp'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhess\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymin\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymax\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    902\u001b[0m     \u001b[0mmean_bias_sqd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbias\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mh_sub\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    903\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mexp_second_moment\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmean_bias_sqd\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0msamp_params\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'n'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/scipy/integrate/quadpack.pyc\u001b[0m in \u001b[0;36mquad\u001b[0;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)\u001b[0m\n\u001b[1;32m    339\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mweight\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    340\u001b[0m         retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,\n\u001b[0;32m--> 341\u001b[0;31m                        points)\n\u001b[0m\u001b[1;32m    342\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    343\u001b[0m         retval = _quad_weight(func, a, b, args, full_output, epsabs, epsrel,\n",
      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/scipy/integrate/quadpack.pyc\u001b[0m in \u001b[0;36m_quad\u001b[0;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points)\u001b[0m\n\u001b[1;32m    446\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mpoints\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    447\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0minfbounds\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 448\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_qagse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    449\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    450\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_qagie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbound\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0minfbounds\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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      "\u001b[0;32m/Users/az/Box Sync/clean-code/continuous-policy-learning/off_pol_eval_functions.pyc\u001b[0m in \u001b[0;36mbias_integrand\u001b[0;34m(y, tau, x, hessian)\u001b[0m\n\u001b[1;32m    874\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbias_integrand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhessian\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    875\u001b[0m     \u001b[0mx0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 876\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mhessian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m0.5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    877\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    878\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mempirical_exp_second_moment\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mregr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/numdifftools/core.pyc\u001b[0m in \u001b[0;36m_derivative_nonzero_order\u001b[0;34m(self, xi, args, kwds)\u001b[0m\n\u001b[1;32m    256\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_derivative_nonzero_order\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    257\u001b[0m         \u001b[0mdiff\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_functions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 258\u001b[0;31m         \u001b[0msteps\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep_ratio\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_steps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    259\u001b[0m         \u001b[0mfxi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_eval_first\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    260\u001b[0m         \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mdiff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msteps\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/numdifftools/core.pyc\u001b[0m in \u001b[0;36m_get_steps\u001b[0;34m(self, xi)\u001b[0m\n\u001b[1;32m    329\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_get_steps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    330\u001b[0m         \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_method_order\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 331\u001b[0;31m         \u001b[0mstep_gen\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_generator_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    332\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mstep\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstep_gen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep_gen\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_ratio\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    333\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/numdifftools/step_generators.pyc\u001b[0m in \u001b[0;36mstep_generator_function\u001b[0;34m(self, x, method, n, order)\u001b[0m\n\u001b[1;32m    267\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mstep_generator_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'forward'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    268\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_state\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_STATE\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 269\u001b[0;31m         \u001b[0mbase_step\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep_ratio\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbase_step\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_nom\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_ratio\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    270\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0muse_exact_steps\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    271\u001b[0m             \u001b[0mbase_step\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_exact\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbase_step\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/numdifftools/step_generators.pyc\u001b[0m in \u001b[0;36mstep_nom\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    258\u001b[0m         \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_state\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    259\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_step_nom\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 260\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnominal_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    261\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfull\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfill_value\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_step_nom\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    262\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/az/anaconda2/lib/python2.7/site-packages/numdifftools/step_generators.pyc\u001b[0m in \u001b[0;36mnominal_step\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 25\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog1p\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'float' object has no attribute 'log1p'"
