JSM 2015 talk

jsm2015.ipynb

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   "source": [
    "%%capture\n",
    "%load_ext rpy2.ipython\n",
    "%matplotlib inline\n",
    "from IPython.display import HTML\n",
    "from matplotlib import pyplot\n",
    "import os, numpy as np\n",
    "np.random.seed(0)\n",
    "import pandas, statsmodels.api as sm\n",
    "from selection.algorithms.lasso import lasso, additive_noise, data_carving\n",
    "import itable\n",
    "HTML(\"\"\"\n",
    "<style type=\"text/css\">\n",
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    "\"\"\")\n",
    "\n",
    "# Run with commit f3f0cb50cba96c1e628668637473390d0468ae33\n",
    "# from http://github.com/jonathan-taylor/selective-inference"
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   "source": [
    "# Selective inference with a selected model \n",
    "\n",
    "\n",
    "Jonathan Taylor (Stanford)\n",
    "\n",
    "JSM 2015\n",
    "\n",
    "[http://statweb.stanford.edu/~jtaylo/talks/jsm2015](http://statweb.stanford.edu/~jtaylo/talks/jsm2015), ([notebook](http://nbviewer.ipython.org/urls/gist.githubusercontent.com/jonathan-taylor/98c01611a9fb6f31509a/raw/99b6bab6734daa431ed76859e11b769d5a1bb45b/jsm2015.ipynb))\n",
    "\n",
    "\n"
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   "source": [
    "## Outline \n",
    "\n",
    "* Selective inference for debiased LASSO\n",
    "\n",
    "* Model selection with the LASSO  ([arxiv.org/1311.6238](http://arxiv.org/abs/1311.6238v4) )\n",
    "(joint with J. Lee, D. Sun, Y. Sun)\n",
    "        \n",
    "* Selected model ([arxiv.org/1410.2597](http://arxiv.org/abs/1410.2597) ) (joint with W. Fithian, D. Sun)\n",
    "\n",
    "* Randomized response ([arxiv.org/1507.06739](http://arxiv.org/abs/1507.06739v1))  (joint with X. Tian)\n"
   ]
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   "source": [
    "# Debiased LASSO\n",
    "\n",
    "* We heard about the debiased LASSO in earlier talks (Montanari, Van der Geer, Zhang, ...):\n",
    "$$\n",
    "\\hat \\beta^d := \\hat \\beta +\\frac{1}{n}  \\Theta X^T (y-X\\hat \\beta)\n",
    "$$\n",
    "where $\\hat \\beta = \\hat\\beta_{\\lambda}$ is the LASSO solution for some $\\lambda$.\n",
    "\n",
    "* Asymptotically unbiased estimate of $\\beta^*$ in model\n",
    "$$\n",
    "M_{\\text{true}} := \\left\\{(y,X): y|X \\sim N(X\\beta^* ,\\sigma^2 I)\\right\\}\n",
    "$$\n",
    "\n",
    "* Yields CIs for $$\\beta_j(F), \\qquad F \\in M_{\\text{true}}.$$\n",
    "\n",
    "* <font class=\"emphblue\">There are still $p$ variables. Which ones will a scientist publish?</font>\n",
    "\n",
    "* <font class=\"emphred\">The important ones, of course.</font>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# Debiased LASSO\n",
    "\n",
    "* <font class=\"emphred\">Cannot just report the large entries of $\\hat{\\beta}^d$, or $\\hat{E}_{\\lambda}=\\{j: \\hat\\beta_{\\lambda,j} \\neq 0\\}$</font>.\n",
    "\n",
    "* Simultaneous inference: Bonferroni?\n",
    "\n",
    "* <font class=\"emphblue\">Selective inference: form selective intervals for those in $\\hat{E}_{\\lambda}=\\{j: \\hat\\beta_{\\lambda,j} \\neq 0\\}$</font>\n",
    "\n"
   ]
  },
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   "source": [
    "# Selective inference for LASSO\n",
    "\n",
    "## Running example\n",
    "\n",
    "- In vitro measurement of resistance of sample of HIV viruses to NRTI drug 3TC.\n",
    "\n",
    "- 633 cases, and 91 different mutations occuring more than 10 times in sample.\n",
    "\n"
   ]
  },
  {
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   "execution_count": 2,
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   "source": [
    "if not os.path.exists(\"NRTI_DATA.txt\"):\n",
    "    NRTI = pandas.read_table(\"http://hivdb.stanford.edu/pages/published_analysis/genophenoPNAS2006/DATA/NRTI_DATA.txt\", na_values=\"NA\")\n",
    "else:\n",
    "    NRTI = pandas.read_table(\"NRTI_DATA.txt\")\n",
    "NRTI_specific = []\n",
    "NRTI_muts = []\n",
    "mixtures = np.zeros(NRTI.shape[0])\n",
    "for i in range(1,241):\n",
    "    d = NRTI['P%d' % i]\n",
    "    for mut in np.unique(d):\n",
    "        if mut not in ['-','.'] and len(mut) == 1:\n",
    "            test = np.equal(d, mut)\n",
    "            if test.sum() > 10:\n",
    "                NRTI_specific.append(np.array(np.equal(d, mut))) \n",
    "                NRTI_muts.append(\"P%d%s\" % (i,mut))\n",
    "\n",
    "NRTI_specific = NRTI.from_records(np.array(NRTI_specific).T, columns=NRTI_muts)"
   ]
  },
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   "source": [
    "# Next, standardize the data, keeping only those where Y is not missing\n",
    "\n",
    "X_NRTI = np.array(NRTI_specific, np.float)\n",
    "Y = NRTI['3TC'] # shorthand\n",
    "keep = ~np.isnan(Y).astype(np.bool)\n",
    "X_NRTI = X_NRTI[np.nonzero(keep)]; Y=Y[keep]\n",
    "Y = np.array(np.log(Y), np.float); Y -= Y.mean()\n",
    "X_NRTI -= X_NRTI.mean(0)[None, :]; X_NRTI /= X_NRTI.std(0)[None,:]\n",
    "X = X_NRTI # shorthand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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     "slide_type": "fragment"
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    {
     "data": {
      "text/plain": [
       "(633, 91)"
      ]
     },
     "execution_count": 4,
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   ],
   "source": [
    "# Design matrix\n",
    "# Columns are site / amino acid pairs\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "(['P6D',\n",
       "  'P20R',\n",
       "  'P21I',\n",
       "  'P35I',\n",
       "  'P35M',\n",
       "  'P35T',\n",
       "  'P39A',\n",
       "  'P41L',\n",
       "  'P43E',\n",
       "  'P43N'],\n",
       " 91)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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    }
   ],
   "source": [
    "# Variable names\n",
    "NRTI_muts[:10], len(NRTI_muts)"
   ]
  },
  {
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   "execution_count": 6,
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    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%capture\n",
    "# Fit OLS model and plot coefficients\n",
    "\n",
    "n, p = X.shape\n",
    "ols_fit = sm.OLS(Y, X).fit()\n",
    "sigma_3TC = np.linalg.norm(ols_fit.resid) / np.sqrt(n-p-1)\n",
    "OLS_3TC = ols_fit.params\n",
    "\n",
    "fig_3TC = pyplot.figure(figsize=(24,12))\n",
    "ax_3TC = fig_3TC.gca()\n",
    "ax_3TC.bar(np.arange(1, len(NRTI_muts)+1)-0.5, OLS_3TC, label='OLS', color='red', alpha=0.7)                                                          \n",
    "ax_3TC.set_xticks(range(1, (len(NRTI_muts)+1)))\n",
    "ax_3TC.set_xticklabels(NRTI_muts, rotation='vertical', fontsize=18) \n",
    "ax_3TC.set_xlim([-1, len(NRTI_muts)+1])\n",
    "ax_3TC.set_title(r'OLS coefficients for 3TC resistance, $\\hat{\\sigma}$=%0.1e' % sigma_3TC, fontsize=50)\n",
    "ax_3TC.set_ylabel('Parameter estimates', fontsize=30)\n",
    "ax_3TC.legend(fontsize=30)\n",
    ";"
   ]
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53L6PvgvccmzeeJcAQ9SberXvdVHfy7dRRNwBeNrY7IuBZ2fmNI+wbzW/UrWi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\nxJIAAGDbZnk967UswIlNKAywQ05J9h9Ojmy3/8HkwDLrAQCAWczyetZ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MiyifbwEXisjt\nQdzjgAXSY+LpnHsOOFpELi6ZdlNaPW1e2XYr67bMmuXAOfdK4CBgQ+AZ4DIRubdXmq0865Afz/Nk\n4AxfPiaezrnTgB+LyJ8N/D8IXCEi8+ug87SVl61zbgdUPtYG7gW+3H40u2TalgHeLSI/8N/rAHcC\nF4vIcV3o/hv4ILB1yLefa5ps/2PlaW3PxjRPEJEnqxoTCvCron3F9JUm+YlpX2UQynsddZLTvqxj\nZnT51KBviJb1iPH9E8ANInKXNf0leE0o29dm2mUT85+YOmlsTlFmDlwGOXNZU7nmxBs7Z69sHOo0\nXlqRlMJ9hnNuZ+BKYAVgPnA/qpBZCdgEGOe/95Iciznn3BhgdeAZEVmY+W0TvDAAY0VkjHPuwJJJ\nFBG5yMdnojUoAPBp7YuSwzk3FtgTOAQdGMcCs0Vk5ZLxnAycKSJj/Pew9AbKijeLyPUZ2v1R5cQY\nQ/ks6hT8AH8V0FZov8CQ/Kzg/f6Eys8jnmZPEfm577i+CkxByyCLl4FvAx9vy1YVdVKXzDrnXgCW\n8/m4BrgQ+LmUsM42pPVU4Hh0N3iWD9eWgy8Cf22TA18DviAin/XhrIqyGJ6lZcCaVrS9CfB9EWkV\nrVcRmRZ+D4L81N1Xep51KIUX9XnOuXuB/xCR/ytAdzzw+aDfOrAk63b5xMj6ecDuIjLMcso591PU\n0vgh4G7g31H5eq+I/MQ5N8OQ1g0M48FFOZPhA4DPoUqfLB4CThGRy4Lw3wcW5oTN4t+ArX1iFz0o\n7JxbA1UyTQSeAKaJ3xRyzm0AnIku4scCt4jIDnWUTxZ+Ub0Z8BPgMAmU/D3oTGn1tNMyvy0DfAC4\nFvhnB9qDrHLgnFsX+CPDF+4LgHeKyC+7JTqCZzaPnZArP0WR6UdawFzgZz6NvRaPIiJHx/R3nvY5\n4FJgqohM7yddQGvJ54moEue1IrJo88sv0r/H8AfBn0AVbHmbZHlp2ho1KNgXWDnon/8T+CgwUURm\ndqFfCX2r5VwROdn7mdc0lv7HytPanj3tog3OXnDOTQBuFJHXVDEmFORZRfuaUZJt2Fea5CemfRVB\nnrz3s066tK8ZJZMejpnm8jG2k9plPWJ8b8+fnwN+B9zg0/OnArSmfBYJH9Bl22Xd85+YOmlkTmGY\nA48XkbnGuaypXENUMGcvMw6ZxssoiEhyfXLAyr7Sn0cVJuMyvy8DHArM9BW+Uub3M9AOfCFqFfVl\n778iqshZALSAm4C3NJjPFjAHtcbaFXglsFo3F9DtW2E6Xgt8Ad0RbaGWN1OBPbJlXzC+k4FWJp/7\nBt+reb9dcmj3b9OiDbqbWx94M7pAbAEveroVgAeBecDngY0yPDZCLZXno1afSwPvB+b53y/28T0I\nnAbs7fnsDZyOWuS10M49N4+GMqtNZn35HOzjann3pC+r1/Qjrf7/izPx5MoBMA29SqH9bZWDGJ6l\nZSAmrRW04YGRHyNPU19ZRdssmL5FfR7ar9wGrNCD5liftjsq4B8j63cD52fCrO9p7wKW8X6rA48C\nV1dQl6XHg8DvTB9+tpeHY9H5wLH+e7ZvByf78MsD1/dI06t8ubyMKgq+Evy2AWrR0Arcs8Br0Inn\nHO93I7BrRbJeqHxyaMcBZ/t8/BO1wuqb3HdIQ6H0WuUA+I6v36+hm9ifQOeK9/db9izyU7Lswn7k\nSrTfno8++LwnuqFXKo8l+Z+BKqPacn4nepJllX7QRebzGuC6jN9SXu7n+T7h9cApXl6+2CO+VwBH\nA9ODfNwGnBSEuR24oGBZfhvftxOxpsHY/8TwzIQr0/+0gEMKhJsA3Acs7Ge77Ef7inER8mNuX1Z5\nr7pOirSviLzE9D+mdtKErGMc31EF2LfR9W7YjzwN/NiX1WYdaE35LFl/Ybusff4TWSe1zykwzoGx\njyVR80prejNxFJ1X1jpfX8S3qoiSy63Uo32l7dgj3E5ekI4K/A4NhO+2QDiORxe/LXSXbPJikM+t\ngK8D/+fTdTtwJLpz2o0uWsmBKnYOAW728c0Hfuv/f09k3JUohXvwWBM416d7AbpQXDvgvxB4e484\n3uo7uV/5v7cBO/i0XQIs3YFuHLoj3QImxdZJkzKLXotwFvBY0IH+L6r0W76qtKIbDcdk/DoprY5D\nrV2LpL+bHJh4WmUgJq2RdTgw8hPBx9RXetq6lcLvR/ufG/AK1ZzwH2do8fKKCvib2xe6MDguE+Yg\nT/uRjP9ZwJORaY2ZgL/Jh70WWL1D/KsDv/RtbBfg98DLHcK+AjgH3UhZ6Nv8Bpkw3/W/fQndKD0G\nnWTe5v2nV9m2ypRPlzi2Q4/Nt1CryZ7tpML091sp/DDwgw7y+up+yZ5VfkqWXXbutCZwQlCXj6Mb\n2h0337J5NKTBoRtvlzC0gJoDXIZaP1VKF5HPfwD/mfHb1dN/PeP/U+CeDmneDfiBr8P2GHYusH5O\n+FnA4QXL8Qj0pB3ErWlM/U8Mz8zvZZQyv0P73fd2CbMWenJlIXBwnszGtst+tq8YZ5WfQFZN7csi\n71XUSdn2FVm21n7L1E6alHUixndUebsP+Urip4AfAUcG4U35LFl3lSiFreUTUydV1GcmTNc5BRFz\nYCLnsha5i0lvJkzReWWt8/VFfKuOMLlhlXo18JuCYa8nsFzywvQQMMF/Lw38j28Qc4APVJC+lYD1\nCobdGL1DpeNCAd2JfL9vFC/7zuAyYLcO4VvAZ4Edi7qA9k2oFfBsH8/9wCfRydFG3m/vyPLpm1IY\nVWafEaT/J+jxwTDMncCPCqb1hz6e3/t6/RY6MI7vQbcsekTk3ArqJFpmff29HVUQHuP/vh1Yo2A5\njAHehk4I5vr8zEKvBvj32LSiitADMn5LodYZr8z4HwTM75HeInJg4mmVgZi0BmEd2kaPB74CnI9O\nEA4FXtWBpi99HrpT/ScK7KYWlZ8ecVTeV8a2zRJlle3zPuL5XgmMyYT9mP9tOrBqlzgLt+mY9uXL\n8JBMmPN8GjfO+B9Kj7ZZoKxiJuD/42V92R48lvXhFqITzQ9lfh+PjnvPMjRh3apDXDMYaYW9P0Mb\nILmK/wLlsBQ5J3HKlE+P+MejV4e8jFo4XZ/nYtLaIWy/lcLz0COM4e8beNo39Uv2rPJTss5O7sJz\nEjoezPQ8b0Y39lfslsfI9KwMHAbcwpDi4GH09EzHObCVrmQ+5zCy3zrV0+ya8f848ELwvT564meG\nD/8suun4HrrMgdGxrZDSw6e5ffosZk0zA0P/E8Mz81sZpfBK6Pz7JXLGZHRMayuPDgn8G1EKW+Su\nA+0q6LHoXqeDTPKT81up9mWR95g6sbavqlyZ8rG2k6ZlnYrGd4Yrie/zaVkY/G7KZ8n6qlQpXLZ8\nImW91jkFEXNgKpjLlpW7mPRmfi86r4zOo0mG+xFpcosq8B/o/SJFwp4CPBJ8P48+pBSG2cYLxOkV\npe/kTKe5NxmFDbpjeT/Dd+H+DOzQI+51gc+gj6G1vIDvmQnTKukWZmjnoA+t7ZSJd7FVCqOKrqMZ\nsoK8qVNZUn43voW3agTuAM4rSHseQ8e7YurELLPofUO/QjvSXD7o4PL6EvW3Knqc6M6q0opaMh5b\nkP/xwLMdfisjByaeVhmISasPvxMjd+5DtwDd0MkujvvS56GPOJXuD3rIT619pQ9nbpsl8jxisQmc\n6OP7fuDXtkq5iw4KYQxtOqZ9oVeknJ0J86e8NggcnvUH3gh8E70S5TF0UvuY//5mth6Jm4A/XlSm\n0UVpC3h/4DcGtWJ/1P92O72tGOcx0mJ6oqffrwft4ajy/ybgbd5vc/+9wNflXeidzp3K55WdyqdA\nGbyLIev6XBeT1g48+60UHkZXB88Y+SlZXx2VVkGYZdEF3u99nZyak8e/0GGxlucKpu116GLwn57H\ny2Sub6iYrlc+nwY+lvH7uQ+7Qsb/IGCu///XDPWtNwD7MXRFTtc5sK/3s3ul3Yc9C3jU/x+zpjH1\nPzE8M7+VUsqgVl/3oZvgkwL/NVArs4XAoTky26hSuKjcBeH287I004dru8dQ5fImVclPj3Bd25dV\n3q11EtO+gvhKzSkiyyembTYq65QY37vEsTFqxHAZquQbMQe25NPaLnPKp+/zn5g6ia1PSs4piJgD\nEzGXtcpdTHozvxWd41WSx7JuKRL6iVVRQSqCJ9BOo40VgUcyYR71f/8Yma4Q4aMEl6ONvX3R+HbA\nL9CF1DR00NkYeB9wrXNuaxG5Py9SEXkM+Jy/ZPsC9P7RrdHJboifAPcUTKtkvpdGd/9Wds6NkWIP\nRL0nJ55OeF1O2Dc45+b6/1fyf//DObdKJty2Obw/CPwn8Gp0R3KKiFzVhf8Yij0qhA/3koi86L/X\nRxVvRfBn1GqxDWudmGTWObcFumAX9MjEH9F2MxfdzVsHtX54H3Czc25HKfb67HiGP8gXyrq1fd0P\nTAa+XID/jugEZBgMcmDlGSMDprQ657ZHFYHPoddKzEGVxJuhj+nMA3YHDgRe55zbSUTmeXKr/Mxm\n6DXXvLbdftTgYufcQvQi/5VywmXRTX6a6CvB0DZj+zwR+YJz7hXAJ52+3ns/+nhh2/r62WwkEW06\npn3dBnzYOfd1EXnCOfdGVDF9eQ7tpuiYi3NuKVRWD/C/PeFdO63rAm8AjvB1dLBkHkD06FbG2d9W\nQ5X/RfAPdHL6I5/evdCF9utQq6H9JHjYoguWRh8qDdH+7vjKtud3LvAi2p5/4pzbBX0AdSnU2n0p\ntD6udM7tKkMPTJ3tnDvJ/9+eb37HOfciORD/un3Ae2XUMmt/VOm/h4jc0qe0VoUyclD292ieVvnx\nj7QUTd8aBcJuidbDZmjf+lxOmE0ZemS3EojIvcAJzrkz0RMg70WPevaFjt75nIH2+V+KIlMHAAAg\nAElEQVQFfUgHfQzzHhHJtte10FM9eN4volZtPyqQjhB/AD7gnDtFMi/Lh3D6UO0HfXiIW9OY+p9I\nnmaIyNPOud1Qq6yrnXM7oRvjN6D3Oh4uIhf0iqbob3W3L+fcMuh1JG/N0C1AN802QE/U7O+cmyIi\nlwRhrPLTEQXaV4y8D2NV8DczvwrnFEMJ610+5nZSt6y3UXZ8z9BuhM4Vd/Z/JzBkqHAZeo3kTcMS\nYchnZLusdf6TF6Xxt1K0xjmFeQ6MfSxpp9dSrjHptSAqj2b0S9uc3Midlx5hu+7aeL+eOwyoAmbH\ngu6CbjxRK65nGfnA2Vbo4PbdDmlYBj3GcS1DR78vIWPlWaZ8cnhsih5Hb1svPoFeIL4xXSwDKW9t\nly2f0rTohP927/coepxqTIE8/gW4sGB5XAj8Jfiej74kWoT2Q8CCCurEKrPXoB1z13tp0WNtfweu\n6RJmHMOP5be8jHyR4KqDiLSehCrge1l/7uD5h4+7WOXAxNMqA5FpbdflyoGfQxWl0wO/vdDFR1g+\n1jppoVb1N6CX7mdd+zG8P/vvG6qWH/rcV3YqnxLt0tTnZeL5VhDmbjLXOXSQg1Jt2irr3m8L7zcT\nuNWX5UJyrv3wPC/0/3/G5+kcYN0O/F6F3u3VAj4TlOs/UOX4nxi6o+zvgV/bPcJwS/OngE8VrL9P\nAf/y/7cfRXwKtdbOvSu8ixxk21dP6xXgN+hYtDLalqeik9IHgTWDcBugVo+/8N8zSrqHM3zfivY9\nC9EJfNdjezFp7RBXIcseqxzk0PWi/VMFPGPkJ6o+fRwT0DbePt77OH7e1qFcK7eIQTejvo0qyVpo\n//yDKulK5rN96uJL6IbpZf770zlhf8bQUeEfopusLfQ0y0fx4y69LYXbdxZfTIfrVNCx8Hs+3K6d\n+pAu5VVkTVOk/zHztLTnHLpNfHt5HO1bFpK59iW2XTbUvk73eTkJ3WxYGbWcewJvcYoat/wvOpfc\nNlZ+YtoXRnm31omVn//dNKeILJ/odkJNsu7pLeP7Iejp4LY16nz0ao3Po/euFrqTuGQ+Z5R0D1fR\nno3lE9P/1DqnwDgH7iTrFJ+vlS7X2PQa02nOY4xznlFCH+Cca6FKmUsLhN0PPZ47JqD9KsN3ulZC\nFzlnkGMtJiJXeLoyEBEZm02vc24Muqg+S0TOzEnvuejxy4mB3xvQ420fRO+muh21ErtURGbmxFG4\nfDrB70S/Ax0s3gKMRcvm9ajp/uWZ8AeWZCEiclEMbVAnt6Mvjc8pQHiFc+4L6B2c/y4id3QK65zb\nCt2J/6qIfNL7lZG9/YHviciYmDqJkNmZwGki8pUCPD4OnCkZS0/n3Dao7O2DXnC/ELVYvRD4mWSs\nGSLSujI6iVgOfdjj+yIyP4h3GVTB+kXUymCztuxHyIGJp1UGItP6HHqs8AuZ+DdHd/A3E5G/er+L\ngC1FZIuAp6VOPo++/no1cLSIPBqG8RYF9wPvE5Efd8i/RX5q6yuzPPN+74SIfitrYTwWXWBOQMv7\n6RzCKzxPU5uOaV/+9z0Z2hx80KdhWJ07596GWg8fKCKXO+ceBG4UkUMLpPUC9HGHjZxzM3qFz0BE\nZAMfz9XAesAW0uWEi5etu9Djt3sE7fIf6BHIIkw393G1N3hC+VoKeC1q3THCekVENnfOPQl8WUS+\n6ON5Pbop8FER+VYmvWd6/yhrPefct4Ep6OLjYBG5viCdOa05FkFdywYWlc+MElnzZLJBpPxYeZrl\nxwrn3Dh0E/AgdI7WQpWbU4FfSQcLuSrmh0Fca6H9xkFonYKOJxei9/aNOO1Qli4in+PRzYw3Bt53\noteivRiEm4AqD84QkbO83ytRBc8h6KmIl9DTJDeglorvbffJOXy/4+lmoMq7u9DN1RXRkyofQo+r\nXiAiH/E0sWsaS/9j4mltzx3i3RLdUF4R7TPO6xBuRq80jmSpbdqKCLl7APhfETko4/9+4CJ0E22W\nl8+7Ucv19wbhSstPThpKtUuLvEf2s6b2ZZ1T5PxWpv8xt83Mb32X9YjxvYUak1yMvvtxs4w8TVEI\nRfPZBCLKZ0ZJVo3NKaxzYO9nHUtM5ep5Wufs1nmlKY9F89Mx/ZKUwn1Dh0rthFWAdWS4grYMRETG\nOr3a4F78seYe2BV4a2bS1lZ0rITe8fkuyTku7pw7DH0ZeZxz7jh00HodeifkxcBUEflzN+ZVTvp9\nfGujx9IPRo+7z0MVOz8GruqkbOk3Iuqyfc/RGODTwDQRaV9dgXNuWeDDqBKkBbxORP4V8Mwq2Dph\nR+AYqUYpXAbtfM5CLRO+WoDHx9CXuld0zq2GTtgOQjcBQHc1p6Jl1e1IdMzmyTaoAnINdLf+b+hk\neCX0CNJ49IjnHhIo8+vmaZWBmLQ65+YAJ4jIN8MfA8XsjiLyv95vCrqRsVwMT0+7JTpJfy2qQP5y\ne+AOeA+bwFcgP7X1lVmevcJWgcj6MLVp/21qX1b4MfNIEZlaIOwhwDdFZHwkz3eii8uLUAuV+Tlh\nxqHW2QcB7xaRK/3EXWDYVSbdUMWk/0V0s2Wqj2dddFL9ThH5WSbNH0HLZ+mSvIbBy9409K7VQgsN\nT2dOaxMKnboRIz8RPJ9Bjzbfg258XSwizxSgi+rvnB7hfgc6H3wbuqk1E7XEnSoit1dMZ8pnwPOd\nDG1mXSkiCzJhtgB2A/5HRP6RE8cbfJr3Yehqs4vRsXDEdVt+8Xo6uvm2TE6y5qKbb6eLXyhGrmlm\nFKAJESodSvOMVJDkHRlfG1gevfs/jzh6QW5BRPuai/aV38n4r48qHf5dRP7g/T6N9sVrBuFKy4+n\nM7WvnPSXkvdYlOEXM6eI6H+s7aR2WY8Y3+9DrXxBr7P7LarY/a2IPNWDdpDatKl8moB1TmGdAwc8\nyyAcS6ZhKNfIObslrSa6kjQjkO4U7i/a92MWub+yxfD7NA8uyavd2d2DKvvP6UXgdAc4e5+URqY7\nxLPRDjMPy6O7pqAD/1x00PoZupO3iXNukw60iyzKqoSIPAGc5Zw7G71G42D03qX2UfW8iUsdMNWl\niPzLOfcO4Er0nsT/ds79DR30V0YVJMugyqV3thXCAT7mXV2wyuytwFHOuR/1UMRNQI+ntO+XfRy9\nd+cl9EjRVBH5bZ/Tiojc4RdoJ6KvEG8RhHsUfaX0izmTlCZ4WmXAmta/oY+wfTPz+7v93xmB37Lo\n8a9YnojIXc65Sahl/WfRe/AOl+73RMXIz1AiBrCvLAhzfWBv0zGybsWTqJVezwUceoQz+j4vP1m8\nGL1zcLLTewXvZKhv3wbdsFgfXeRf6ekmRvC00j6BPtTWRnsDZUtUhkNsQY4FuQEjlLgFYU5rTNkO\nChrK46ponzcGtbg72Lnu68cKlA7/jT4MtRraL/0Ota67XIKN9aroPMz5FD2JknuKJQh7N2qx2en3\n24DbnHPHovPeQ3xe9nfOPQxcISInBOFbwKnOuW+gR6//DV2rzELXEVeLSLYtm9c0EbJn4hkp6yvm\n+L3gXV46+m5d5ZWFY3KUEVa5mwnkKRHW93/nBX5PoYrEMI7S8hPZvrJ5KCXvsSjJzzSniCwfa9ts\nQtZN47uIvNbPGSd7tyv6sCzOuftRJfFvUSVx9n7lvuTTObccqry/xesgqoB1/lM7rP2sdQ4cw5OI\ncq17zt7UfDRZCi9hcM6dh+5SrJC1NMgJezJ6bDdrHRju+nxZRI7PoT0X2FlENo2wKpyI3rvS82i6\nFU6PI++DHhXYriTtSsAqIpJ9/Cov7ARgO3SwvVk6HEe0wOkRohNQBcl6wU+PoMegRyhInP3I+ET6\nXCdZOH2c7LfoxPZ/0KswHkcnpcugj1LtgD5KtQx61OoW59xt6L3Yl4nIrLrSm4VzbkX8ZLiuXd0i\nPK0yEJmuw9ENjGvQHdU56MTtSLRd7BKEvRA9ijPiUcbINKyP7ta+FZWPC1ClY9ZS2Cw/dfeVPp6J\nGNqmc24f9BhpZX1SAZ6mNt0hrsLty0/Qd0Mn+te3LZScc7ui1vBLoQ/SXRn8dib6avSXgK/kLCba\nFqcfR6/N+JyInFK4MDqndSxqaXU8nS2tzkEtrcrKTWXwi/6DgU+ii9ez0Ss+dkavZLnWh3sfajl1\nuYjs1yGuMeiVKbujC9+n0OtZ8h4D7JSeZdFJ+LNZBUmVaU3ojSL1GWFJNA04r8fGXqd0tdANgmno\nZt9D/aTztDPogxV2F2VgkTRtiLaHA4EJknNcPGHxgZ8/HYaOX58TkV86vXrrm6jycAyqcP20iPzC\n08zA1r4uAfZET4ve4uNaEzVCeQ16fcR8738q+sjwqyLzZ25fBeMvJe/dxpIYftY5Rb/LZ1BQps/L\nKIkno6ctAB5ClcOH9CeVi/jnnkTsEDZ6/hODsmOJc24V9Cq3WWK8pqNH/AMxB25j0NJrQVIKL2Fw\n+rLmfuikoeuulZ9sbCVDd+ZOywn2pIh8KkM3Hj1edJ2IfLgfyiff0a4GPCUiD5eMvxJ4pfkZbaWM\n9zsWtUacjyrUL3Z6DP5rDHUSL6FH6M/tQ5r6roD0ipU3o3fWFFKsVMBzElqG3RSEt6PHPv5QBc+E\n6uHUROVcdGET4l7g7RLc9+uVwn8UkfP7lJZ9gK+gk5rlKTBpKxH3tBzvRvpKz6djf+kXGvOAq9D7\n/a4rmQYT6m7TTq/b+QND1k83oncsnou+oh7iD8CbReQlp/cU/xA9UQLwGCMV2Ov6336OKhfnUQJO\n7zreW0RGWF/7dBe11Ksdzrn10P5+de91FzoO/Aq1hpqFKitWQK0mtheR+50e1/xkoLwYh5bfm308\nLU8H8FMR2TvguSmwmojcFPjtCnwOfbXdoVb2NwDHi79+xZrWyCJqp28PYDN0oXeliDyfE2YS8JFQ\nD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N9JHcEroPtr8D0d+E1OuBN8POsGfscwZLW7G2op2fN1W1R5dkDw/V8EHXcXunG+0/qO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\nbJXa57RarXaP8Xl7DL0Oon1k6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61gy6e1XTY1/xmUOUUTp5ZgsObstRtGJKVwQkJCQkJC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10deae390>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_3TC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference for the LASSO \n",
    "\n",
    "\n",
    "- Use the LASSO to select variables with \n",
    "$$\n",
    "\\lambda = \\kappa \\cdot \\frac1n \\mathbb{E}( \\|X^T\\epsilon\\|_{\\infty}), \\qquad \\epsilon \\sim N(0, \\sigma^2 I).\n",
