selective inference after cross validation -- results

cross_validate.ipynb

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    "# Selective inference for cross-validation\n",
    "\n",
    "Rob keeps saying that we can't do cross-validation with selective inference, and \n",
    "I keep telling him it's a matter of computation, not theory.\n",
    "\n",
    "Here is a randomized algorithm that allows us to choose $\\lambda$ by CV. \n",
    "I didn't use LASSO, I used square-root LASSO instead [arxiv.org/1504.08031](http://arxiv.org/abs/1504.08031), and not too fine a grid. The square root LASSO has the advantage that it makes sense to choose a completely fixed grid.\n",
    "\n",
    "The scheme is an example of what Xiaoying has been doing here: [arxiv.org/1507.06739v1](http://arxiv.org/abs/1507.06739v1)\n",
    "\n",
    "## The setup\n",
    "\n",
    "I randomized the response a few times, which can make sampling a little easier, at least the code is \n",
    "more structured.\n",
    "\n",
    "* $Y|X \\sim N(X\\beta, \\sigma^2 I)$ -- the usual instance in [arxiv.org/1410.2597](http://arxiv.org/abs/1410.2597)\n",
    "\n",
    "* $Y_{\\text{inter}} | Y \\sim N(Y, \\sigma^2_1 I)$\n",
    "\n",
    "* $Y_{\\text{CV}}, Y_{\\text{select}} | Y, Y_{\\text{inter}} \\overset{IID}{\\sim} N(Y_{\\text{inter}}, \\sigma^2_2 I)$\n",
    "\n",
    "* Use cross-validation over a grid with $Y_{\\text{CV}}$ to choose $\\lambda$.\n",
    "\n",
    "* Use that fixed $\\lambda$ to choose variables and signs with $Y_{\\text{select}}$. Because $Y_{\\text{CV}}$ \n",
    "and $Y_{\\text{select}}$ have the same distribution a good choice based on $Y_{\\text{CV}}$ should be good also for\n",
    "$Y_{\\text{select}}$.\n",
    "\n",
    "* Now, sample from\n",
    "$$\n",
    "{\\cal L} \\left(Y \\bigl \\vert \\hat{\\lambda}(Y_{\\text{CV}})=\\lambda, (\\hat{E}(Y_{\\text{select}}), z_{\\hat{E}}(Y_{\\text{select}})) = (E,z_E) \\right)\n",
    "$$\n",
    "For computational reasons,\n",
    "I also conditioned on $(I - P_E)Y_{\\text{select}}$\n",
    "\n",
    "* We see ${\\cal L}(Y_{\\text{CV}} \\vert Y_{\\text{inter}}, Y_{\\text{select}}, Y ) = {\\cal L}(Y_{\\text{CV}} | Y_{\\text{inter}})$ is $N(Y_{\\text{inter}}, \\sigma^2_2 I)$. Similarly for $Y_{\\text{select}}$. We sample from Metropolis-Hastings to move $Y_{\\text{CV}}$ and Gibbs to move $Y_{\\text{select}}$.\n",
    "\n",
    "* We see ${\\cal L}(Y_{\\text{inter}} \\vert Y_{\\text{CV}}, Y_{\\text{select}}, Y )$ is Gaussian with mean a\n",
    "weighted average of $Y, Y_{\\text{select}}, Y_{\\text{CV}}$.\n",
    "\n",
    "* To sample $Y$, and inference for some $\\beta_{j| E}$ we do the usual conditioning on $X_{E \\setminus j}^Ty$ and look at the law of $X_j^Ty$. With $\\sigma$ known, this step is again a Gaussian distribution. With $\\sigma$ unknown, it should be a sampling on the sphere. Metropolis-Hastings could be used, but maybe there is a Hamiltonian Monte-Carlo step that would be faster. There is also a Gaussian approximation, which is what I used below.\n",
    "\n",
    "* When $\\sigma$ is unknown, the variances $\\sigma^2_1, \\sigma^2_2$ should probably depend on $Y$. I made a very rough\n",
    "estimate of $\\sigma$ based on a rough guess at a population  $R^2$. The estimate just has to be rough, the inference is \"valid\" for whatever rough guess we use.\n",
    "\n",
    "* The first results below used $\\sigma$ known.\n",
    "\n",
    "* Just conditioning on screening and plotting $p$-values for one of the null variables."
   ]
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   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jonathantaylor/anaconda/lib/python2.7/site-packages/selection/algorithms/lasso.py:32: UserWarning: cvx not available\n",
      "  warnings.warn('cvx not available')\n"
     ]
    }
   ],
   "source": [
    "%load_ext rpy2.ipython\n",
    "from cross_valid import simulate\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Known $\\sigma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P = []\n",
    "for _ in range(50):\n",
    "    pval = simulate(sigma_known=True)\n",
    "    if pval is not None:\n",
    "        P.append(pval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [
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WtH37dvM8WO969bnvXXfdZaqkHaVOYRBAAAGHCwwcONA8WtT2PJ701FNPyZIlS6Rs2bKe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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R -i P\n",
    "plot(ecdf(P))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unknown $\\sigma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "P = []\n",
    "for _ in range(50):\n",
    "    pval = simulate(sigma_known=False)\n",
    "    if pval is not None:\n",
    "        P.append(pval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Yv5J27NhhngfrXa8+923QoIGpknaUOoVBAAEEHC4wevRo82hR2/N4UufOneXHH3+UihUr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\nEAiDAAE4DKgcEgEEEEAAgeQE/g/hxY5u8t/kDwAAAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R -i P\n",
    "plot(ecdf(P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}