     ]
    }
   ],
   "source": [
    "def generate_data_moving_parabolas(m,n, d, t_lo, t_hi): \n",
    "    xs = np.array(np.random.uniform(0,1,(n*m,d)))\n",
    "    if t_lo < -10: \n",
    "        t_lo = -10\n",
    "    if t_hi > 10: \n",
    "        t_hi = 10\n",
    "    Ts = np.array(np.random.uniform(t_lo,t_hi, (n*m,d))) \n",
    "    Z = np.concatenate([xs,Ts], axis = 1)\n",
    "    F = np.zeros([m*n,1])\n",
    "    a = 2\n",
    "    b = 7\n",
    "    for i in np.arange(m*n): \n",
    "        F[i] = 2*pow(np.abs(xs[i] - Ts[i]),1.5)\n",
    "#         F[i] = max(a*(np.abs(xs[i] - Ts[i])),b*(np.abs(xs[i] - Ts[i]))) + xs[i]\n",
    "# Ensure outcomes are positive\n",
    "    if min(F) < 0:\n",
    "        F = F + abs(min(F))  \n",
    "    Y = F + 0.2*np.random.randn(m*n,1)\n",
    "    return { 'y': Y, 'z': Z, 'f': F , 'x': xs}\n",
    "\n",
    "def oracle_evaluation(**params): \n",
    "    # does oracle evaluation include randomness? \n",
    "    X = params['x_samp']; tau = params['tau']\n",
    "    return 2*pow(np.abs(X - tau),1.5) + 0.2*np.random.randn(params['n'],1)\n",
    "\n",
    "data = generate_data_moving_parabolas(m,n, d, t_lo, t_hi)\n",
    "sub_params = { 'n': n, 'y': data['y'],'f': data['f'], 'x': data['x'],'d': d, 'T': data['z'][:,d], 'z': data['z'], 'm': m, 'h': 0.001, 'Q': unif_Q , 't_lo': t_lo ,'t_hi': t_hi  }\n",
    "\n",
    "# output = open('data_exp' + str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + '.pkl', 'wb')\n",
    "# pickle.dump(sub_params, output)\n",
    "# output.close()\n",
    "\n",
    "sub_params['Q'] = unif_Q \n",
    "sub_params['sampling'] = \"uniform\"\n",
    "plot_surface(**sub_params)\n",
    "\n",
    "# Set Kernel Function (and integral) \n",
    "sub_params['kernel_func'] = epanechnikov_kernel\n",
    "sub_params['kernel_int_func'] = epanechnikov_int\n",
    "sub_params['threshold'] = 0.01\n",
    "# Set Oracle Function Structure (known or interpolated? )\n",
    "sub_params['oracle_func'] = oracle_evaluation\n",
    "#Set data generation scheme (grid of values or uniformly sampled?)\n",
    "sub_params['data_gen'] = \"uniform\"\n",
    "\n",
    "# sub_params['oracle_func'] =  evaluate_oracle_interpolated_outcomes\n",
    "spl_x = sub_params['z'][:,0]\n",
    "spl_t = sub_params['z'][:,1]\n",
    "# f is positive\n",
    "splined_f_tck = interpolate.bisplrep(spl_x,spl_t, sub_params['f'])\n",
    "sub_params['spline'] = splined_f_tck\n",
    "\n",
    "h = bandwidth_selection(200, 10, **sub_params)\n",
    "print h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_dataset(m,n,d,t_lo,t_hi, sampling, Q ): \n",
    "    data = generate_data_moving_parabolas(m,n, d, t_lo, t_hi)\n",
    "    sub_params = { 'n': n, 'y': data['y'],'f': data['f'], 'x': data['x'],'d': d, 'T': data['z'][:,d], 'z': data['z'], 'm': m, 'h': 0.001, 'Q': unif_Q , 't_lo': t_lo ,'t_hi': t_hi  }\n",
    "    sub_params['x_samp'] = data['x']\n",
    "    sub_params['T_samp'] = sub_params['T']\n",
    "    data['y_samp'] = data['y']\n",
    "    sub_params['Q'] = Q \n",
    "    sub_params['sampling'] = sampling\n",
    "    # Scaling ought to be different for the unbounded case (closer to 0.5)\n",
    "    sub_params['h'] = 0.1\n",
    "    # Set Kernel Function (and integral) \n",
    "    sub_params['kernel_func'] = epanechnikov_kernel\n",
    "    sub_params['kernel_int_func'] = epanechnikov_int\n",
    "    sub_params['threshold'] = 0.01\n",
    "    sub_params['n_bins'] = 10 \n",
    "    # Set Oracle Function Structure (known or interpolated? )\n",
    "    sub_params['oracle_func'] = oracle_evaluation\n",
    "    #Set data generation scheme (grid of values or uniformly sampled?)\n",
    "    sub_params['data_gen'] = \"uniform\"\n",
    "    return sub_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing constant off-policy evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def off_policy_evaluation(**params):\n",
    "    \"\"\"\n",
    "    Takes in a choice of kernel and dictionary of parameters and data required for evaluation\n",
    "    tau is a vector of treatment values (assumed given)\n",
    "    If y_samp, T_samp is present, use that instead. \n",
    "    \"\"\"\n",
    "    THRESH = 0.015\n",
    "    y_out = params['y']; x = params['x']; h = params['h'];Q = params['Q']; n = params['n']; t_lo = params['t_lo'];  t_hi = params['t_hi']\n",
    "    kernel = params['kernel_func'];kernel_int =  params['kernel_int_func']\n",
    "    if ('y_samp' in params.keys()):\n",
    "        y_out = params['y_samp']\n",
    "    if ('T_samp' in params.keys()): \n",
    "        T = params['T_samp']\n",
    "    else: \n",
    "        T = params['T']\n",
    "    if ('x_samp' in params.keys()):\n",
    "        x = params['x_samp']\n",
    "    loss = 0\n",
    "    tau = params['tau']\n",
    "    clip_tau = np.clip(tau, t_lo, t_hi)\n",
    "    Qs = np.zeros(n)\n",
    "    for i in np.arange(n): \n",
    "        Q_i = Q(x[i], T[i], t_lo, t_hi)\n",
    "        if (abs(clip_tau[i] - t_lo) <= h):\n",
    "            alpha = kernel_int((t_lo-clip_tau[i])/h, 1)\n",
    "            if alpha < 0.5: \n",
    "                print alpha\n",
    "        elif (abs(clip_tau[i] - t_hi) <= h):\n",
    "            alpha = kernel_int(-1,  (t_hi - clip_tau[i])/h )\n",
    "            if alpha < 0.5: \n",
    "                print alpha\n",
    "        else:\n",
    "            alpha = 1\n",
    "        Qs[i] = kernel( (clip_tau[i] - T[i])/h )*h/Q_i\n",
    "        loss += kernel( (clip_tau[i] - T[i])/h )*1.0 * y_out[i]/max(Q_i,THRESH) * 1.0/alpha\n",
    "    norm_sum = sum(Qs)    \n",
    "    return loss/(norm_sum*1.0*h*n)\n",
    "\n",
    "n_sub = 200\n",
    "samp_params = evaluate_subsample( n_sub, evaluation = False, cross_val = False, **sub_params )\n",
    "samp_params['tau'] = 0.5*np.ones(n)\n",