    "$$\n",
    "\n",
    "\n",
    "- Used $\\kappa=1$ below, $\\sigma^2$ the usual estimate from full model.\n",
    "\n",
    "#### [arxiv.org/1311.6238](http://arxiv.org/abs/1311.6238)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Choose a LASSO parameter\n",
    "lambda_fixed = []\n",
    "for i in range(10000):\n",
    "    lambda_fixed.append(np.fabs(np.dot(X.T, np.random.standard_normal(n))).max())\n",
    "lambda_fixed = np.round((1 * np.mean(lambda_fixed) * sigma_3TC)) / n\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Variables chosen for 3TC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.067930489731437602"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_fixed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from selection.algorithms.lasso import lasso\n",
    "lasso_3TC = lasso(Y, X, lambda_fixed * n, sigma=sigma_3TC)\n",
    "lasso_3TC.fit()\n",
    "active_3TC = [NRTI_muts[i] for i in lasso_3TC.active]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['P62V',\n",
       " 'P65R',\n",
       " 'P67N',\n",
       " 'P69i',\n",
       " 'P75I',\n",
       " 'P77L',\n",
       " 'P83K',\n",
       " 'P90I',\n",
       " 'P115F',\n",
       " 'P151M',\n",
       " 'P181C',\n",
       " 'P184V',\n",
       " 'P190A',\n",
       " 'P215F',\n",
       " 'P215Y',\n",
       " 'P219R']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "active_3TC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1042c1590>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%capture\n",
    "ax_3TC.bar(np.arange(1, len(NRTI_muts)+1)-0.5, lasso_3TC.soln, label='LASSO', color='gray') \n",
    "ax_3TC.set_title(r'LASSO coefficients ($\\lambda=%0.03f$)' % lambda_fixed, fontsize=50)\n",
    "ax_3TC.legend(fontsize=30, loc='upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FDZt9GTi4Y/nZwK8G0PfKjHcSy6Vd/H2uJ0rv1GMf9cksB5kUHkVs9frBvSaF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\n+akRcwIAAAAAMIExofDxQ3vZmv23ZOVD5L5uP+P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AsESEwgAAAAAAS0QoDAAA\nAACwRITCAAAAAABLRCgMAAAAALBEhMIAAAAAAEtEKAwAAAAAsESEwgAAAAAAS0QoDAAAAACwRITC\nAAAAAABLRCgMAAAAALBEdm13AQDb5WPJ6ZWcvt11AAAAAGwloTCw1Pbs2TNpP5Ljq/Yemxyz2f7X\nJtdf3b17gSUBAAAAqwiFAZjUsckxlyZXbbb/acmJi6wHAAAA+GrWFAYAAAAAWCJCYQAAAACAJSIU\nBgAAAABYIkJhAAAAAIAl4oPmAAAAAGAbHV+199jkmM30vTa5/uru3QsuiUOcUBgAAAAAttGxyTGX\nJldtpu9pyYmLrodDn+UjAAAAAACWiFAYAAAAAGCJCIUBAAAAAJaIUBgAAAAAYIkIhQEAAAAAlohQ\nGAAAAABgieza7gIAlsXxVXuPTY7ZbP9rk+uv7t69wJIAAGDTZnk967UswMFNKAywRY5Njrk0uWqz\n/U9LTlxkPQAAMItZXs96LQtwcBMKAwAAAMCcvDuUnUQoDAAAAABz8u5QdhIfNAcAAAAAsESEwgAA\nAAAAS8TyEQBb5GPJ6ZWcvt11AAAAAMtNKAywhfbs2bOQvgAAAOxcTiJiqwmFAQAAAGCbbfbEICcQ\nMQWhMACT8h/uxTi+au+xyTGb7X9tcv3V3bsXWNIBzVLvdtcKAAAc3Px9MT2hMACTs0zG9I5Njrk0\nuWqz/U9LTlxkPRuZpd7trhUAADi4+ftierfa7gIAAAAAANg6QmEAAAAAgCUiFAYAAAAAWCLWFAYA\nYHI77cMRAQBgmQiFAQCY3E77cEQAAFgmQmEAgEOcs3YBmMLHktMrOX2r5vP7C2BxhMIAAIc4Z+0C\nMJU9e/ZM2u9A/P4CWByhMAAc4mY5y8YZNgCz2WlnMvqdAAAkQmEAGGUn/VE9y1k2zrABmM01ycOu\n2e4iZuB3AgDLZKf983YrCYUBYAR/VAOwzyxvk5/iLfUcOoQVAItlGZr9EwoDAADANhBWwMZ20j9P\ntvrDGOexHffrTvpeLgOhMAAc4rbjxelOekHMwWfs8iz+0ACAQ89O++fJTnn3yHbcrzvte3moEwrD\nFtlJ64/uJFXVs47p7lpELXAw28pPCt/OOTk0jF2exR8aAACwOUJh2CLWH12cnfKfWIBl4mxxAJaN\nE4GAnUQoDHwNb78FYAr+abcYyxA6eC0C7EROBILFccLB9A6ZULiqHpPkN5McluT3uvvX1unzoiSP\nTfLZJD/W3RdtbZWwM3j7LQAcvJYhdPBaBGBj/oF2YO6fQ4/l6aZ1SITCVXVYkt9K8sisvHh8f1W9\nobsvWdXnzCR36e67VtUDk7wkyYO2pWAAAACAOfgH2oG5f+DADolQOMkDkny0uy9Lkqo6L8n3Jrlk\nVZ+zkrwiSbr7vVV1bFWd0N2f3OpiZ7EMbw+EncZ/nEm8fYnt4fmHeXj8AInnAgBWHCqh8IlJrli1\nfWWSB26iz0lJDupQeBneHgg7jf84s4+3LzHW2H/6ev5hHh4/hw6hHvPwXABAkqS7d/wlyeOT/PdV\n2z+c5MVr+pyf5CGrtt+a5N+uc1udZM+qy+556zsyuWy43U1djkwuGzN27LjVY3dSre6fjccmed0M\nY18375wzzjd6zjVf4yzzdZIeO3aC+2d0rXPcPzvme7IDf7629PGzHbWO/V7utPvH76/F1DrP42cn\n3T/Z4t+1O+3+WYafr1nG7Lss0/2zTc8/2/H6Z9ScO+35Z8avce7XFDvpsb4sP187ac6d9vpn7Lid\ndP9sx/PPstw/qy9Jduers81er9+hcqbwVUlOXrV9clbOBD5Qn5Oyn/+OdveeKYv7xuTqS5MPbrb/\n6v/Efq771K2cc55avy657BuTqzcz7trk+nlr3Y45t+N7OcvXmHz119ndjx8z59hax86XzHbfrr5f\n75RcNPZMh+6u2apcMcf9M2q+ZPz9sx3fk7Ff5zw/X2NrnWfOrf46xz7ukvkee7Oc5by671bfPzvt\n8TP2+7nV45Ktfy5Itv7rnPO5YNTz7E56/GzHz9d2PGbHfp3b8ft9nvtnJ/19scNe/2zp6+5tnHPU\n432rX3cnO+v3+3a8PtyO+2ern/N22uufnfT3xXb8/trq55F5spjt+Plarbv3Jtm7b7uqzl6v36ES\nCl+Y5K5VdWqSjyd5UpIfWtPnDUmeneS8qnpQkmv7IF9PeB7XJtfP8jaf1Q/esca+JW2eWpfhbXDL\n8DWysVl+Tqb4eQY2th2/azl07KTHz06qFYDN8fcFHNg8WczYn6+tfs11SITC3f2lqnp2kjcnOSzJ\nS7v7kqp6xnD83O5+U1WdWVUfTfKZJD++jSUv3E4KEndSrSyOFyUHtgw/J0IHtsvY559l+LlcFjvp\nn+nbYSfVutN4/XNg7h+Whd9DcGgZ+/O11T+Xh0QonCTdfUGSC9bsO3fN9rO3tCgOWsKng48XJXgM\nMA/vOmEeHgOHlp0UJO6kx57QChZnWR7rO+n5eSfZjudn38tDwyETCjONZQlLl+WXLnDwWZbn2bHG\n3j+e14F9PB8shvuVZeG12uJ4HlmM7bhffS8PDULhLbCTfqn4wT6wnfS9XBa+J+w0nmcPzP0DbBev\nKYDEaxFgeQiFt4BfKocO38uDj+/J4nhLEADLxGuKxRC2w6HFzzQcOoTCAKzLH8cAwLy8noBDi59p\nOHQIhQGA/dqzZ892lwAAAMDEhMIA7HiWuliMOyUXXZpctdn+s7yVEFgOnp/ZaTxmAVgWQmEAdjxv\nYwM4OHl+ZqfxmAVgWQiFAQAAAGDgXQMsA6EwAAAAcEgR6jEP7xpgGQiFAVhas/yxsK//IusBAGAa\nQj2AAxMKA7C0/LEAAADAMhIKAwDrciY1ibffAgDAoai6e7trOKhUVXd3bXcdAAAAAADz2F/Weavt\nKAYAAAAAgO0hFAYAAAAAWCJCYQAAAACAJSIUBgAAAABYIkJhAAAAAIAlIhQGAAAAAFgiQmEAAAAA\ngCUiFAYAAAAAWCJCYQAAAACAJSIUBgAAAABYIkJhAAAAAIAlIhQG/n/2zjxckqLK2280+47IYiOy\nKLiOCLi1jh8giCui4oqorK2IO6CDyiaOMCo6OiqDKAiK6+CCGwoKKqOirG6ogNCyijpAN9DQ3fSN\n748T1Tdv3qyqzBNZVV3U732efO7NrDx5ImPLiBMnIoQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQ\nQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBC\nCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBC\nCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoL\nIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEII\nIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGj\nsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQggh\nhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQ\nMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGE\nEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHE\nBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQ\nQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQ\nQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBC\nCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBC\nCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoL\nIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEII\nIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGj\nsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQggh\nhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQ\nMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGE\nEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHE\nBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQ\nQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQQkwQMgoLIYQQQgghhBBCCCHEBCGjsBBCCCGEEEIIIYQQ\nQkwQMgoLIYQQQgghhBBCCCHEBDH2RuEQwkYhhPNDCFeHEM4LIWzY5b4FIYTfhhCuCCH8etjh7EYI\nYddhy46TznEK6yh0jlNYR6FznMI6Cp3jFNZR6BynsI5C5ziFdRQ6xymso9A5TmEdhc5xCusodI5T\nWEehc5zCOgqd4xTWUegcp7COQuc4hXUUOscprKPQOU5hHYXOcQrrKHTmhLUbY28UBo4Ezo8xPhL4\ncTqvIgK7xhh3jDE+ZWih68+uI5AdJ51euUnR6ZWbFJ1euUnR6ZWbFJ1euUnR6ZWbFJ1euUnR6ZWb\nFJ1euUnR6ZWbFJ1euUnR6ZWbFJ1euUnR6ZWbFJ1euUnR6ZWbFJ1euUnR6ZXrygPBKLwXcGb6/0zg\nxT3uDYMPjhBCCCGEEEIIIYQQQqy8PBCMwpvFGG9L/98GbNblvgj8KIRwaQhh/nCCJoQQQgghhBBC\nCCGEECsXIcY46jD0JYRwPvCQip/eC5wZY3xQ4d7bY4wbVTxjbozx1hDCJsD5wFtijBdV3LfyR4gQ\nQgghhBBCCCGEEELUIMY4a/WEVUcRkKbEGPfo9lsI4bYQwkNijH8LIcwF/t7lGbemv/8IIXwTeAow\nyyhcFUlCCCGEEEIIIYQQQgjxQOGBsHzEt4H90v/7Ad8q3xBCWDuEsF76fx3g2cDvhhZCIYQQQggh\nhBBCCCGEWEkYi+UjehFC2Aj4GrAlsAB4RYzxzhDC5sBnYowvCCE8HPhGElkV+GKM8cSRBFgIIYQQ\nQgghhBBCCCFGyNgbhYUQQgghhBBCCCGEEELUZyzWFH4gkZavWB9YFGO8ZwDPfynQyNIfY/xGrqyY\nTQhhToxxatThWNkZ93wXQlgN2IvZ7/C3GOMvHig6+xFC2CWF56IYYwwh7FxHLsb4s0y9Q88/455n\nB02b8dNWXg8hPBTYHLgmxnhnk7CtLKSZUY2IMd7u1PXwGON1HtlcQgibxxhvGbLOocXtqBjWO6aZ\nelvEGH8dQtjSofOGpjKjZlLes8yg+jS96p86Oh/I5XkSy5dozqDtDV5G8X0fBsVymfuccYmfcahn\nO9+SB3K7sq32ujyFh0AI4RHAkcDzgLmFn24FvgecGGNckPH8bYH3xBgPDCE0NULGGOMq6Tku2RDC\n52huAOiE9TUxxi811FubEMJDsLWm948xPqah7KuA18UYn5/OrwEOizF+J52vDfwH8IkY4zUl2dcA\nZ6b4+QTN4+ethWetCRwIvBR4PLAecBtwDfAF4KsxxiU93mMr4DnAdqQGAvBn4IcxxhtL9w48TZKe\n7DwbQvgTcDoWz7e1H0qjFNaHAn/B0vyd6feNqd7g8l5gu85HyJsPcnQW3qF2HvCGFXhzklkrxri0\nZrquqH+aMOr8M+y6sqBz0PXlijovhPDQGOPNDWTfGWP8cCGsTejET0752gHYDfh8jPGfhXBtDJyF\n7SUAsAw4Icb4vvT772ieJtuHEF4N/KL47U4NwEUxxvuL94cQtgdeFmM8pvysZPSeR6lujzH+vOLe\nqRTWuhviNi5fIYTtgKOAfWKMq2fEz38Dp8UYLy08e3VgWezT8Awh3AG8JcZ4VsOwu8KaZKvitldc\nd/KsOx+EEB4MHAA8Avgn8OUY41X9wuzVOYz8k3QeBbwvxY9LZwjhWODrMcbfO/S/CvhGjHHpMOSS\nbOtxG0J4OpY/NgeuAj7a2TS7YdjWAF4SY/xKOn8ocDlwVozx8B5y/wm8CtipqHeQfZpy/ePV6S3P\nzjDPjTHe2tY3oYa+NspXTl3pyj855asJxfw+jDSpKF/eb2Z2/AzB3pCd1zO+7+8ALowxXukNfwNd\nc5vWtaVyOYr2T06ajKxN0aQN3ISKtqwrXiuem9tmb+071O176UVG4QETQngmcA6wLrAUuBozyKwP\nPBJYPZ3vFSs85kIIc4BNgH/GGJeXfnskKTMAq8QY54QQ9m8YxBhjPDM9zyXrMACQwjoQI0cIYRVg\nT+Ag7MO4CnBXjHGDhs85Cjg+xjgnnc8Ib8FY8awY4wUl2ddgxok5jvhZUSmkD/y3gY5B+26m88+6\n6dpvsfxzQ5LZM8b43VRxfRyYj8VBmfuBTwNv7+StNtJkWHk2hHA3sHZ6j3OB04Dvxgbe2Y6wHgMc\ngY0GL0r3dfLBh4E/dsSB/wI+FGN8f7rPayjL0dk4D3jDipW3CHwhxjhVN11jjGcUz8ch/wy7rkw6\nh2EUXlHnhRCuAv5fjPH/asgdAXywUG/t31B1J35y8vopwPNjjDM8p0II38I8ja8DfgP8K5a/XhZj\n/GYIYYEjrNs4vgdnVjSG9wM+gBl9ylwHHB1j/HLh/i8AyyvuLfMvwE4psCs2FA4hbIoZmbYGbgHO\niGlQKISwDXA81olfBbg4xvj0YcRPmdSpfhzwTeANsWDk7yPnCmuSPaP02xrAK4HzgL91kT3Amw9C\nCFsAv2Jmx30Z8KIY4w96BTpDZ/kdu1GZf+pSqkemgPuA76Qw9us8xhjjW3LquyR7B/Al4PQY4xWD\nlCvIet7zXZgR59ExxhWDX6mT/nlmbgh+C2ZgqxokqwrTTphDwauBDQr1878DbwK2jjEu7CG/PrZX\ny8kxxqPSNXefxlP/eHV6y3OSXTHA2Y8QwlzgJzHGR7XxTaips43ytaCh2mJd6co/OeWrDlX5fZBp\n0qN8LWgY9OI30x0/znIy9Lye8X3vtJ/vAH4GXJjC89sasq73rHN/Qa5cLofd/slJk5G0KRxt4DVj\njPc527KueC3SQpu9yXfI9b3MIsaoY0AHsEFK9Dsxg8nqpd/XAA4GFqYEX7/0+/uwCnw55hX10XR9\nPcyQswyYAi4Cnj3C95wCFmPeWLsDDwY27nUU5F7dYjgeDXwIGxGdwjxvTgdeUI77ms87Cpgqveer\nC+cbp2u7Vci+piOLFehex1bAs7AO4hRwT5JbF7gWWAJ8ENi2pGNbzFN5Keb1uRrwCmBJ+v2s9Lxr\ngWOBvZOevYHjMI+8Kaxyr3xHR5wNLc+m+DkwPWsqHbemuHrUIMKa/j+r9JzKfACcgS2l0Dn35oMc\nnY3zQE5YWyjDY5N/nDpddWUbZbNm+FbUeVi9cgmwbh+Zw1LYLmtBf05e/w1waumerZLslcAa6dom\nwI3A91pIy8bfg8K149P9d6X8cBjWHjgsnd+VysFR6f51gAv6hOlhKV7uxwwFHyv8tg3m0TBVOG4H\nHoU1PBenaz8Bdm8pr9eKnwrZ1YET03v8DfPCGli+7xKGWuH15gPgMyl9/wsbxH4H1la8etB5z5N/\nGsZdsR45B6u3l2IbPu+JDeg1eseG+t+HGaM6+fxybCbLhoOQy3zPc4HzS9dWTfl+SaoTHg8cnfLL\nh/s870HAW4ArCu9xCXBk4Z5Lgc/WjMtPk+p2Mvo0OOufHJ2l+5rUP1PAQTXumwv8CVg+yHI5iPKV\nc2TkH3f58ub3ttOkTvnKeJec+sdVTkaR13F+3zED2Kex/m6xHvkH8PUUV4/rIut6z4bpVyyXQ2//\nZKbJ0NsUONvA+L8lWe1Kb3hLz6jbrhxqe32F3rYepKMyUd+SEm3nPvftkjLSmwvXDi5kvksKmeMI\nrPM7hY2S7boSvOeOwCeA/0vhuhQ4FBs57SWXbeTADDsHAT9Pz1sK/DT9/9LMZ7diFO6jYzPg5BTu\nZVhHcfOC/uXA8/o84zmpkvth+nsJ8PQUti8Cq3WRWx0bkZ4C5uWmySjzLLYswgnATYUK9H8xo986\nbYUVG2h4a+laN6PV4Zi3a53w98oHLp3ePJAT1sw0HJv8k6HHVVcm2WEbhV+B1T8XkgyqFfe/nenO\ny4Na0O8uX1jH4PDSPQck2deXrp8A3JoZ1pwG+DPSvecBm3R5/ibAD1IZ2w34BXB/l3sfBJyEDaQs\nT2V+m9I9n0u/fQQbKH0r1si8JF2/os2y1SR+ejzjKdi0+SnMa7JvOWkx/IM2Cl8PfKVLfn34oPKe\nN/80jLty22kz4J2FtLwZG9DuOvhWfkdHGAI28PZFpjtQi4EvY95PrcplvOdfgX8vXds9yX+idP1b\nwO+6hHkP4CspDTvfsJOBrSruXwQcUjMe34jNtIO8Po2r/snRWfq9iVHmZ1i9+7Ie9zwEm7myHDiw\nKs/mlstBlq+cw5t/CnnVVb48+b2NNGlavjLj1ltvucrJKPM6Gd93zHi7D9VG4tuArwGHFu53vWfD\ntGvFKOyNn5w0aSM9S/f0bFOQ0QYmsy3ryXc54S3dU7ddOdT2+gq9bT9Qx4xE/R7w45r3XkDBcyll\npuuAuel8NeB/UoFYDLyyhfCtD2xZ897tsDVUunYUsJHIV6RCcX+qDL4M7NHl/ing/cDOdY+C7DMw\nL+C70nOuBv4Naxxtm67tnRk/AzMKY8bs9xXC/01s+mDxnsuBr9UM61fTc36R0vW/sQ/jmn3k1sKm\niJzcQppk59mUfs/DDIRvTX+fB2xaMx7mAM/FGgT3pfdZhC0N8K+5YcUMofuVrq2KeWc8uHT9AGBp\nn/DWyQcund48kBPWwr0BK6NHAB8DTsUaCAcDD+siM5A6Dxup/i01RlPr5p8+z2i9rswtmw3iqlzn\nvT7pPQeYU7r3bem3K4CNejyzdpnOKV8pDg8q3XNKCuN2pesH06ds1oirnAb4/6S8vlYfHWul+5Zj\nDc3Xln5fE/vu3c50g3XHLs9awGwv7NcwPQBSafivEQ+rUjETp0n89Hn+mtjSIfdjHk4XVB05Ye1y\n76CNwkuwKYzF37dJss8YVN7z5p+GaXZUD53zsO/BwqTz59jA/nq93jEzPBsAbwAuZtpwcD02e6Zr\nG9gr1/A9FzO73jomyexeuv524O7C+VbYjJ8F6f7bsUHHl9KjDYx922oZPVKYO7PPcvqZc5n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Cx10N6F7UL8hMJ9N2K7lH64opEyCp3ePOAN65+xTdg+Vfr9JenvgsK1tbDpX7k6iTFeGUKYh3nW\nvx9bB++Q2HudqJz8Mx2IMawra+JOD/xlOieve7kV89Lr24HDpnBmr+eVGotnYWsO7hpsXcHLma7b\nn4gNWGyFdfLPSXJbZ+j0yt6CbdTWoTOAsgOWh4s8gQoPcgezjLg1cYc1J27HhRG940ZYnTcH87g7\nMITe/ccWjA7/iW0MtTFWL/0M8647OxYG1tuSS7jfM9pMlMpZLIV7f4N5bHb7/RLgkhDCYVi796D0\nLq8JIVwPfCPG+M7C/VPAMSGET2JTr/8F66sswvoR34sxlsuyu0+TkfdcOjPz+noV1+5OR1U4Bu5d\nlYyFcyqMEd58txCoMiJslf4uKVy7DTMkFp/ROP9klq/yOzTK77k01OdqU2TGj7dsjiKvu77vMcZH\npzbjrunYHdtYlhDC1ZiR+KeYkbi8vvJA3jOEsDZmvL842SDawNv+GTreetbbBs7RSUa8DrvNPqr2\nqDyFH2CEEE7BRinWLXsaVNx7FDZtt+wdWBz1+WiM8YgK2ZOBZ8YYH5PhVbg1tu5K36npXoJNR94H\nmyrwlIay6wMbxhjLm19V3TsXeAr2sf157DId0UOwKUTvxAwkWxZ+ugGbBj3LQBL8U8a3ZsBpUibY\n5mQ/xRq2/4MthXEz1ihdA9uU6unYplRrYFOtLg4hXIKti/3lGOOiYYW3TAhhPVJjeFijunV0evNA\nZrgOwQYwzsVGVBdjDbdDsXKxW+He07CpOLM2ZcwMw1bYaO1zsPzxWczoWPYUduefYdeV6Tlb4yib\nIYR9sGmkrdVJNXS6ynSXZ9UuX6mBvgfW0L+g46EUQtgd84ZfFduQ7pzCb8dju0Z/BPhYRWei43H6\ndmzZjA/EGI+uHRndw7oK5ml1BN09rU7CPK2a5pvWSJ3+A4F/wzqvJ2JLfDwTW5LlvHTfyzHPqbNj\njPt2edYcbMmU52Md39uw5VmqNgPsFp61sEb47WUDSZthFf2pk54ZnkRnAKf0GdjrFq4pbIDgDGyw\n77pByiXZBQzAC7uHMbBOmB6BlYf9gbmxYrq4WHlI7ac3YN+vD8QYfxBs6a1PYcbDOZjB9T0xxu8n\nmQX4ytcXgT2x2aIXp2dthjmhPApbPmJpun4MtsnwwzLfz12+aj6/UX7v9S3J0edtUww6fsaFJnVe\nyUi8KzbbAuA6zDh80GBCuUJ/5UzELvdmt39yaPotCSFsiC3ltig6l+no8/yxaAN3GLfwepBR+AFG\nsJ0198UaDT1HrVJjY8c4vWbuGRW33RpjfHdJbk1setH5McbXDcL4lCrajYHbYozXN3x+KySj+fs6\nRpl07TDMG3EpZlA/K9g0+P9iupK4F5tCf/IAwjRwA2QyrDwLW7OmlmGlBZ3zsDjsZSC8FJv28cs2\ndIr2CeaicjLWsSlyFfC8WFjvNxmFfxVjPHVAYdkH+BjWqFmHGo22Bs8+o+LySOrKpKdrfZk6GkuA\nb2Pr+53fMAwuhl2mgy2380umvZ9+gq2xeDK2i3qRXwLPijHeG2yd4q9iM0oAbmK2AXuL9Nt3MePi\nEhoQbK3jvWOMs7yvU7jreuoNnRDCllh9v0m6dCX2Hfgh5g21CDNWrIt5TTw1xnh1sOma/1YwXqyO\nxd+z0nOmkhzAt2KMexd0PgbYOMZ4UeHa7sAHsF3bA+ZlfyFwREzLr3jDmhlFnfC9AHgc1tE7J8Z4\nZ8U984DXF/NBhtyG2MZQSzEvtfuCrYF5THrnKWyt2hNjjHe08H7u9Bw2KU7Pbdox88rl4jEGNnz+\nKsBzY4zfazHYrZFrnHPqbN3DL3krfhvbxPSPDWX3Ar6FtbsXY9+C3dLzVsU2fFsVK9urY5u3/Swj\nrI/Avr/rYzO8FmPLWq2JLSX2ycK9l2BrZGaV6WGVr2J+935LvPrSuatNMar6x0NOXk/yA6nzQgjP\nBI7FyskKpwovwZZ869XP3RjbrPFM0r4nMcaPtv29rGtQzo3XYOtNH4CVjXULP90KfB84qV+bqakx\nuY02cNsG7GG12b2DvjmDxT2JA9rBTkff3QnXwnZ8rdy5tXTvZsDzsI7tW9Pf5wGbjijsa2PTMTfL\nfM7ewMNK13bHRt2mCsfv6bIbPfZBfwZwOGYAOhUbqTm4/GxH+I5i5u7Je6bw/A0zci3DphEtw6b5\nHAK8I4V3ObZ+aj8dc7G15F4IbLQS5MtNsXVVO3F/AdYQPbWUJlPAz6nYubOQJkc0TRNsV999Unoe\nnf7uAzyihTy7Zc17t8M+nttU/LaPN50yZddO+WR30mBeur47tobuBzADQfA8v4deV1qm+uEdWGNp\nT2CVhnpbqfOwqZUfx9aCmtdQ9mHYTrt9d87uk27ZdWV6lqu+TNfuKPx+XSpblbti1wxL7XqraZn2\n5nVsaY5l2PIhh2IeN58F7sc8Rp8IPBXzIp/C1jEuyj8f8x79M7ZhxvL098/Y8iLPz4ivoyjtvp3x\nrA0xz6RXA2umaw9O+fwK4DLgQ8CD2pLFOiEHp3RbI13bIMX5FSnPnU5hl3tKuyentJvCdlDfEuuc\nbAt8JV0/pHDv97FNFzvnz07puBTzQP8KZiRZjhl3H5MTVkca7Il5coF9H3/AzDJ4O/DKCrkVu757\n5dL5pthSPB25K1LaXs50G+XO9P9VwDot5AF3erZ1JB2vxsrpD7CO+Mva1jPMAzMcTWF1zW2YU8HT\nsKVN7sCWPTkXMxYuo0a7soHuF2DL9OyHzYqrumdeJ69n6noM8P9K13YHLk7luDN4+QPgX/o8a0Ns\nPdB1M8KzbdK5t0N2bex7vHnpeqc8LsfaxwcAa9d85o+xWQ0bYO2u0zFDzLUU2g/YoOc/gO+3kCaP\nxgzRCzEvt0uBfSruexzO/iaFutIbr5nv6P6WtKB7YG2KUR+Zeb21Og/rr80HvogZ34vf02tafM/a\nR0HO2/75XTFvYINA5xV03F/4/xttxCs2WHFuxfsswWZa/j2dLwb2rYinfYEfpTK0vHDchPUbHzmA\nPDgwnbTbZj8Ea1tdhA0egS1zdlFKh+WYA8Pz25DLCmvbiaRjRoJmNYKwUYgfFu4tH8tTRfH4Ub+r\nM37KleZTUnzcjTWIjsU+qJ1rjyzJ74J9XLtVzsvSc9Yryexc8/gsMztiP8Qabeuk80+myuhX2IhN\n5751sLUvzy5cOwzrxF2NbZ4C9iG7txDee7DNCerEXZYxmS4GL/INK43TJDMP7Yp5hi3GPDKPo2Kg\nBetULy+c5xjY7sW8APZw5PfGsmQa6vEbdoealknnSlPnAY/A2WkcUHhc9WWS2xdrHJ6GNRg76ff9\nVBYqjfa0XG8NMq8DfwJOLZzvne47tULPt4E/DTHtZgwwZsbPgkIcNDEGumVbyq83AD+ouG8OZoz4\nReHarcDhhfPLk/y2JdknAP9H4Vs7xPRcnv5/Y3rXL2Df4zdiAy9TwJEluaJR2CWXzk/EyvkRwCuw\nb9/3U1l8duG+/bA68+gW8o87PZ1x7OoY93hebYMywzWWZhkDPWElY0AiQ2eWcY6GBgBs8PGwHscJ\n6b0/17nWIM0qDcrp2mnMbMMsTOF7Sp9n3orNMOycPz7Jv7Hi3uOB/6sZ1lWp4Xw0qIMGxpVu8Vq6\n52mY1+OvUtrfnv7+Kl1/eun+rG9JU30txZmr/sE/4NdYLjOvu+s8rF1+EFaPl43AC7Dy/FrynB6K\ng753YJ6gR2B9ol1Lx75J9zGda4X48bZ/yrK1DMqZ8XpcSscjMYfFDTDni1uYbj88CaujlwJPStey\njMkV+bDvYF+bOnvoaKvN7jLUe+Wyw9vGQ3R0zQw53i5PwCqihZhRbj426rhb+jsfq5AXpWOHUb9v\nlzjo5XVZrvjOwz645Y/1jtgo9ucK156art2KVZT/iX3sl2AeiodiUzWmMCP8GgWdTY6iIfEm4N2l\nNJrCpnWW3+0E4Kb0v9vDmAEZZehi8CLDsOJNkz7h7OpRj3k53JeOy7CP11TSObd0b7lTnWNgc3ld\nemXJMNTjNOwOOy0L5WlodR72sV1U+Fs+7ma6YXEXNi1pJHVllzxbq76skFsXa1T/spAP/pby2aMK\n97U6M4IaDb7MvH43cHDh/GF06WACbwLuy0yvCzGjdZ3jOio6xjTs/OE0BubKOuNnRb7DPMCmgAO6\n3PvuYvlK+Xf/9P8aSfYNXWSPpaaBpMWyuqLDgG2qeG7p93UxD7wp4JjC9dfkyqXzq7Bpu53zlySZ\nkyrC+k3gshbyjzs9K37va6Bldr01DE+rLGNpg/xTNDq4jIE5YcU/kJGj02Wcw2kAqLi/71GQdRmU\nmVlGtsIMLX8t6PgNNvOpahbHPdjeJ53zLZLMCyvufT2wrHA+dI+yBnm9WFe6DfUp732uEJc3YXXo\nz9Lfmwu/nUka6Mb5LfHqy4yroc8eyZDLyeveOu+GUtzcBHwe81LeuuU82xn0nYvt3XM/thxaua/U\na4DI2/4pf/tqGZS98ZrOr6FgYylcfwVmb1g/na+J9Sk79fNxOIzJhec39vb16iSzzY5v8MRlqPfK\nZef9tgqRjsqC7h6hxBpB19JnGg3Wyf4LszsXQxtpJM/rslNpzsE+3sd0CevJwIKK+NmgcC1gC/Rf\nUbi2F9YoOjKd35fS4Ygax7nM/OguITUu0vmm6R2eXRHe+cDS9L/Lw5g8Y7LL4EWGYSUjTVwe9cCX\nsHLzmEIeOjSl8bUU8iT9jcJNDGxer0uXLE5DPRmG3WGnZU6dh9UzJ9Fw2l8KyyKsofCTiuNXTNdb\nPwEuLMh6dbqXzMFZX1LK66X7HotthvL3gu6Lcuqt0vObenflDErdhq1P3Dl/dJJ9TYXsO4F7Kq5v\nhg1A9F22JD17KdM7WPc67mPmAKN3yQGXMTBXthQ/tZZ1KeXXNVO679klH84HlhTObyDlbawjv5zu\nXp1vAe5tUg6T3PoUlhTC2WFI6TZrUBZYBTMWTGF7E5TT0iWXzu+iYNjAjKTdvtOHA3e1kH9c6Ynf\nQOvqGHeRretp5fbebpj3ikYHlzEwJ6z4BzJydHqNc8fhMwC4PPwK+afRUZXvCvnzOcDXsLbPFGZk\n+TKFmXqYUeZjhfPnpXtnDc5hHqq3pP+9nmg5y5l560pXvCbZ96ZrJ9HFkQLrr3wk3ffeQr3R+Fvi\n1VdxT5M2xShmj3jlcvK6t867Fev3zafUV2vzoMJLFCtnN2Jt15cXrtcxCjdt/xRlaxuUvfGazu/D\nNpMs37dVesbTCtfeg+1fAn5jstvbN0NnTpvdO3jiHQAZyMyRvnl/UIVKh78RlM4XAm+vqefthUph\nFCON5QZ4E6/LTsW3fjrfq8s7voFkZE3ndwDvqrhv+/Scotf1mcBv0v+XAJfWjNfymsK3Ae8onG+c\ndO1WIXsYcGf63+thnLNcxRQOgxcZhpWMNHF51GOGwX+v0Pf0FJbrgK265PVi3nMb2KjpdZkji9NQ\nj9OwO4q0TPd667xO3DVa2wz4YHrvb1GxjAbTjb2XVvzm1emqKyvybO36sqyzy/2rYwNO5wL3p2uu\neiude727cgalLsKMHaun85NSPj6/JLcq5jVVNHg1XrYkxc93aubX8rfE66nnMga2IOuJnynMw+YY\nLF8vAt7UJX7eh23U2Dk/NcXHuun8Z9gmbGW5VbD65Mo66VCRJstL4W3cYcDaV93adXOwcj2Feb/v\nW0hLl1z6fRGFDhy92yIHM22gzckDrvRkdp1X10Dr6hh30VnX08rtve3Ie5184DUG5niaewcycnR6\njXNeA4DLwy/91sqU8YrnPphpR44pZtY/n8S+h2/BvsXXML3eb9E493LsO/rFdO71ROsY7LxLoXnq\nyhxD/bXYRrl1wvdZ4Nr0v+tb4tVXuOb5Zo5i9ohXLievu+q8nIN2Znath5XT+7G+zjb0Ngp72z/F\nb1+TAVh3vGJ9/xMq7ts5PWOnwrWDCjq9xuTjcHoYZ+jMabN7B0+8AyBuA39WOWnjITq6Ziq3t0uq\nQN5WU8/bmPYEGcVIY7kB7p3WvJCKTQ7Sb4cBCwvni6moYJmuoJ9RuDYfWJz+P2MLXF4AACAASURB\nVCW942o14rVcKfwCOLl0z7oUDLSF658C/pD+93oY5xhlXAYv8gwr3jTxTitcTPdO4hNTHrwe2Jre\nRuFWDGz08LrMkcVpqMdp2B1FWqZr3jpvCv/aZjtgA0V3YfXenIp3reo0unSW8wDNlsxx