    "off_policy_evaluation(**samp_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Consistency of policy evaluation wrt n "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "n_trials = 50\n",
    "n_treatments = 10\n",
    "n_spacing = 20\n",
    "n_0 = 5\n",
    "sub_params['n_bins'] = 10\n",
    "n_max = 300\n",
    "sub_params['h'] = 0.1\n",
    "sub_params['sampling'] = \"normal\"\n",
    "sub_params['Q'] = norm_Q\n",
    "\n",
    "# sampling = \"uniform\"\n",
    "# Q = unif_Q\n",
    "\n",
    "def comp_policy(t, x): \n",
    "#     return t*x\n",
    "    if x < t: \n",
    "        return 0\n",
    "    if x > t: \n",
    "        return 0.3\n",
    "\n",
    "sub_params['threshold'] = 0.1\n",
    "def direct_method(**subsamples_pm): \n",
    "    X_train = np.hstack([subsamples_pm['x_samp'], subsamples_pm['T_samp']])\n",
    "    lin_regressor = LinearRegression()\n",
    "    poly = PolynomialFeatures(3)\n",
    "    X_transform = poly.fit_transform(X_train)\n",
    "    lin_regressor.fit(X_transform,subsamples_pm['y_samp']) \n",
    "    # get the predictions\n",
    "    X_test =np.hstack([subsamples_pm['x_samp'], subsamples_pm['tau']]) # evaluate predictor at tau and average \n",
    "    y_preds = lin_regressor.predict(poly.fit_transform(X_test))\n",
    "    return np.mean(y_preds)\n",
    "\n",
    "def direct_method(**subsamples_pm): \n",
    "    X_train = np.hstack([subsamples_pm['x_samp'], subsamples_pm['T_samp']])\n",
    "    lin_regressor = LinearRegression()\n",
    "    poly = PolynomialFeatures(3)\n",
    "    X_transform = poly.fit_transform(X_train)\n",
    "    lin_regressor.fit(X_transform,subsamples_pm['y_samp']) \n",
    "    # get the predictions\n",
    "    X_test =np.hstack([subsamples_pm['x_samp'], subsamples_pm['tau']]) # evaluate predictor at tau and average \n",
    "    y_preds = lin_regressor.predict(poly.fit_transform(X_test))\n",
    "    return np.mean(y_preds)\n",
    "\n",
    "def direct_method_rf(**subsamples_pm): \n",
    "    X_train = np.hstack([subsamples_pm['x_samp'], subsamples_pm['T_samp']])\n",
    "    clf = RandomForestRegressor(n_estimators=10)\n",
    "    clf = clf.fit(X_train,y=subsamples_pm['y_samp'])\n",
    "    # get the predictions\n",
    "    X_test =np.hstack([subsamples_pm['x_samp'], subsamples_pm['tau']]) # evaluate predictor at tau and average \n",
    "    y_preds = clf.predict( X_test )\n",
    "    return np.mean(y_preds)\n",
    "\n",
    "\n",
    "def off_pol_eval_comp_test(n_max, n_trials, n_treatments, n_spacing, n_0, t, **sub_params):\n",
    "    '''\n",
    "    Test for a single value of t \n",
    "    '''\n",
    "    n = sub_params['n']; m = sub_params['m']\n",
    "    off_pol_evals = np.zeros([n_spacing, n_trials])\n",
    "    oracle_evals = np.zeros([n_spacing, n_trials])\n",
    "    discrete_off_pol_evals = np.zeros([n_spacing, n_trials])\n",
    "    dm_evals = np.zeros([n_spacing, n_trials]); dm_rf_evals = np.zeros([n_spacing, n_trials])\n",
    "    oracle_func = sub_params['oracle_func']\n",
    "    splined_f_tck = sub_params['spline']\n",
    "    h_orig = sub_params['h']\n",
    "    for i, n_sub in enumerate(np.linspace(n_0, n_max, n_spacing)): \n",
    "        # sub_params['h'] = h_orig * (np.power(n_sub,0.2))/np.power(n_0,0.2)\n",
    "        n_rnd = int(np.floor(n_sub))\n",
    "        print \"testing with n = \" + str(n_rnd)\n",
    "        for k in np.arange(n_trials):\n",
    "            # Use evaluate subsample because that samples appropriately \n",
    "            subsamples_pm = evaluate_subsample( n_rnd, evaluation = False, cross_val = False, **sub_params )\n",
    "#             subsamples_pm = generate_dataset(n_rnd,1,d,t_lo,t_hi, sampling, Q )\n",
    "            subsamples_pm['tau'] = t*subsamples_pm['x_samp']\n",
    "#             subsamples_pm['tau'] = subsamples_pm['x_samp']\n",
    "            #np.asarray( [ comp_policy(t,x) for x in subsamples_pm['x_samp'] ] ).flatten()\n",
    "            oracle_evals[i, k] = np.mean(oracle_func(**subsamples_pm))\n",
    "            # oracle_evals[t_ind, i, k] = np.mean(evaluate_oracle_interpolated_outcomes(splined_f_tck, m,n_rnd, subsamples_pm['f'], t_lo, t_hi, subsamples_pm['tau'], subsamples_pm['x_samp']))\n",
    "            off_pol_evals[i, k] = off_policy_evaluation(**subsamples_pm)\n",
    "            discrete_off_pol_evals[i, k] = off_pol_disc_evaluation(discretize_tau_policy , **subsamples_pm)\n",
    "            dm_evals[i,k] = direct_method(**subsamples_pm)\n",
    "            dm_rf_evals[i,k] = direct_method_rf(**subsamples_pm)\n",
    "            \n",
    "    off_pol_evals.dump( str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'off_pol_vals_for_consistency-norm.np')\n",
    "    oracle_evals.dump(str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'off_pol_oracles_for_consistency-norm.np')\n",
    "    discrete_off_pol_evals.dump(str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'discrete_pol_evals_for_consistency-norm.np')\n",
    "    return [oracle_evals, off_pol_evals, discrete_off_pol_evals, dm_evals, dm_rf_evals]\n",
    "\n",
    "t_lo = -0.5\n",
    "t_hi = 1.3\n",
    "[oracle_evals, off_pol_evals, off_pol_disc_evals, dm_evals, dm_rf_evals] = off_pol_eval_comp_test(n_max, n_trials, n_treatments, n_spacing, n_0, 1, **sub_params)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def off_pol_estimator(**params): \n",
    "\n",
    "    THRESH = params['threshold']\n",
    "    y_out = params['y']; x = params['x']; h = params['h'];Q = params['Q']; n = params['n']; t_lo = params['t_lo'];  t_hi = params['t_hi']\n",
    "    kernel = params['kernel_func'];kernel_int =  params['kernel_int_func']\n",
    "    if ('y_samp' in params.keys()):\n",
    "        y_out = params['y_samp']\n",
    "    if ('T_samp' in params.keys()): \n",
    "        T = params['T_samp']\n",
    "    else: \n",
    "        T = params['T']\n",
    "    if ('x_samp' in params.keys()):\n",
    "        x = params['x_samp']\n",
    "\n",
    "    BMI_IND = params.get('BMI_IND') # propensity score for warfarin data evaluations \n",
    "    if (params.get('DATA_TYPE') == 'warfarin'): \n",
    "        x = params['x'][:,BMI_IND]\n",
    "\n",
    "    loss = 0\n",
    "    tau = params['tau']\n",
    "    clip_tau = np.clip(tau, t_lo, t_hi)\n",
    "    Qs = np.zeros(n)\n",
    "    for i in np.arange(n): \n",
    "        Q_i = Q(x[i], T[i], t_lo, t_hi)\n",
    "        if (abs(clip_tau[i] - t_lo) <= h):\n",
    "            alpha = kernel_int((t_lo-clip_tau[i])/h, 1)\n",
    "        elif (abs(clip_tau[i] - t_hi) <= h):\n",
    "            alpha = kernel_int(-1,  (t_hi - clip_tau[i])/h )\n",
    "        else:\n",
    "            alpha = 1\n",
    "        Qs[i] = (1.0/h)*kernel( (clip_tau[i] - T[i])/h )/max(Q_i,THRESH)\n",
    "        loss += kernel( (clip_tau[i] - T[i])/h )*1.0 * y_out[i]/max(Q_i,THRESH) * 1.0/alpha\n",
    "    norm_sum = np.mean(np.maximum(Qs,THRESH*np.ones(n)))\n",
    "    print loss \n",
    "    print norm_sum \n",
    "    print loss/(norm_sum*1.0*h*n)\n",
    "    return [loss, norm_sum]\n",
    "\n",
    "subsamples_pm = evaluate_subsample( 15, evaluation = False, cross_val = False, **sub_params )\n",
    "subsamples_pm['tau'] = subsamples_pm['x_samp']\n",
    "off_pol_estimator(**subsamples_pm)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_off_pol_vals = np.nanmean(off_pol_evals, axis = 1)\n",
    "mean_oracle_vals = np.mean(oracle_evals,axis=1)\n",
    "sds_off_pol = np.std(off_pol_evals, axis = 1)\n",
    "sds_oracle = np.std(oracle_evals, axis = 1)\n",
    "mean_off_pol_disc_evals = np.mean(off_pol_disc_evals,axis=1)\n",
    "sds_off_pol_disc = np.std(off_pol_disc_evals, axis = 1)\n",
    "mean_off_pol_dm_vals = np.mean(dm_evals,axis=1)\n",
    "sds_off_pol_dm = np.std(dm_evals, axis = 1)\n",
    "\n",
    "mean_off_pol_dm_rf_vals = np.mean(dm_rf_evals,axis=1)\n",
    "sds_off_pol_dm_rf = np.std(dm_rf_evals, axis = 1)\n",
    "\n",
    "ns = np.linspace(n_0, n_max, n_spacing)\n",
    "\n",
    "plt.figure(figsize=(6,2.5))\n",
    "ax = plt.subplot(111)\n",
    "plt.style.use('seaborn-notebook')\n",
    "\n",
    "error_1 = 1.96*sds_off_pol/np.sqrt(n_trials)\n",
    "error_2 = 1.96*sds_oracle/np.sqrt(n_trials)\n",
    "error_3 = 1.96*sds_off_pol_disc/np.sqrt(n_trials)\n",
    "error_4 = 1.96*sds_off_pol_dm/np.sqrt(n_trials)\n",
    "error_5 = 1.96*sds_off_pol_dm_rf/np.sqrt(n_trials)\n",
    "\n",
    "\n",
    "# ax = fig.add_subplot(1,1,1) \n",
    "ax.tick_params(labeltop='off', labelright='off')\n",
    "\n",
    "plt.fill_between(ns, mean_oracle_vals-error_2, mean_oracle_vals+error_2, alpha=0.4, edgecolor='blue', facecolor='blue')\n",
    "plt.scatter( ns , mean_oracle_vals, c = \"blue\", label=\"true outcomes\",marker='+',s=35)\n",
    "plt.scatter(ns, mean_off_pol_disc_evals, c = \"green\", label=\"discretized OPE\",s=35)\n",
    "plt.fill_between(ns, mean_off_pol_disc_evals-error_3, mean_off_pol_disc_evals+error_3, alpha=0.4, edgecolor='g', facecolor='g')\n",
    "plt.scatter(ns, mean_off_pol_vals[:], c = \"red\", label=\"continuous OPE\",marker='v',s=35)\n",
    "plt.fill_between(ns, mean_off_pol_vals-error_1, mean_off_pol_vals+error_1, alpha=0.5, edgecolor='#CC4F1B', facecolor='#FF9848')\n",
    "plt.fill_between(ns, mean_off_pol_dm_vals-error_4, mean_off_pol_dm_vals+error_4, alpha=0.35, edgecolor='purple', facecolor='purple')\n",
    "plt.scatter(ns, mean_off_pol_dm_vals[:], c = \"purple\", label=\"DM Poly\",marker='*',s=35)\n",
    "plt.fill_between(ns, mean_off_pol_dm_rf_vals-error_5, mean_off_pol_dm_rf_vals+error_5, alpha=0.35, edgecolor='brown', facecolor='brown')\n",
    "plt.scatter(ns, mean_off_pol_dm_rf_vals[:], c = \"brown\", label=\"DM RF\",marker='o',s=35)\n",
    "\n",
    "plt.title(\"\")\n",
    "plt.ylabel(\"estimated policy values\")\n",
    "plt.xlabel(\"number of samples in sampled dataset\")\n",
    "\n",
    "plt.legend(prop={'size':8}, )\n",
    "max_y = .12\n",
    "# plt.yticks(np.arange(0, max_y+0.1, 0.3))\n",
    "\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['top'].set_visible(False)\n",
    "# Only show ticks on the left and bottom spines\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "\n",
    "plt.ylim((-0.02,.2))\n",
    "# plt.xlim((10,300))\n",
    "plt.yticks(np.arange(0, max_y+0.02, 0.04))\n",
    "ax.legend(bbox_to_anchor=(1, 1.3),ncol=2)\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print mean_off_pol_dm_rf_vals[-1]\n",
    "\n",
    "print mean_off_pol_vals[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test for multiple values of beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_lo = -0.5\n",
    "t_hi = 1.3\n",
    "beta_0 = -0.5\n",
    "beta_hi = 1.3\n",
    "[full_oracle_evals, full_off_pol_evals, full_off_pol_disc_evals] = off_pol_eval_linear_test( n_max, beta_0, beta_hi, n_trials, n_treatments, n_spacing, n_0, **sub_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot full surface with errors "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_off_pol_evals(off_pol_evals, oracle_evals, off_pol_disc_evals, n_0, n_max, n_trials, n_treatments, n_spacing, t_lo, t_hi, \"treatment values\", \"Constant Policy Evaluations vs true counterfactual policy evaluations (truncated y)\", truncate_y = 1  )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing of a nontrivial policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_off_pol_evals(off_pol_evals, oracle_evals, off_pol_disc_evals, n_0, n_max, n_trials, n_treatments, n_spacing, t_lo, t_hi, \"treatment values\", \"Constant Policy Evaluations vs true counterfactual policy evaluations (truncated y)\", truncate_y = 3  )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "n_trials = 10\n",
    "n_treatments = 20\n",
    "n_spacing = 3\n",
    "n_0 = 100\n",
    "sub_params['n_bins'] = 10\n",
    "n_max = 500\n",
    "sub_params['h'] = 0.1\n",
    "sub_params['sampling'] = \"normal\"\n",
    "import sys\n",
    "\n",
    "t_lo = -0.5\n",
    "t_hi = 1.5\n",
    "[oracle_evals, off_pol_evals, off_pol_disc_evals] = off_pol_eval_cons_test(n_max, n_trials, n_treatments, n_spacing, n_0, t_lo, t_hi, check_alpha = True, **sub_params)\n",
    "plot_off_pol_evals(off_pol_evals, oracle_evals, off_pol_disc_evals, n_0, n_max, n_trials, n_treatments, n_spacing, t_lo, t_hi, \"treatment values\", \"Constant Policy Evaluations vs true counterfactual policy evaluations (truncated y)\", truncate_y = 3  )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def off_pol_disc_evaluation(policy, **params):\n",
    "    THRESH = params['threshold']\n",
    "    y_out = params['y']; x = params['x_samp']; h = params['h']; Q = params['Q']; n = params['n']; t_lo = params['t_lo']; t_hi = params['t_hi']\n",
    "    n_bins = params['n_bins']\n",
    "    if ('y_samp' in params.keys()):\n",
    "        y_out = params['y_samp'].flatten()\n",
    "    if ('T_samp' in params.keys()):\n",
    "        T = params['T_samp'].flatten()\n",
    "    else:\n",
    "        T = params['T'].flatten()\n",
    "\n",
    "    BMI_IND = params.get('BMI_IND') # propensity score for warfarin data evaluations \n",
    "    if (params.get('DATA_TYPE') == 'warfarin'): \n",
    "        x = params['x'][:,BMI_IND]\n",
    "\n",
    "    t_lo = min(T)\n",
    "    t_hi = max(T)\n",