1Ze98l0X\n2Yelv656K50fh8+7K2dQ6tXp3puwjsgy7Bu4NOl5R5K5Mt13aCEvNl62BPNUrtVZYfa3xOup5zIG\n5shmxE9VR/hHXeLnfGZ64m+B1Q+XYbOenpHyxk+AA5PeN2Bld4qKDoIjTVwdBqyOm+XJXri3aOC9\ngmkDiUsu/XYNcGzhfC3sWz3LewrzIrm5hfzjSk/8BlpXx7hCtomnVY739oX4vCe9xsCcsOYMZHh1\neo1zLgNA4VojD7/0W/aU8Rp1yFOZOStmS6yO65Sty7Fvws/T+Z1Y+Z3C2nYd5xqvJ1rnOR1911F/\nKTRvXZljqL+PgpGkj86DmHaOcH1LvPrSufebOYrZI165nLzuqvNyDpwDGV2eNQ+bAXMP5jTUrS7w\ntn9cBuWceMU26ltIYUNuzMv9YqyeWL1w/RjgxvS/15jsGuzL1JnTZvcOnngHfYc+cBJjlFF4kAcZ\n3i7YlNtrKK2NWiE7FxvR/FE6H8VIY7EB3tTrcoqZI6mzdBXk/lg4vwL4ccV970zP2aJw7a1Me+3u\ngXlK9t3dFjOe7Vc4/w8KFXcPudVTpfWZdO71MHYbZdK1xgYvnIaVzDTxTitcQJcpW+n3nbBG1gLs\nI9Zr+YjWDGxUeF3myOI01OM07I4iLdO5t84r1j9b0WBtsySzSsrXd6f4m9erjOToxFlXFmQb15d1\n8l2XZ7jqrXTu9e5yD0ql68dgddefC/H8aqaXy+nE38lASL97ly05Nj2vzrfkzcD1hXOvp57LGJgj\nmxE/W1ccVQOUGwHfoNQBxwZGrimkW9WxDPhAQWYX/BvJujoMKQ7/QY/NnLCyflon/+XIpetnA9+r\nGdbzSOUnM/+40hO/gdbVMa7Q2cTTKsd722V0wG8MzAmrdyAjR6fXOOcyAJTure3hV5JzTxn3HNg3\n9mBsaYfOPigbYLPHrsDa5KcD2xVkvJ5oU/iXQnMbVzzxmn67ntSnqqHzM8z83nq+JTn6vN/MUcwe\n8cq58zrOOq8g33jzPzK8RLvcs1q6r7O/T9nBauuKo1b7p0v+rDMA645XbJ+hO7Bv5VXYAO3idO+b\nSzovIS31hN+Y7B7sy9CZ02b3Dp54B32HPnASY5RReJAHGd4uTK8Heif2wTkQW6tn1/T3QKxTszDd\n1zFkjGKksdgAb+J1eUbFcWKFzJrYaPjnC9cOSXq+hxka9sTWTF0CXFCSP42aS0a0lO4bYl5xD0/n\nXg9jt1GmlO5NDV6NDSs5aYJ/WuE5wE/7pMVOWBlczuypwgM3sDFzXWOXLH4PSJdhdxRpmc69dd6s\neKXm2mYlma2wztBybGrzk6lhFG6iE2ddmc7PqDj61pdYY7Tv0hYVz3HVW+ncO73LPSjV5102BV6E\nNa62Kv3mXbZknRS3jXd2x++p5zIG5sh646eNI+Xl12FLC1yBdbR/h3W6j2N2Z7FXp7/qKH4TXB0G\n7BvzFfrsQo9N7T6J6Q6cSy5dmwe8tkY4H4J1DDtLMrjzT0Yaeg20ro5xQdbjaZXjvZ0zNdVjDMwJ\nq3cgw60z/e4xzrkMAF3C19fDr0KmyZTxM4rhHMaB3xNtRhuGZkuhuepKb7ym+49Pv30YeGgXXVuk\nvD0FvL/0W9NviVsf/jbFKGaPeOWy8jq+Os+9+R+ZAxk97p2LOWCt742LimduXXHUNSg3jteC7KOZ\nNjzehxmGZzlLAY8jrYmN35jsHuzL0JnTZvcOnrgM9V657LzXVibW0TUjNW4EFWTnYRVdL9lfM7OD\nPYqRxnLjovYyEDXjcG2s0i2ujxWY3oG+ePye2Rs5nUbFkgtDzANeD2O3Uabi962oafDq8YyuhpWc\nNME/rXB+ev72NcrgP0t5/YyKo46BrZFht/SsHNljaO4B6R44GXZaFq576rye8UqPtc263L8PVg47\nnjO1jMJ1dJblaLmuTHKz6ktnnnPVW+laToOvcV7PfE/XsiWZOr2eei5jYI7sKOInI15zNpJ1dxjG\n5cjJPxk6vQbarSuOQXta5XhvD8To0OMZOWH1DmS4dRZ+b2qccxkAeoSvp4dfn7LTyKA8jAO/J1rX\nNgz9l0Jrra6sG6+Yk8G3CuG5ATNg/yT9vaHw27cpbJzsDJdbH/6l0EYxe2ToA4UZaeLe/I8WBjJ0\ndI0vjzE5a7DPozPzHXNmWbkM9V65rPccdWaahIOGjaAK+W1TpjgcW/Pp8HT+iIp7RzHSWOyod/6v\ntQxEC3G7A2Z8ORIzelVOd2rwvLWxaVN9Pxxtyib5soex2yjT496+Bq9hpwn+aYVrYB+GvjsoY0bx\nXZ1pusLAhtPrMle2xzN7eUBmD5wMKy0rntOkzqttbKe0tlmP+zYCPo4tkzPLG8KrkxHWlYM6KNVb\n6Vpr3l118nqfsG1OGqToco9r2ZLMOMs2rgwxfQceP5jX/JYthNW9kayOrHifm8rmCyl9j5n9/all\noM0Mz9YVR52lLnK8t4dqdMgJ6zjpTM9r3QCAw8MPp0G55rP3KZedmnIujzJqtGHoshRa20eTeMXa\nkGdhg8Z3YW2pu9L5F4Dntxy2xvrwL4U2itkjQx8ozEgL9+Z/DGHQF2c7xis3zgctD/YNIbxjM3iS\nc3Q8ysQACSFsAjwcWz/z2gHrOgnbCO6hMcalXe6Zg03PPgCIMcZV0vWzgbVijC+ooec8zEtrjxDC\nGRW33BpjfHdJZk1snabzY4yva/BaQyOEsC1wNTbl/RvDks0hhLAhNsX+tzHG62rcvxHWgdkS+GCM\n8eIGutYGngtcHGO8xRfiyufuiE27f0SP25YDH4oxvrctvZNACGEH4JmYEf332Pplyweob6hpGUKY\nwjYi+1LuswatcxR1ZQjhasyT5bQY4x9zntVA5yOwRt76WOdpMeZ9tCbw1hjjJwv3XoIZhfduSfe+\n2LftyVjnuMOt2GyJk2KMVxfufyrwU8zY8D+YF9DNmFfVGsBDgadjnlZrYINLM+rMEMJmWIfuodhA\n0uL0jMtijH+vCONOwLuA/4ox/qLHuwTMK+CJMcZn1o+F9mgjfmroOApb1moVR/jWBzaMMd4QQjgF\nS/t1Y4zLaug8PsY4p6lOL+n7uXGM8YZhyOXKVjzrMGypoaVY3J0VQpiPbRq1RrrtXmzjq5OTzNYV\nj1oeY7yx9OyNsI78d2OMp+eGddiEENYBNsG8hSvb3o5nbofNOrktxnh9G88U+YQQ5mKDnNfFGBcV\nru8D/DDGeLvjmVNYnfptzPB1fgPZjbGB2Xsw48mSEMIGmKH1WZjR9dfYbLhrCvpqt2FCCA8rl9m2\n6RavLT07AP+KGUG3wL7Ti4A/YWnW2rsN45u5MtG0/eOVDSHchy0Z1vf7EEI4CPhUjHHN5m/kw9uO\naav9Mwy5XNnScx6NOb8V+6cfiTF+uXTf44B/9MtLbVJuN4UQ5mEeuV/oI/cQrJ9xaozxlMGHtGVG\nbZV+IB+Yp8+nmfYKW46N3m4yQJ1DH2lsELaqZSA2BPbHpgevma49GPPSuwLzOPwQXTaJcsTP4di0\n7G7HCSmtPte51oZsjXhxexgPOU/33ZzD+55ketSXnrVWyqeetYNcsuOmMyMP9NXZZlrWCM8ZDH8d\nv4Hq7FJXXp3q7Mc0fFbRO/nnmNEs22MdW9+tVx4oe3ddhsO7ixrevum+NVL+KnslLsE2IOlMhV0M\n7FuSbbxsSZL7F+CHzPT8Lh7LMa+Bxw8gj2yGrR95MGaoOzid9/WUayrrjZ8G7+L22k2yneU13BvJ\nNtS5NgXPHmxQ9pKUt67H6rhZZQPbx2F5rlyurPMd90zp/DfMs2cZ5kW4DFsm6BCml8xZDuzcdp4v\nhKWrZ/K4HVibqDxzZ3esvi/P8OnZrm8hLM8FTgROwWYDDvy7OiidOD1vM3VOYYMiXwX2cMjeUUjv\n67BZUpXT5FsKa86meGtjG8btzsy9RXbHloH5AGaozl7iqYV33QUbnO727VqGzaBdr0WdA/1mrgwH\nGe0fjywZm/8NKT5c7RivXEHW8313yWXqHLpHdFknA243ZYZ1bU/8eOUqnzXMF560A+tsTWHrI57N\n9OY432zwjBdgHkX7YSMzVffMA04vXdsUm7Y8a7p1DZ1uWYeeBYWPwBWYAeBypjsfd6b/rwLWKck3\nNih3+fj0PNqQ7RMPLkMrA1jqggEZvuu8J+Zl81Qqlivpcv9jgP9XurY7NkW909BYAvwA+Jc2ZMdN\nZ4+462nYzdXZNC2TjMvoWZBvVG/l6vPozDkK9Uoj426SOY2ZDfCF2PrPT+kjewhWl14EPDdd2z6d\nL0vPu5IuUzZT/Mxrkg+S3L7YFMyFSUfnuCmFe9agAta4W44tdfIQbO2tFwO3kDbdAZ6ErWW9FHhS\nxTOaLFvyBMzTaCHm4Tgfm2q6W/o7P8X7onTs0FI+GGpHLCN+dsHWkK5zfJa8TlEry0Dg6DBggx/3\nMT3wcQvT07jnVshN5ci1INv4HdP5D4E/kNph2FqmC7EBlzmF+9YBbgTObiE9DsPaiFdjXo1g5aoz\nzXwK846steFkkncblLH1Kn9Ll81Kne84wzgHPAX7tt6NGaqOxaavd671W26ur5E1lZlTC+frABdQ\nXSd8rsY7rHQ6yTPQepdycBt20/37Ak/DvhudJd6WYZ5ne5O5PF5J39b4l0LbFPhL4T0vwAaJT61I\ny59jM1A7slnGZMyh6RnYuvAfSzpPwgY2q5aI6WxgfCvmpPWfWD25BBvEOhT4bgrrxVSsRYwNoj4f\n3wBs7W9mhc6hDPp65Mho/3hlydxssEH+XmFIxNmO8co5wjoqQ7RX57ANrUWnAXe7KTMMuzJkpwF3\nWIeZOJN2YNNnryKNPmIfs89gH/lKA29BdlXM4FL8uN4OvLJLhuhURG7v5BxZZ/yciH2Yj8A2wroe\na/zcw8wNEvZLYTm6cM1lUMYabIuSzl1SoSse+yaZYzrXCjpdsgzOwzjHa7fb7sluw7f3Pb35LuWV\nLxXOn43tZLwUm7r1FcwAtBxrfDwmV3acdJJnwPbqzKl/vEZPb/5x6RtFXVkIb2PjLgWjA7a29nHA\nXwvv/xusA/Cgktxe6fe7sDUL78U6rP/A6sLvYJ6592DftJ0Lsp34uZ9pg26dNMnx9r2GCmMC9m25\nl7R2JObF/mcyjVYpnNfSZ1AO83L+C7ZsS9XvK3VHLDO/NjmKjeGhdKhK4fUad7+EraNerAMPTc+5\nloKhog25TJ05xuSbgHeX8tMU1WvRnwDcVCPOe61FnOWZzGAMyo/A0ebC2lvzgG26lJOiUfg8rK2/\nbem+HVO6fS6du42s2KydEwvnnb0HPoe1XR+NLTvw9XT9HeOmk3wDbWODMhmG3Yp8sC62CesvC+/w\nN8wg9qjCfaPwiP5weqf3Y/XOLVg9fD/Wr3siZoztpPG/Jzm3MTnJ70JDj1+mv9MbFK4FbEbJFYVr\neyX5IwvXhj4TKEenV9YjR0b7xyvLkDYbZKYh0dWO8coV8nnj9o9XLle2Ybx65NwexkWdZLS5Gupc\n4bnLCJwGsuqfNh6io2vGuAt4V+na9ilh+3lovTHd9wWswfxGrFEzReGjVZGR3N7JmbIer92rsHUu\nO+cvSfpmbbyEbfh0WeHcZVDGOiFnY42X/6I0XYgehlavLM0/Dp20HPpSF+QZzb3v6cp32Mj/4YXz\ny7FGQbkz9QTsQ3B2ruw46STPgO3VmVOHTOEzenrzj0tfpk63dzKFTiPNjLsr5ArX5gDPwdZ+XpLu\nuRf4MskLDvgx5hm4AdaJOj3li2uZuazFNpih+PstxM9xOL19scbTrI0LU1xNUZimCbwHW6ezURqU\nnrsQeHvNe98OLCpdG4uOWEb83IfVG0fUOM6FrFk52V4S+A2tfyEZPUrPezr2Pb2OtDFiG3KZOnMM\n0UuA/Qvnm6a4f3ZFOOYDSwvnjQ20ZHgm4zQoY232RYW/5ePu9NzFnXsKOl3LQDCzXp+T0uKYLnn0\nZGBB+t9lZC28Z2fD3oA5UJzeRed3gT+Mm870f46BtrFBuZiW6byWYbdKtvTbY4GPMD0oOgVcVJBz\neUR7D2wd3qKhfu8Ujlmb+GLGuT+l/13G5CTr8vhN6fiuinB1+uLFdu+ZwG/S/0OfCZSj0yubIedu\n/+TIpmsD3WyQmYZEVzvGK1co043bP165TJ27MBxjchtGc3ebK13bleYzyYbuNJCV99t4iI6uGXmK\n2d5Mm6Trz+wj+2tKnTKsgdEZJTumcL2YkXK8k12y+L127wLeUHjOlumeKoPs4cBdhXO3QTld2wvr\nSNwEvLxwva/3bVNZ/B7GTSvp7KUuyDOae9/Tm+/uI3VSsRHkqWJ+Kt17LLbRY5bsOOkkz4Dt1ZlT\n/xQ7x1tR3+jpzT8ufS3onMLnnTyr00g9427Xzmb6/cFMG0iKjb1bsQ2jOvc9Pv3+xopnHM/MvO6N\nH7e3L+bNfEKF7M4p3DsVrh0ELKkT76Vn7UkyZGB13dtqyr2Nmd+vseuIOeLnEuDSmnIzPEjI6FB5\nwprOvYbWxcABXXQ8EfP6vB6brp0tl6kzxxB9GzONfBuncrVbxfMOA+4sxHOnHdjEQOv2TMZpUE7P\nXwRciHmflY9fpXt+n84vLDxrRj1LzWUgmPkdWj+d79Ulbd9AMrbjNLIW6oI3pP/XSzpf0kX2UFJd\nOU46K9KjqYG2sUG5rLP0W1fDbj/Zwj2rY2XnXOD+gtxA1yJmdl15N3Bw4fxhdO8XvAm4L/3vMian\nc5fHL1ZXvqni+Z2+zDMK1+YDi0v63IOoNFz+MUenVzZDLqf945bNyMO74DMkutoxXrl0PgpDtFdn\nU1uDd/3jNozmOW0ur8fv0J0GsspJGw/R0TUjV3XiuzakS/fdTsW0NmAVbDRzCtutspyRcryTXbL4\nvXYXUfDs6hU32JTaJaWwugzKhevrYZ2F+1N4t6HmkgxNZPF7GA99qYuCfGOjecZ7evPdDaTBEcxw\nuRx4WZd73wLcmys7TjrJM2B7debUP16jpzf/uPS1oNPrnew17vbtbBae8VRSBw2rvw8s/LZFetYL\nK+ReDyxrIX7c3r7AF1Nczitc2wzzGrqDwog+Vu/dWCdOSuEoTiv8EWbEnttHZi7W6fpR4doDsiNW\nip9TUhlaraZcsQHu7lB5wprOvYbWBcB7e+jZKckuSPkuSy5TZ06n6BfAySWZdSkYWQvXP8W0cc5r\noM3xTHYZlIEPYgalb1G9PmmnDfPSit/KRsi6y0CU5RZSsSFn+u0wYGHhvsZG1nT+c+ArhfP/o8uy\nZSlO/j5uOsvxWrqvkYGW+ks5uAy7dWVLz3lYQW6gaxEzu668jcK3BDOYTJFmAZRk3wnck/53GZPT\nudfj9wrgx13CNUXBeI45AXQGs3IGYL3LPw590DdDLqf945bNyMNeQ6KrHeOVS+ejMER7dXqNybvg\nX+rCq3MB/jaX1+N36E4DWeWkjYfo6JrBpjDPgOK0/aPT9f+mYlp/QfZ2uhtw5mCeB1PYNJx9Cxlp\nCr93sksWp9cu9lE4tvDbWtjU6lmbEmGeaDcXzt0G5Yrf52FT1O7Bpuf1NQp7ZGnuYTz0pS5K97iM\n5o739Oa7U7HRsnXT+c+AcyruWwWbbn5lruw46STPgO3VmVv/eI2envzj0teWTpp7J3uNu406m4Vn\nXAN8rHD+vPSsoyvu/RRwSwvx4/b2xdb7vCPl86swb+XFSe7NpeddAnzDESfFxnBnOuudmBf0gdiA\nwq7p74FYY3Zhuq9orH5AdsRK8bMH5sXVdyNUrGO/X+Hc3aHyhDWdL8BnaD0H+GkfXTthHYrlTNdb\nLrlMna53TL/9BwXP2B7PWB0rx59J514DrcszOZ3nGJR3wOqHu7BOZdFw3avNVazbmywDscIIUfh/\nVtu5IPfH9L/LyJrOX4u16/ZN50djdeduJbkXY3XoWeOmkxrfPRwGWvov5dDYsOuR7SZHA4/oBjrK\ndeVF2GzW1dP5SSktzy/JrYotHdXp87mMyenc6/F7SPr9e5jT0p7Y0hNLgAtKzzqNZBgjbwDWu/zj\n0Ad9M+Ry2j9u2QZ5dsY6tPgNia52jFcunY/CEO3V6TUmu4z0mTpz2lxej98FDNlpIOfIfoCOnpmr\naaYvFtDLqZhSU/i9aBi+gh5eYdT3TnbJ4vTaxYyW36sZl+dRaHCQYVDu8vzVUuXRWeNulidIG7I4\nDK0McamLLs9obDRv8p4Z+W4LrPK+DJum9Qys0fkTrFHxfGy65SXpWfNzZcdJJ3kGbK/OVuufHvf2\nNHrWzD8ufW3rpL53srfTeAa+RvUnsY7YW7CO8zWYB91CZs4AeXkK9xdbiJ8sb1+sk9kJY2ea1yyv\nO+BxpI3csKniF9Q8rmNmQ3Ee1jnu9V3/NQUP5yQ3Nh2xnPjxHvg7Yjlp6TW0zk/pvH0f2R2BfzLd\n6HfJZep0d4oapN2GmGHv4encZ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6ojWTgKs7AHiVlEFIObUZPgJK460ZW4SEBBzCiC0aAM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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10deae390>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_3TC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "selected_OLS = sm.OLS(Y, X[:,lasso_3TC.active]).fit()\n",
    "OLS_lower, OLS_upper = np.asarray(selected_OLS.conf_int()).T\n",