    "    bin_width = t_hi-t_lo\n",
    "    bins = np.linspace(t_lo, t_hi, n_bins)\n",
    "    T_binned = np.digitize(T, bins, right = True).flatten()\n",
    "    bin_means = [T[T_binned == i].mean() for i in range(1, len(bins))]\n",
    "\n",
    "    loss = 0\n",
    "    tau_vec = policy(**params).flatten()\n",
    "    #! FIXME need to establish whether policy returns discrete bins or means\n",
    "    treatment_overlap = np.where(np.equal(tau_vec.flatten(), T_binned))[0]\n",
    "    n_overlap = len(treatment_overlap)\n",
    "    Qs = np.zeros(n_overlap)\n",
    "    i=0\n",
    "    for ind in treatment_overlap:\n",
    "        Q_i = Q(x[ind], bin_means[T_binned[ind]-1], t_lo, t_hi) * bin_width*1.0/n_bins # BUG FIX: this is going to have to be integrated against \n",
    "        Qs[i] = 1.0/max(Q_i,THRESH)\n",
    "        \n",
    "        loss += y_out[ind]/max(Q_i,THRESH)\n",
    "        i+=1 \n",
    "    \n",
    "    norm_sum = np.mean(np.maximum(Qs,THRESH*np.ones(n_overlap)))\n",
    "    if n_overlap == 0:\n",
    "        print \"no overlap\"\n",
    "        return 0\n",
    "    print norm_sum\n",
    "    return loss/(1.0*n*norm_sum)\n",
    "\n",
    "\n",
    "subsamples_pm = evaluate_subsample( 100, evaluation = False, cross_val = False, **sub_params )\n",
    "subsamples_pm['tau'] = 0.4*subsamples_pm['x_samp'] \n",
    "\n",
    "print off_pol_disc_evaluation(discretize_tau_policy , **subsamples_pm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Off-policy evaluation for linear treatment policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def off_pol_eval_linear_test( n_max, beta_0, beta_hi, n_trials, n_treatments, n_spacing, n_0, **sub_params):\n",
    "    '''\n",
    "    '''\n",
    "    treatment_space = np.linspace(beta_0, beta_hi, n_treatments)\n",
    "    off_pol_evals = np.zeros([n_treatments, n_spacing, n_trials])\n",
    "    oracle_evals = np.zeros([n_treatments, n_spacing, n_trials])\n",
    "    discrete_off_pol_evals = np.zeros([n_treatments, n_spacing, n_trials])\n",
    "    dm_evals = np.zeros([n_treatments, n_spacing, n_trials])\n",
    "    dm_rf_evals = np.zeros([n_treatments, n_spacing, n_trials])\n",
    "    t_lo = sub_params['t_lo']; t_hi = sub_params['t_hi']; spl_x = sub_params['z'][:,0]; spl_t = sub_params['z'][:,1]\n",
    "    # f is positive\n",
    "    splined_f_tck = interpolate.bisplrep(spl_x,spl_t, sub_params['f'])\n",
    "    sub_params['spline'] = splined_f_tck\n",
    "    oracle_func = sub_params['oracle_func']\n",
    "    n = sub_params['n']; m = sub_params['m']; h_orig = sub_params['h']\n",
    "    for i, n_sub in enumerate(np.linspace(n_0, n_max, n_spacing)): \n",
    "        n_rnd = int(np.floor(n_sub))\n",
    "        \n",
    "        print \"testing n = \" + str(n_rnd)\n",
    "        for k in np.arange(n_trials):\n",
    "            for beta_ind, beta in enumerate(treatment_space):\n",
    "                subsamples_pm = evaluate_subsample( n_rnd, evaluation = False, cross_val = False, **sub_params )\n",
    "                tau = np.clip(np.dot( subsamples_pm['x_samp'], beta ) , t_lo, t_hi)\n",
    "                subsamples_pm['h'] = h_orig * (np.power(n_sub,0.2))/np.power(n,0.2)\n",
    "                subsamples_pm['tau'] = tau\n",
    "                oracle_evals[beta_ind, i, k] = np.mean(oracle_func(**subsamples_pm))\n",
    "                # oracle_evals[beta_ind, i, k] = np.mean(evaluate_oracle_interpolated_outcomes(splined_f_tck,m,n_rnd, subsamples_pm['f'], beta_0, beta_hi, tau, subsamples_pm['x_samp']))\n",
    "                # off_pol_evals[beta_ind, i, k] = off_policy_evaluation(**subsamples_pm)\n",
    "                off_pol_evals[beta_ind, i, k] = off_policy_evaluation(**subsamples_pm)\n",
    "                discrete_off_pol_evals[beta_ind, i, k] = off_pol_disc_evaluation(discretize_tau_policy , **subsamples_pm)\n",
    "                dm_evals[beta_ind, i,k] = direct_method(**subsamples_pm)\n",
    "                dm_rf_evals[beta_ind, i,k] = direct_method_rf(**subsamples_pm)\n",
    "#     off_pol_evals.dump( str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'off_pol_linear_vals.np')\n",
    "#     oracle_evals.dump(str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'off_pol_linear_oracles.np')\n",
    "    return [oracle_evals, off_pol_evals, discrete_off_pol_evals, dm_evals, dm_rf_evals]\n",
    "\n",
    "def plot_off_pol_evals_gen(off_pol_evals, oracle_evals, off_pol_disc_evals, dm_evals, dm_rf_evals, n_0, n, n_trials, n_treatments, n_spacing, t_lo, t_hi, x_label, title_stem, y_min = False, y_max = False):\n",
    "    mean_off_pol_vals = np.mean(off_pol_evals, axis = 2)\n",
    "    mean_oracle_vals = np.mean(oracle_evals,axis=2)\n",
    "    sds_off_pol = np.std(off_pol_evals, axis = 2); sds_oracle = np.std(oracle_evals, axis = 2)\n",
    "    mean_off_pol_disc_evals = np.mean(off_pol_disc_evals,axis=2); sds_off_pol_disc = np.std(off_pol_disc_evals, axis = 2)\n",
    "    mean_off_pol_dm_vals = np.mean(dm_evals,axis=2); sds_off_pol_dm = np.std(dm_evals, axis = 2)\n",
    "    \n",
    "    mean_off_pol_dm_rf_vals = np.mean(dm_rf_evals,axis=2)\n",
    "    sds_off_pol_dm_rf = np.std(dm_rf_evals, axis = 2); ts = np.linspace(t_lo, t_hi, n_treatments); ns = np.linspace(n_0, n, n_spacing)\n",
    "    \n",
    "    for i in np.arange(n_spacing):\n",
    "        plt.style.use('seaborn-notebook')\n",
    "        plt.figure(figsize=(7,2.75))\n",
    "        ax = plt.subplot(111)\n",
    "        error_1 = 1.96*sds_off_pol[:,i]/np.sqrt(n_trials)\n",
    "        error_2 = 1.96*sds_oracle[:,i]/np.sqrt(n_trials)\n",
    "        error_3 = 1.96*sds_off_pol_disc[:,i]/np.sqrt(n_trials)\n",
    "        error_4 = 1.96*sds_off_pol_dm[:,i]/np.sqrt(n_trials)\n",
    "        error_5 = 1.96*sds_off_pol_dm_rf[:,i]/np.sqrt(n_trials)\n",
    "        \n",
    "        plt.fill_between(ts, mean_oracle_vals[:,i]-error_2, mean_oracle_vals[:,i]+error_2, edgecolor='blue', facecolor='blue',alpha=0.3)\n",
    "        plt.plot(ts, mean_oracle_vals[:,i], c = \"blue\", markersize = 10 ,label=\"oracle values\",alpha=0.4)\n",
    "        \n",
    "        plt.plot(ts, mean_off_pol_disc_evals[:,i], c = \"green\", marker='s', label='naively discretized OPE', markersize = 7)\n",
    "        plt.fill_between(ts, mean_off_pol_disc_evals[:,i]-error_3, mean_off_pol_disc_evals[:,i]+error_3, alpha=0.4, edgecolor='g', facecolor='g')\n",
    "        \n",
    "        plt.fill_between(ts, mean_off_pol_vals[:,i]-error_1, mean_off_pol_vals[:,i]+error_1, alpha=0.5, edgecolor='#CC4F1B', facecolor='#FF9848')\n",