    "selective_lower = lasso_3TC.intervals['lower'] \n",
    "selective_upper = lasso_3TC.intervals['upper'] \n",
    "\n",
    "selective_intervals = ([['Mutation', 'OLS Lower', 'OLS Upper', 'Selective Lower', 'Selective Upper']] + \n",
    "                       zip(active_3TC, OLS_lower, OLS_upper, selective_lower, selective_upper))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11206cf10>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%capture\n",
    "fig_select = pyplot.figure(figsize=(24,12))\n",
    "ax_select = fig_select.gca()\n",
    "ax_select.bar(np.arange(1, len(active_3TC)+1)-0.5, selected_OLS.params, color='grey', alpha=0.5)                                                          \n",
    "ax_select.set_xticks(range(1, (len(active_3TC)+1)))\n",
    "ax_select.set_xticklabels(active_3TC, rotation='vertical', fontsize=18) \n",
    "ax_select.set_xlim([0, len(active_3TC)+1])\n",
    "ax_select.set_title(r'Selective' % sigma_3TC, fontsize=50)\n",
    "ax_select.set_ylabel('Parameter values', fontsize=30)\n",
    "ax_select.errorbar(np.arange(1, (len(active_3TC)+1)), selected_OLS.params, \n",
    "                yerr=[selected_OLS.params - OLS_lower, \n",
    "                      OLS_upper - selected_OLS.params],\n",
    "                capsize=10,\n",
    "                capthick=5,\n",
    "                fmt=None,\n",
    "                label='OLS (no coverage guarantees)',\n",
    "                elinewidth=3,\n",
    "                ecolor='k')\n",
    "ax_select.legend(fontsize=30, loc='upper left', numpoints=1)\n",
    "ax_select.plot([0, len(active_3TC)+1], [0,0], 'k--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10fb5e690>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%capture\n",
    "ax_select.errorbar(np.arange(1, (len(active_3TC)+1)), selected_OLS.params,\n",
    "                yerr=[selected_OLS.params - selective_lower, \n",
    "                      selective_upper - selected_OLS.params],\n",
    "                capsize=10,\n",
    "                capthick=5,\n",
    "                fmt=None,\n",
    "                label='Selective',\n",
    "                elinewidth=3,\n",
    "                ecolor='r')\n",
    "ax_select.legend(fontsize=30, loc='upper left', numpoints=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BWh3fbNi/oLZ/MiOGd2LxkV9/pAQ91pnG87Jjrb3P9FF+YVsfP9RQJoDv1sq8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KOBn9OqEncDPp9ka3v532xzWuJtytndz8/NMPYUWkWsmicAR1XV6wCS/D+WJ9UPGBj3zSSbAbvS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\nSZIkSRPm/wfytUn2CE2hBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0789d0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_select"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<font class=\"emphred\">Some intervals are long...</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Setup for selective inference \n",
    "\n",
    "\n",
    "\n",
    "* <font class=\"emphred\">Data</font> $y \\sim F$.  \n",
    "    - <font class=\"emphblue\">We have no model for $F$ at this point!)</font>\n",
    "\n",
    "* <font class=\"emphred\">Set of questions</font> ${\\cal Q}$ we might ask about $F$. \n",
    "    - Each $Q \\in {\\cal Q}$ has a corresponding model.\n",
    "\n",
    "* <font class=\"emphred\">Use some algorithm</font> to generate questions \n",
    "$$\n",
    "\\widehat{\\cal Q}(y) \\subseteq {\\cal Q}.\n",
    "$$\n",
    "\n",
    "* Test some or all of the hypotheses suggested by $\\widehat{\\cal Q}(y)$.\n",
    "\n",
    "* Intervals can be formed by inverting tests.\n",
    "\n",
    "###  [arxiv.org/1410.2597](http://arxiv.org/abs/1410.2597)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# What are the questions?\n",
    "\n",
    "## Linear regression: saturated model\n",
    "\n",
    "* The model is\n",
    "$$\n",
    "M_{\\text{sat}} = \\left\\{N(\\mu, \\sigma^2 I): \\mu \\in \\mathbb{R}^n\\right\\}\n",
    "$$\n",
    "with $\\sigma^2$ considered known and fixed.\n",
    "\n",
    "* Questions are\n",
    "$${\\cal Q} = \\left\\{(j,E): E \\subset \\{1, \\dots, p\\}, j \\in E\\right\\}.$$\n",
    "\n",
    "* These are the OLS functionals, i.e. <font class=\"emphblue\"> partial regression coefficients </font>:\n",
    "$$\n",
    "\\beta_{j|E}(\\mu) = e_j^TX[:,E]^{\\dagger}(\\mu), \\qquad (j,E) \\in {\\cal Q}.\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference  for LASSO\n",
    "\n",
    "* Our inference is based on the <font class=\"emphred\">selective model</font>\n",
    "$$\n",
    " \\left\\{ {\\mathbb{P}}\\left( \\ \\cdot \\  \\big\\vert (\\hat{E}, z_{\\hat{E}}) = (E, z_E) \\right)\n",
    ": \\mathbb{P} \\in M_{\\text{sat}} \\right\\}.$$\n",
    "\n",
    "\n",
    "* Can derive <font class=\"emphred\">exact pivots</font> for $\\beta_{j|E}(\\mu)$ or any $\\eta^T\\mu$ under this model.\n",
    "\n",
    "\n",
    "* Report tests and intervals based on pivots.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Selective hypothesis tests\n",
    "\n",
    "* Under $\\mathbb{Q}_{E,z_E}$, can construct tests $\\phi_{(j|E)}$ of \n",
    "$$\n",
    "H_{0,(j|E)} : \\beta_{j|E}(\\mu) = 0.\n",
    "$$\n",
    "\n",
    "* Tests  satisfy <font class=\"emphred\">selective type I error</font> guarantee\n",
    "$$\n",
    "\\mathbb{Q}_{E,z_E}(\\phi_{j|E})  \\overset{H_{0,(j|E)}}{\\leq} \\alpha.\n",
    "$$\n",
    "\n",
    "* <font class=\"emphred\">Conditional control implies marginal control.</font>\n",
    "\n",
    "* We report results $\\phi_{(j| \\hat{E})}(y), j \\in \\hat{E}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "selective_pvalues = pandas.DataFrame({'Mutation':active_3TC, 'Naive OLS':selected_OLS.pvalues, \n",
    "                                      'Selective':[p for _, p in lasso_3TC.active_pvalues]})\n",
    "pvalue_table = itable.PrettyTable(selective_pvalues, tstyle=itable.TableStyle(theme=\"theme1\"), center=True)\n",
    "signif_select = selective_pvalues['Selective'] < 0.05\n",
    "signif_OLS = selective_pvalues['Naive OLS'] < 0.05\n",
    "pvalue_table.set_cell_style(cols=[1], rows=np.nonzero(signif_OLS)[0], color='red', font_weight='bold', format_function=lambda p: \"%0.3f\" % p)\n",
    "pvalue_table.set_cell_style(cols=[1], rows=np.nonzero(~signif_OLS)[0], format_function=lambda p: \"%0.3f\" % p)\n",
    "pvalue_table.set_cell_style(cols=[2], rows=np.nonzero(signif_select)[0], color='red', font_weight='bold', format_function=lambda p: \"%0.3f\" % p)\n",
    "pvalue_table.set_cell_style(cols=[2], rows=np.nonzero(~signif_select)[0], format_function=lambda p: \"%0.3f\" % p)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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       "<center><table style=\"color: black;border: 1px solid black;\"><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;font-weight: bold;background-color: lightgray;\">Mutation</td><td style=\"color: black;font-weight: bold;background-color: lightgray;\">Naive OLS</td><td style=\"color: black;font-weight: bold;background-color: lightgray;\">Selective</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P62V</td><td style=\"\">0.137</td><td style=\"\">0.369</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P65R</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P67N</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P69i</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P75I</td><td style=\"\">0.484</td><td style=\"\">0.553</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P77L</td><td style=\"\">0.270</td><td style=\"\">0.469</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P83K</td><td style=\"color: red;font-weight: bold;\">0.003</td><td style=\"\">0.051</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P90I</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.014</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P115F</td><td style=\"color: red;font-weight: bold;\">0.014</td><td style=\"\">0.168</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P151M</td><td style=\"color: red;font-weight: bold;\">0.008</td><td style=\"\">0.081</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P181C</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.002</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P184V</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P190A</td><td style=\"\">0.063</td><td style=\"\">0.309</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P215F</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.016</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P215Y</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P219R</td><td style=\"color: red;font-weight: bold;\">0.001</td><td style=\"\">0.099</td></tr></table></center>"
      ],
      "text/plain": [
       "<itable.itable.PrettyTable at 0x112173f50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvalue_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference for debiased LASSO\n",
    "\n",
    "On the event $(\\hat{E}, z_{\\hat{E}})=(E,z_E)$:\n",