    "        plt.plot(ts, mean_off_pol_vals[:,i], c = \"red\", marker='v', label='continuous OPE', markersize = 10 )\n",
    "        \n",
    "        plt.fill_between(ts, mean_off_pol_dm_vals[:,i]-error_4, mean_off_pol_dm_vals[:,i]+error_4, alpha=0.35, edgecolor='purple', facecolor='purple')\n",
    "        plt.plot(ts, mean_off_pol_dm_vals[:,i], c = \"purple\", marker='*', label='DM poly', markersize = 10)\n",
    "        \n",
    "        plt.fill_between(ts, mean_off_pol_dm_rf_vals[:,i]-error_5, mean_off_pol_dm_rf_vals[:,i]+error_5, alpha=0.35, edgecolor='brown', facecolor='brown')\n",
    "        plt.plot(ts, mean_off_pol_dm_rf_vals[:,i], c = \"brown\", marker='o', label='DM RF', markersize = 8)\n",
    "    #     plt.ylim( (0, 10) )\n",
    "        print ns[i]\n",
    "#         plt.title(title_stem+ \" with n = \" + str(ns[i]))\n",
    "        plt.ylabel(\"Regret compared to true policy value\")\n",
    "        plt.xlabel(x_label)\n",
    "#         if y_min!=False: \n",
    "#         plt.ylim(y_min,y_max)\n",
    "#         plt.yticks(np.arange(y_min, y_max, 0.1))\n",
    "        plt.xlim(0,1.3)\n",
    "        \n",
    "        ax.spines['right'].set_visible(False)\n",
    "        ax.spines['top'].set_visible(False)\n",
    "        # Only show ticks on the left and bottom spines\n",
    "        ax.yaxis.set_ticks_position('left')\n",
    "        ax.xaxis.set_ticks_position('bottom')\n",
    "        \n",
    "        plt.legend(prop={'size':8})\n",
    "        ax.legend(bbox_to_anchor=(.3, .95),ncol=2)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "beta_hi = t_hi/max(sub_params['x'])\n",
    "n_trials = 50\n",
    "sub_params['n_bins'] = 10\n",
    "n_treatments = 20\n",
    "n_spacing = 3\n",
    "n_0 = 100\n",
    "n_max = 500\n",
    "sub_params['h'] = 0.1\n",
    "\n",
    "sub_params['Q'] = norm_Q\n",
    "sub_params['sampling']='normal'\n",
    "\n",
    "\n",
    "[lin_oracle_evals, lin_off_pol_evals, off_pol_disc_evals, dm_evals, dm_rf_evals] = off_pol_eval_linear_test( n_max, 0, beta_hi, n_trials, n_treatments, n_spacing, n_0, check_alpha = True, **sub_params)\n",
    "lin_off_pol_evals.dump( str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'off_pol_linear_vals_normal.np')\n",
    "oracle_evals.dump(str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'off_pol_linear_oracles_normal.np')\n",
    "off_pol_disc_evals.dump(str(datetime.datetime.now().strftime(\"%Y-%m-%d_%H-%M\")) + 'disc_off_pol_linear_normal.np')\n",
    "\n",
    "plot_off_pol_evals_gen(lin_off_pol_evals, lin_oracle_evals, off_pol_disc_evals, dm_evals, dm_rf_evals, n_0, n_max, n_trials, n_treatments, n_spacing, 0, beta_hi, \"beta values\", \"Linear Policy Evaluations vs true counterfactual policy evaluations\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_off_pol_evals_gen(lin_off_pol_evals, lin_oracle_evals, off_pol_disc_evals, dm_evals, dm_rf_evals, n_0, n_max, n_trials, n_treatments, n_spacing, 0, beta_hi, \"beta values\", \"Linear Policy Evaluations vs true counterfactual policy evaluations\", y_min=-0.3, y_max =0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## plots of regret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print np.mean(np.abs(lin_off_pol_evals-lin_oracle_evals)[:,1,:])\n",
    "print np.mean(np.abs(lin_oracle_evals-lin_oracle_evals)[:,1,:])\n",
    "print np.mean(np.abs(off_pol_disc_evals-lin_oracle_evals)[:,1,:])\n",
    "print np.mean(np.abs(dm_rf_evals-lin_oracle_evals)[:,1,:])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_off_pol_evals_gen(lin_off_pol_evals-lin_oracle_evals, lin_oracle_evals-lin_oracle_evals, off_pol_disc_evals-lin_oracle_evals, dm_evals-lin_oracle_evals, dm_rf_evals-lin_oracle_evals, n_0, n_max, n_trials, n_treatments, n_spacing, 0, beta_hi, \"beta values\", \"Linear Policy Evaluations vs true counterfactual policy evaluations\", y_min=-0.3, y_max =0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "sub_params['Q'] = unif_Q\n",
    "sub_params['sampling']='uniform'\n",
    "\n",
    "[lin_oracle_evals, lin_off_pol_evals, off_pol_disc_evals] = off_pol_eval_linear_test( n_max, 0, beta_hi, n_trials, n_treatments, n_spacing, n_0, check_alpha = True, **sub_params)\n",
    "plot_off_pol_evals(lin_off_pol_evals, lin_oracle_evals, off_pol_disc_evals, n_0, n_max, n_trials, n_treatments, n_spacing, 0, beta_hi, \"beta values\", \"Linear Policy Evaluations vs true counterfactual policy evaluations\")\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_off_pol_evals(off_pol_evals, oracle_evals, off_pol_disc_evals, n_0, n, n_trials, n_treatments, n_spacing, t_lo, t_hi, x_label, title_stem, truncate_y = False):\n",
    "    mean_off_pol_vals = np.mean(off_pol_evals, axis = 2)\n",
    "    mean_oracle_vals = np.mean(oracle_evals,axis=2)\n",
    "    sds_off_pol = np.std(off_pol_evals, axis = 2)\n",
    "    sds_oracle = np.std(oracle_evals, axis = 2)\n",
    "    mean_off_pol_disc_evals = np.mean(off_pol_disc_evals,axis=2)\n",
    "    sds_off_pol_disc = np.std(off_pol_disc_evals, axis = 2)\n",
    "\n",
    "    ts = np.linspace(t_lo, t_hi, n_treatments)\n",
    "\n",
    "    ns = np.linspace(n_0, n, n_spacing)\n",
    "    for i in np.arange(n_spacing):\n",
    "        plt.figure(i+1)\n",
    "        plt.style.use('seaborn-notebook')\n",
    "        plt.figure(figsize=(4.5,2.2))\n",
    "        error_1 = 1.96*sds_off_pol[:,i]/np.sqrt(n_trials)\n",
    "        error_2 = 1.96*sds_oracle[:,i]/np.sqrt(n_trials)\n",
    "        error_3 = 1.96*sds_off_pol_disc[:,i]/np.sqrt(n_trials)\n",
    "\n",
    "        \n",
    "        plt.fill_between(ts, mean_oracle_vals[:,i]-error_2, mean_oracle_vals[:,i]+error_2, edgecolor='blue', facecolor='blue',alpha=0.1)\n",
    "        plt.plot(ts, mean_oracle_vals[:,i], c = \"blue\", marker='s', markersize = 1 ,label=\"oracle values\")\n",
    "        \n",
    "        plt.scatter(ts, mean_off_pol_disc_evals[:,i], c = \"green\", label='naively discretized OPE')\n",
    "        plt.fill_between(ts, mean_off_pol_disc_evals[:,i]-error_3, mean_off_pol_disc_evals[:,i]+error_3, alpha=0.4, edgecolor='g', facecolor='g')\n",
    "        \n",
    "        plt.fill_between(ts, mean_off_pol_vals[:,i]-error_1, mean_off_pol_vals[:,i]+error_1, alpha=0.5, edgecolor='#CC4F1B', facecolor='#FF9848')\n",
    "        plt.scatter(ts, mean_off_pol_vals[:,i], c = \"red\", marker='v', label='continuous OPE')\n",
    "    #     plt.ylim( (0, 10) )\n",
    "        print ns[i]\n",
    "#         plt.title(title_stem+ \" with n = \" + str(ns[i]))\n",
    "        plt.ylabel(\"outcome Y\")\n",
    "        plt.xlabel(x_label)\n",
    "        if truncate_y: \n",