    "\n",
    "1. Recall $$\\hat{\\beta}_E = (X_E^TX_E)^{-1} X_{E} ^T y - \\lambda \\left(\\frac1n X_E^TX_E \\right)^{-1} z_E.$$\n",
    "\n",
    "2. The debiased estimator is affine in $y$. In particular:\n",
    "$$\n",
    "\\hat\\beta^d = \\frac1n \\Theta X^T y + (I - \\Theta \\hat \\Sigma ) \\begin{bmatrix}(X_{E}^T X_{E} )^{-1} X_{E} ^T y - \\lambda \\left(\\frac1n X_{E} ^T X_{E} \\right)^{-1} z_{E}\\\\ 0 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "3. Define the debiased target\n",
    "$$\n",
    "\\beta^d(\\mu) = \\frac1n \\Theta X^T \\mu + (I - \\Theta \\hat \\Sigma ) \\begin{bmatrix}(X_{E}^T X_{E} )^{-1} X_{E} ^T \\mu - \\lambda \\left(\\frac1n X_{E} ^T X_{E} \\right)^{-1} z_{E}\\\\ 0 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "4. The selective inference framework described provides exact inference for \n",
    "any coordinate of $\\beta^d(\\mu)$.\n",
    "\n",
    "5. Report intervals for $\\beta^d_j(\\mu), j \\in \\hat{E}_{\\lambda}$.\n",
    "\n",
    "6. Small widening of intervals provides coverage of $\\beta^*_j$ under same assumptions appearing in other debiasing\n",
    "literature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference for debiased LASSO\n",
    "\n",
    "<img src=\"montanari_ci.png\" width=\"600\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference\n",
    "\n",
    "## The selected model\n",
    "\n",
    "* In [arxiv.org/1410.2597](http://arxiv.org/abs/1410.2597) we allowed the questions $Q \\in {\\cal Q}$ to include a model to consider the\n",
    "<font class=\"emphblue\">selected model</font>.\n",
    "\n",
    "* In the regression setting, with $\\sigma^2$ known one version of the selected model is\n",
    "$$\n",
    "M_{k,E} = \\left\\{N(X_E \\beta_E, \\sigma^2 I): \\beta_E \\in \\mathbb{R}^E\\right\\}.\n",
    "$$\n",
    "\n",
    "* With $\\sigma^2$ unknown \n",
    "$$\n",
    "M_{u,E} = \\left\\{N(X_E \\beta_E, \\sigma^2 I): \\beta_E \\in \\mathbb{R}^E, \\sigma^2 > 0 \\right\\}.\n",
    "$$\n",
    "\n",
    "* What's the difference between these models and $M_{\\text{sat}}$?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference\n",
    "\n",
    "## The selected model\n",
    "\n",
    "\n",
    "* <font class=\"emphblue\">For LASSO at a fixed $\\lambda$, tests and intervals for OLS parameters of $M_{\\text{sat}}$ are identical to $M_{k,E}$</font>\n",
    "\n",
    "* Changing variables $\\hat{E} \\cup \\{P65R\\}$ yields different tests and intervals.\n",
    "\n",
    "* Inference for $\\beta^d(\\mu)$ does not make sense for $M_{\\text{sel},E}$.\n",
    "\n",
    "* Forward stepwise has very different results as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why use the selected model?\n",
    "\n",
    "* <font class=\"emphblue\">Short answer: power.</font>\n",
    "\n",
    "* Distribution for inference under $M_{\\text{sat}}$ for $\\beta_{j|E}(\\mu)$ can be realized as a conditional\n",
    "distribution for $\\beta_{j|E}$ under $M_{k,E}$ (for any algorithm $\\hat{\\cal Q}$).\n",
    "\n",
    "* <font class=\"emphred\">Conditioning on more than needed sacrifices power.</font> [arxiv.org/1410.2597](http://arxiv.org/abs/1410.2597)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why use the selected model?\n",
    "\n",
    "## Model selection with the  LASSO$^\\frac12$\n",
    "\n",
    "\n",
    "- When $p \\geq n$ we cannot use the full model to estimate $\\sigma^2$.\n",
    "\n",
    "- Square-root LASSO [Belloni et al. (2011)]\n",
    "$$\n",
    "\\hat{\\beta}_{\\lambda} = \\text{argmin}_{\\beta \\in \\mathbb{R}^p} \\|y-X\\beta\\|_2 + \\lambda \\|\\beta\\|_1\n",
    "$$\n",
    "does not require $\\sigma^2$.\n",
    "\n",
    "- Exact inference for $\\beta_E$ under $M_{u,E}$ goes through.\n",
    "\n",
    "#### [arxiv.org/1504.08031](http://arxiv.org/abs/1504.08031)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why use the selected model?\n",
    "\n",
    "## Dominating sample splitting \n",
    "\n",
    "* Split data into two groups \n",
    "$$\n",
    "y = \\begin{pmatrix}\n",
    "y_1 \\\\\n",
    "y_2\n",
    "\\end{pmatrix}, \\qquad\n",
    "X = \\begin{pmatrix}\n",
    "X_1 \\\\\n",
    "X_2\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "* <font class=\"emphblue\">Build a model with the LASSO</font> $\\hat{E}_1(y_1)$. \n",
    "\n",
    "* Form usual $Z$-statistics based on\n",
    "$$\n",
    "\\hat{\\beta}_2 = X_{2,\\hat{E}_1(y_1)}^{\\dagger}y_2.\n",
    "$$\n",
    "\n",
    "* Distribution for inference are conditionals of <font class=\"emphblue\">selective model</font>\n",
    "$$\n",
    "M^*_{k,E} = \\left\\{ \\mathbb{P}_{\\beta_E}( \\  \\cdot \\ \\vert (\\hat{E}_1, z_{\\hat{E}_1})=(E, z_{E})): \\mathbb{P}_{\\beta_E} \\in M_{k,E} \\right\\}.\n",
    "$$\n",
    "\n",
    "* <font class=\"emphred\">Data splitting conditions unnecessarily on $X_{1,E}^Ty_1$.</font>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jonathantaylor/anaconda/lib/python2.7/site-packages/selection/constraints/affine.py:923: UserWarning: bound violation\n",
      "  use_random_directions=use_random_directions)\n"
     ]
    }
   ],
   "source": [
    "active_carve, selective_pval_carve, split_pval = [], [], []\n",
    "carve_results = data_carving(Y, X, lam_frac=1., sigma=sigma_3TC, burnin=2000, ndraw=8000, split_frac=0.9,\n",
    "                            compute_intervals=False, splitting=True)[0]\n",
    "for result in carve_results:\n",
    "    active_carve.append(NRTI_muts[result[0]])\n",
    "    selective_pval_carve.append(result[1])\n",
    "    split_pval.append(result[3])\n",
    "\n",
    "carve_pvalues = pandas.DataFrame({'Mutation':active_carve, \n",
    "                                  'Data splitting':np.maximum(split_pval, 0), \n",
    "                                  'Data carving':np.maximum(selective_pval_carve, 0)})\n",
    "carve_pvalues = carve_pvalues.reindex_axis(['Mutation', 'Data splitting', 'Data carving'], axis=1)\n",
    "carve_pvalue_table = itable.PrettyTable(carve_pvalues, tstyle=itable.TableStyle(theme=\"theme1\"), center=True)\n",
    "signif_carve = carve_pvalues['Data carving'] < 0.05\n",
    "signif_split = carve_pvalues['Data splitting'] < 0.05\n",
    "carve_pvalue_table.set_cell_style(cols=[1], rows=np.nonzero(signif_split)[0], color='red', font_weight='bold', format_function=lambda p: \"%0.3f\" % p)\n",
    "carve_pvalue_table.set_cell_style(cols=[1], rows=np.nonzero(~signif_split)[0], format_function=lambda p: \"%0.3f\" % p)\n",
    "carve_pvalue_table.set_cell_style(cols=[2], rows=np.nonzero(signif_carve)[0], color='red', font_weight='bold', format_function=lambda p: \"%0.3f\" % p)\n",
    "carve_pvalue_table.set_cell_style(cols=[2], rows=np.nonzero(~signif_carve)[0], format_function=lambda p: \"%0.3f\" % p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<center><table style=\"color: black;border: 1px solid black;\"><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;font-weight: bold;background-color: lightgray;\">Mutation</td><td style=\"color: black;font-weight: bold;background-color: lightgray;\">Data splitting</td><td style=\"color: black;font-weight: bold;background-color: lightgray;\">Data carving</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P41L</td><td style=\"\">0.155</td><td style=\"color: red;font-weight: bold;\">0.038</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P62V</td><td style=\"\">0.555</td><td style=\"\">0.131</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P65R</td><td style=\"\">0.261</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P67N</td><td style=\"\">0.173</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P69i</td><td style=\"\">0.479</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P77L</td><td style=\"color: red;font-weight: bold;\">0.025</td><td style=\"\">0.174</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P83K</td><td style=\"\">0.876</td><td style=\"color: red;font-weight: bold;\">0.015</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P115F</td><td style=\"\">0.068</td><td style=\"color: red;font-weight: bold;\">0.015</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P116Y</td><td style=\"\">0.220</td><td style=\"\">0.180</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P181C</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P184V</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P215F</td><td style=\"color: red;font-weight: bold;\">0.000</td><td style=\"color: red;font-weight: bold;\">0.004</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P215Y</td><td style=\"\">0.284</td><td style=\"color: red;font-weight: bold;\">0.000</td></tr><tr style=\"color: black;border: 1px solid black;\"><td style=\"color: black;border: 1px solid black;\">P219R</td><td style=\"\">0.090</td><td style=\"\">0.051</td></tr></table></center>"
      ],
      "text/plain": [
       "<itable.itable.PrettyTable at 0x111ffa490>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carve_pvalue_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Dominating sample splitting\n",