    "            plt.ylim((0,truncate_y))\n",
    "        plt.yticks(np.arange(0, 1+0.1, 0.3))\n",
    "        plt.xlim(0,1.3)\n",
    "#         plt.legend(prop={'size':8})\n",
    "        plt.show()\n",
    "\n",
    "plot_off_pol_evals(lin_off_pol_evals, lin_oracle_evals, off_pol_disc_evals, n_0, n_max, n_trials, n_treatments, n_spacing, 0, beta_hi, \"beta values\", \"Linear Policy Evaluations vs true counterfactual policy evaluations\", truncate_y=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# print np.abs(np.mean(off_pol_evals,axis = 2)  - np.mean(oracle_evals, axis =2 ))\n",
    "print \"Percent errors: \"\n",
    "print (np.abs(np.mean(off_pol_evals,axis = 2)  - np.mean(oracle_evals, axis =2 ))) / np.mean(oracle_evals, axis =2 ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## testing out of sample convergence "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sub_params['h']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sub_params['Q'] = norm_Q\n",
    "sub_params['sampling']='normal'\n",
    "sub_params['h'] = 0.1\n",
    "def off_pol_opt_test(n_max, n_trials, n_spacing, n_0, t_lo_sub,t_hi_sub, **sub_params):\n",
    "    \n",
    "    n = sub_params['n']; m = sub_params['m']; t_lo = t_lo_sub; t_hi = t_hi_sub\n",
    "    d = sub_params['d']\n",
    "    n_space = np.linspace(n_0, n_max, n_spacing)\n",
    "    best_beta = np.zeros([len(n_space),n_trials])\n",
    "    best_oracle_beta = np.zeros([len(n_space),n_trials])\n",
    "    OOS_OPE = np.zeros([len(n_space),n_trials])\n",
    "    OOS_oracle = np.zeros([len(n_space),n_trials])\n",
    "    # discrete_off_pol_evals = np.zeros([n_treatments, n_spacing, n_trials])\n",
    "    oracle_func = sub_params['oracle_func']\n",
    "    h_orig = 0.1\n",
    "    n_restarts = 5\n",
    "    TEST_N = 250\n",
    "    TEST_SET = evaluate_subsample( 250, evaluation = False, cross_val = False, **sub_params )\n",
    "    def eval_oracle_tau_evaluation(beta, *args):\n",
    "        params = dict(args[0])\n",
    "        t_lo = params['t_lo']\n",
    "        t_hi = params['t_hi']\n",
    "        tau_candidate = beta*params['x_samp']\n",
    "        #!FIXME graceful handling of loss function of y_i\n",
    "        params['tau'] = tau_candidate\n",
    "        return np.mean(oracle_func(**params)) \n",
    "    \n",
    "    for i, n_sub in enumerate(np.linspace(n_0, n_max, n_spacing)): \n",
    "        # sub_params['h'] = h_orig * (np.power(n_sub,0.2))/np.power(n_0,0.2)\n",
    "        n_rnd = int(np.floor(n_sub))\n",
    "        sub_params['h'] = h_orig * (np.power(n_0,0.2))/np.power(n_sub,0.2)\n",
    "        print \"testing with n = \" + str(n_rnd)\n",
    "        for k in np.arange(n_trials):\n",
    "            subsamples_pm = evaluate_subsample( n_rnd, evaluation = False, cross_val = False, **sub_params )\n",
    "            samp_params = subsamples_pm\n",
    "            # oracle_evals[t_ind, i, k] = np.mean(evaluate_oracle_interpolated_outcomes(splined_f_tck, m,n_rnd, subsamples_pm['f'], t_lo, t_hi, subsamples_pm['tau'], subsamples_pm['x_samp']))\n",
    "            ### Compute best betas with random restarts \n",
    "            oracle_betas = np.zeros([n_restarts, d]);eval_vals = np.zeros([n_restarts, d]);emp_betas = np.zeros([n_restarts, d]);emp_eval_vals = np.zeros([n_restarts, d])\n",
    "            for i_restart in np.arange(n_restarts):\n",
    "                beta_d = np.random.uniform() \n",
    "                res = minimize(lin_off_policy_loss_evaluation, x0 = beta_d, jac = off_pol_epan_lin_grad, bounds = ((t_lo/max(samp_params['x_samp']), t_hi/max(samp_params['x_samp']) ),) , args=samp_params.items() )\n",
    "                emp_betas[i_restart] = res.x; emp_eval_vals[i_restart] = res.fun\n",
    "\n",
    "                oracle_res = minimize(eval_oracle_tau_evaluation, x0 = beta_d, bounds = ((0, 1.0/np.mean(samp_params['x']) ),) , args=samp_params.items() )\n",
    "                oracle_betas[i_restart] = oracle_res.x; eval_vals[i_restart] = oracle_res.fun  \n",
    "\n",
    "                # get best beta value from random restarts\n",
    "            best_ind = np.argmin(emp_eval_vals)\n",
    "            best_beta[i,k] =  emp_betas[best_ind,:]\n",
    "            \n",
    "            best_oracle_ind = np.argmin(eval_vals)\n",
    "            best_oracle_beta[i,k] =  oracle_betas[best_oracle_ind,:]\n",
    "            TEST_SET['tau'] = best_beta[i,k] * TEST_SET['x_samp']\n",
    "            OOS_OPE[i,k] = off_policy_evaluation(**TEST_SET)\n",
    "            OOS_oracle[i,k] = np.mean(oracle_func(**TEST_SET))\n",
    "\n",
    "    return [best_beta, best_oracle_beta, OOS_OPE, OOS_oracle]\n",
    "n_spacing = 10\n",
    "n_trials = 10\n",
    "t_lo_sub = min(sub_params['T'])\n",
    "t_hi_sub = max(sub_params['T'])\n",
    "\n",
    "[best_beta, best_oracle_beta, OOS_OPE, OOS_oracle] = off_pol_opt_test(300, n_trials, n_spacing, 10, t_lo_sub,t_hi_sub, **sub_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_beta = pickle.load( open('BEST-BETA-h-0-1.p','rb'))\n",
    "best_oracle_beta = pickle.load( open('BEST-ORACLE-BETA-h-0-1.p','rb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "uniform_params = deepcopy(sub_params)\n",
    "uniform_params['sampling'] = 'uniform'\n",
    "uniform_params['Q'] = unif_Q\n",
    "\n",
    "\n",
    "TEST_SET = evaluate_subsample( 300, evaluation = False, cross_val = False, **uniform_params )\n",
    "OOS_OPE_unif = np.zeros([n_spacing,n_trials])\n",
    "h_orig = .1\n",
    "TEST_SET['h'] = h_orig\n",
    "for i in range(n_spacing): \n",
    "    TEST_SET['h'] = h_orig * (np.power(n_0,0.2))/np.power(ns[i],0.2)\n",
    "    for k in range(n_trials): \n",
    "        \n",
    "#         print TEST_SET['h']\n",
    "        TEST_SET['tau'] = best_beta[i,k] * TEST_SET['x_samp']\n",
    "#         print off_pol_estimator(**TEST_SET)\n",
    "        OOS_OPE_unif[i,k] = oracle_evaluation(**TEST_SET)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print TEST_SET['h']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_0 = 10; n_max = 300\n",
    "h_orig = TEST_SET['h']\n",
    "for i, n_sub in enumerate(np.linspace(n_0, n_max, n_spacing)): \n",
    "    print h_orig * (np.power(n_sub,0.2))/np.power(n_0,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn-notebook')\n",
    "plt.figure(figsize=(4.5,2.5))\n",
    "plt.ylim(-0.05,.4)\n",
    "ns = np.linspace(10,300,n_spacing)\n",
    "mean_OOS = np.mean(OOS_OPE_unif,axis=1)\n",
    "mean_OOS_oracle = np.mean(OOS_oracle,axis=1)\n",
    "\n",
    "plt.xlim(10,300)\n",
    "sds_off_pol = np.std(OOS_OPE_unif, axis = 1)\n",