    "\n",
    "<img src=\"data_carving.png\" width=\"450\">\n",
    "\n",
    "\n",
    "#### [arxiv.org/1410.2597](http://arxiv.org/abs/1410.2597)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Selective inference\n",
    "\n",
    "* A selection algorithm returns a model and a statistical task (i.e. a hypothesis test or confidence interval).\n",
    "\n",
    "* Examples of algorithms we've considered:\n",
    "    - LASSO with fixed $\\lambda$\n",
    "    - LASSO$^\\frac12$ with fixed $\\lambda$\n",
    "    - Data splitting, using LASSO with fixed $\\lambda$ on some subset of the data.\n",
    "    \n",
    "* Examples of models we've considered (only for linear regression):\n",
    "    - $M_{\\text{sat}}$: saturated model\n",
    "    - $M_{k,E}$: selected model with known variance\n",
    "    - $M_{u,E}$: selected model with unknown variance\n",
    "    \n",
    "* Examples of statistical tasks:\n",
    "    - Selective hypothesis tests.\n",
    "    - Selective intervals.\n",
    "    \n",
    "* <font class=\"emphblue\">What about estimation?</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Selective inference\n",
    "\n",
    "## Estimation\n",
    "\n",
    "- Drop the losers designs (Sampson & Sill, 2008)\n",
    "\n",
    "- Effect size estimation in neuroimaging (Benjamini & Rosenblatt, 2014)\n",
    "\n",
    "- If the selected model is an exponential family, selective pseudolikelihood can be used.\n",
    "\n",
    "<img src=\"variance_plot.png\" width=\"450\">\n",
    "\n",
    "- <font class=\"emphblue\">For some selection algorithms selective UMVU estimation is possible!</font> ["
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference\n",
    "\n",
    "## Randomized response\n",
    "\n",
    "- Typically, for data splitting the split is *random*, so really $y_1=y[\\omega], y_2=y[-\\omega]$ where\n",
    "$\\omega$ is the random split.  \n",
    "\n",
    "- If we don't condition on $\\omega$ the selected model is really\n",
    "$$\n",
    "\\bar{M}_{k,E} = \\left\\{N(X_E \\beta_E, \\sigma^2 I) \\times \\mathbb{Q}: \\beta_E \\in \\mathbb{R}^E\\right\\}.\n",
    "$$\n",
    "where $\\mathbb{Q}$ is the uniform distribution over splits.\n",
    "\n",
    "- In this case the <font class=\"emphred\">selective model</font> is equivalent to the exponential family\n",
    "$$\n",
    "\\left\\{F^*_{E,z_E}: \\frac{dF^*_{E,z_E}}{dF_E}(y) \\propto \\mathbb{Q}\\left(\\omega: (\\hat{E}_1(y,\\omega), z_{\\hat{E}_1(y,\\omega)}) = (E,z_E) \\right), F_E \\in M_{k,E} \\right\\}\n",
    "$$\n",
    "\n",
    "- Each $y$ is weighted by the proportion of splits that choose $(E,z_E)$.\n",
    "\n",
    "### [arxiv.org/1507.06739v1](http://arxiv.org/abs/1507.06739v1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Selective inference\n",
    "\n",
    "## Randomized response\n",
    "\n",
    "- A simpler randomization is to add some noise \n",
    "$$\n",
    "y^*(y,\\omega) = y + \\omega, \\qquad \\omega \\sim N(0, \\gamma^2 I).$$\n",
    "\n",
    "- In this case the <font class=\"emphred\">selective model</font> is the exponential family\n",
    "$$\n",
    "\\left\\{F^*_{E,z_E}: \\frac{dF^*_{E,z_E}}{dF_E}(y) \\propto \\mathbb{Q}\\left(\\omega: (\\hat{E}(y+\\omega), z_{\\hat{E}_1(y+\\omega)}) = (E,z_E) \\right), F_E \\in M_{k,E} \\right\\}\n",
    "$$\n",
    "\n",
    "- Saturated model also makes sense here.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1150c8690>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%capture\n",
    "active_add, selective_pval_add, selective_interval_add, split_pval, split_interval = [], [], [], [], []\n",
    "additive_results = additive_noise(Y, X, lam_frac=1., sigma=sigma_3TC, burnin=5000, ndraw=20000, perturb_frac=0.2)[0]\n",
    "for result in additive_results:\n",
    "    active_add.append(NRTI_muts[result[0]])\n",
    "    selective_pval_add.append(result[1])\n",
    "    selective_interval_add.append(result[2])\n",
    "\n",
    "\n",
    "selective_interval_add = np.array(selective_interval_add).T\n",
    "split_OLS = np.dot(np.linalg.pinv(X[:,[r[0] for r in additive_results]]), Y)\n",
    "\n",
    "fig_add = pyplot.figure(figsize=(24,12))\n",
    "ax_add = fig_add.gca()\n",
    "ax_add.bar(np.arange(1, len(active_add)+1)-0.5, split_OLS, color='grey', alpha=0.5)                                                          \n",
    "ax_add.set_xticks(range(1, (len(active_add)+1)))\n",
    "ax_add.set_xticklabels([v[1:] for v in active_add], rotation='vertical', fontsize=18) \n",
    "ax_add.set_xlim([0, len(active_add)+1])\n",
    "ax_add.set_title(r'Intervals after adding $N(0,\\sigma^2/5)$', fontsize=50)\n",
    "ax_add.set_ylabel('Parameter values', fontsize=30)\n",
    "ax_add.legend(fontsize=30, loc='upper left', numpoints=1)\n",
    "ax_add.plot([0, len(active_add)+1], [0,0], 'k--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "ax_add.errorbar(np.arange(1, (len(active_add)+1)), split_OLS,\n",
    "                yerr=[split_OLS - selective_interval_add[0],\n",
    "                      selective_interval_add[1] - split_OLS],\n",
    "                capsize=10,\n",
    "                capthick=5,\n",
    "                fmt=None,\n",
    "                elinewidth=3,\n",
    "                ecolor='r')\n",
    "ax_add.legend(fontsize=30, loc='upper left', numpoints=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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M2r6uBNZocCwO6tKvQ+bZ5gZKMP2Eer96bLMDcGKXtj40QF/37rJ9z7qgwH922eYzwMZ9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\npZRSSjXyv3/lYtSVzCttAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112061fd0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_add"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<font class=\"emphblue\">The intervals are not so long...</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Randomized response\n",
    "\n",
    "<img src=\"additive_power.png\" width=\"600\">\n",
    "\n",
    "Additive noise beats conditioning on split..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Randomized response\n",
    "\n",
    "- Lower bound\n",
    "on leftover Fisher information $\\implies$ intervals of bounded length.\n",
    "\n",
    "- Lower bound is derived using a selectively unbiased estimator independent of $y^*$.\n",
    "\n",
    "- Same unbiased estimator implies <font class=\"emphblue\">selective UMVU estimation is possible for both the saturated and selected models.</font> [W. Fithian, 2015, [arxiv.org/1507.06739v1](http://arxiv.org/abs/1507.06739v1)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Randomized response\n",
    "\n",
    "* Selective model $\\bar{M}^*_{k,E}$ is related to $\\bar{M}_{k,E}$ by likelihood ratio\n",
    "$$\n",
    "\\mathbb{Q}\\left(\\omega: (\\hat{E}(y+\\omega), z_{\\hat{E}_1(y+\\omega)}) = (E,z_E) \\right)\n",
    "$$\n",
    "\n",
    "* Properties of $\\bar{M}_{k,E}$ transfer to properties of $\\bar{M}^*_{k,E}$ (under assumptions) (<font class=\"emphblue\"> whether or not the models in question are parametric</font>):\n",
    "     - Consistency. \n",
    "     - CLT.\n",
    "     \n",
    "* The likelihood ratio is controlled by the randomization scheme (<font class=\"emphblue\">which is completely under our control). \n",
    "\n",
    "* Heavier tailed noise leads to better behavior (reminiscent of Laplace vs. Gaussian noise in differential privacy).\n",
    "     \n",
    "### [arxiv.org/1507.06739v1](http://arxiv.org/abs/1507.06739v1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Acknowledgements\n",
    "\n",
    "### Selective inference is joint work with many:\n",
    "\n",
    "* Yuval Benjamini\n",
    "* Yunjin Choi\n",
    "* Will Fithian\n",
    "* Sam Gross\n",
    "* Jason Lee\n",
    "* Richard Lockhart\n",
    "* Joshua Loftus\n",
    "* Stephen Reid\n",
    "* Dennis Sun\n",
    "* Yuekai Sun\n",
    "* Xiaoying Tian\n",
    "* Rob Tibshirani\n",
    "* Ryan Tibshirani\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Thanks\n",
    "\n",
    "* NSF-DMS 1208857 and AFOSR-113039.\n",
    "\n",
    "* Many collaborators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "ipython nbconvert --to slides    --reveal-prefix=http://statweb.stanford.edu/~jtaylo/reveal.js  jsm2015.ipynb;\n",
      "mkdir www;\n",
      "cp -r jsm2015.slides.html www/index.html;\n",
      "cp *png www;\n",
      "cp convex.svg www; \n",
      "cp jsm2015.ipynb www;\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "def build():\n",
    "    cmd = '''\n",
    "\n",
    "ipython nbconvert --to slides    --reveal-prefix=http://statweb.stanford.edu/~jtaylo/reveal.js  %(title)s.ipynb;\n",
    "mkdir www;\n",
    "cp -r %(title)s.slides.html www/index.html;\n",
    "cp *png www;\n",
    "cp convex.svg www; \n",
    "cp %(title)s.ipynb www;\n",
    "''' % {'title':'jsm2015'}\n",
    "    print cmd\n",
    "    os.system(cmd)\n",
    "build()\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}