    "sds_oracle = np.std(OOS_oracle, axis = 1)\n",
    "error = 1.96*sds_off_pol/np.sqrt(n_trials)\n",
    "error_oracle = 1.96*sds_oracle/np.sqrt(n_trials)\n",
    "\n",
    "plt.fill_between(ns, mean_OOS_oracle-error_oracle, mean_OOS_oracle+error_oracle, alpha=0.5,edgecolor='blue', facecolor='blue')\n",
    "plt.fill_between(ns, mean_OOS-error, mean_OOS+error, alpha=0.5, edgecolor='#CC4F1B', facecolor='#FF9848')\n",
    "plt.scatter(ns,mean_OOS_oracle,c='b')\n",
    "plt.scatter(ns, mean_OOS,c='r')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "TEST_SET['oracle_func']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimizing for best linear treatment policy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
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   "source": [
    "''' Test policy optimization routine '''\n",
    "from scipy.optimize import minimize\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "\n",
    "h = sub_params['h']\n",
    "\n",
    "n_lo = 125 \n",
    "n_hi = 600\n",
    "for n_ind, n_sub in enumerate(np.linspace(n_lo, n_hi)): \n",
    "    # Out of sample testing \n",
    "    trainind = np.random.choice(range(n_sub),size =  round(0.8*n_sub),replace = False)\n",
    "    test_mask = np.ones(n, dtype=bool)\n",
    "    test_mask[trainind] = False\n",
    "    \n",
    "    samp_params = evaluate_subsample( n_sub, evaluation = False, cross_val = False, **sub_params )\n",
    "    test_T = samp_params['T_samp'][test_mask], test_x = samp_params['x_samp'][test_mask], test_y = samp_params['y_samp'][test_mask]\n",
    "    samp_params['T_samp'] = samp_params['T_samp'][trainind]; samp_params['x_samp']=samp_params['x_samp'][trainind], samp_params['y_samp']=samp_params['y_samp'][trainind]\n",
    "    # samp_params['T'] = sub_params['z'][:,1]\n",
    "    # Center losses\n",
    "    samp_params['mean'] = np.mean(samp_params['y_samp'])\n",
    "    samp_params['y'] = samp_params['y'] - np.mean(samp_params['y'])\n",
    "    samp_params['f'] = samp_params['f'] - np.mean(samp_params['f'])\n",
    "    samp_params['y_samp'] = samp_params['y_samp'] - np.mean(samp_params['y_samp'])\n",
    "    samp_params['f_samp'] = samp_params['f_samp'] - np.mean(samp_params['f_samp'])\n",
    "    n_restarts = 2\n",
    "    def eval_oracle_tau_evaluation(beta, *args):\n",
    "        params = dict(args[0])\n",
    "        t_lo = params['t_lo']\n",
    "        t_hi = params['t_hi']\n",
    "        tau_candidate = beta*params['x_samp']\n",
    "        #!FIXME graceful handling of loss function of y_i\n",
    "        params['tau'] = tau_candidate\n",
    "        return np.mean(oracle_evaluation(**params)) \n",
    "\n",
    "    oracle_betas = np.zeros([n_restarts, d])\n",
    "    eval_vals = np.zeros([n_restarts, d])\n",
    "    emp_betas = np.zeros([n_restarts, d])\n",
    "    emp_eval_vals = np.zeros([n_restarts, d])\n",
    "    for i in np.arange(n_restarts):\n",
    "        [res, oracle_res, spline_f_tck] = pol_opt(verbose = False, oracle_eval = eval_oracle_tau_evaluation, **samp_params)\n",
    "        print 'empirical beta' \n",
    "    #     print res\n",
    "        print res.x \n",
    "        print 'empirical est value'\n",
    "        print res.fun\n",
    "        emp_betas[i] = res.x\n",
    "        emp_eval_vals[i] = res.fun\n",
    "\n",
    "        print 'beta' \n",
    "        print oracle_res.x\n",
    "        oracle_betas[i] = oracle_res.x\n",
    "        print 'oracle best linear treatment policy value'\n",
    "        print oracle_res.fun\n",
    "        eval_vals[i] = oracle_res.fun    \n",
    "    # get best beta value from random restarts\n",
    "    best_ind = np.argmin(emp_eval_vals)\n",
    "    best_beta =  emp_betas[best_ind]\n",
    "    \n",
    "    best_oracle_ind = np.argmin(eval_vals)\n",
    "    best_oracle_beta =  emp_betas[oracle_betas]\n",
    "    \n",
    "    # get out-of-sample error \n",
    "    \n",
    "\n",
    "    params_neg_y = samp_params\n",
    "    params_neg_y['spline'] = spline_f_tck\n",
    "    grid_vals = 20\n",
    "    vals = np.zeros(grid_vals)\n",
    "    beta_max = 1.5\n",
    "    print beta_max\n",
    "    for ind,b in enumerate(np.linspace(0.02,beta_max,grid_vals)): \n",
    "        params_neg_y['tau'] = b*params_neg_y['x_samp']\n",
    "        val = oracle_evaluation(**params_neg_y)\n",
    "        vals[ind] = np.mean(val)\n",
    "\n",
    "    plt.xlabel('beta')\n",
    "    plt.ylabel('average oracle outcome')\n",
    "\n",
    "    plt.scatter(np.linspace(0.02,beta_max,grid_vals), vals,label=\"policy values\" )\n",
    "    plt.plot(emp_betas, emp_eval_vals + samp_params['mean'], 'ro',label = \"value of empirically best beta\")\n",
    "\n",
    "    plt.plot(oracle_betas, eval_vals,'go',label= \"value of known best beta\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eval_oracle_tau_evaluation(1, samp_params.items())\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "samp_params['y_samp'] = samp_params['y_samp'] - np.mean(samp_params['y_samp'])\n",
    "print lin_off_policy_loss_evaluation(0.5, samp_params.items())\n",
    "samp_params['tau'] = 0.5*samp_params['x_samp']\n",
    "samp_params['tau'] = np.clip(samp_params['tau'] , t_lo, t_hi)\n",
    "print off_policy_evaluation(**samp_params)\n",
    "\n",
    "\n",
    "samp_params = evaluate_subsample( n, evaluation = False, cross_val = False, **sub_params )\n",
    "print lin_off_policy_loss_evaluation(0.5, samp_params.items())\n",
    "samp_params['tau'] = 0.5*samp_params['x_samp']\n",
    "samp_params['tau'] = np.clip(samp_params['tau'] , t_lo, t_hi)\n",
    "print off_policy_evaluation(**samp_params)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimizing for best constant treatment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "''' Test policy optimization routine '''\n",
    "[res, oracle_res, spline_f_tck] = pol_opt(verbose = False, samp_func = constant_off_policy_loss_evaluation, oracle_func = eval_const_interpolated_oracle_tau, **samp_params)\n",
    "\n",
    "params_neg_y = samp_params\n",
    "grid_vals = 20\n",
    "vals = np.zeros(grid_vals)\n",
    "for ind,b in enumerate(np.linspace(0.02,1,grid_vals)): \n",
    "    beta = [b]\n",
    "    val = eval_const_interpolated_oracle_tau(beta, params_neg_y.items())\n",
    "    vals[ind] = val\n",
    "plt.xlabel('beta')\n",
    "plt.ylabel('average interpolated oracle outcome')\n",
    "plt.plot(np.linspace(0.02,1,grid_vals), vals)\n",
    "plt.plot(res.x, res.fun, 'ro')\n",
    "plt.plot(oracle_res.x,oracle_res.fun, 'go')"
   ]
  }
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