prevalidation

Prevalidation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prevalidation_test = function(y, P) {\n",
    "    n = length(y)\n",
    "    Py = P %*% y\n",
    "    N = sum(y*Py)\n",
    "    D = sqrt(sum(Py*Py))\n",
    "    \n",
    "    beta = N / D^2\n",
    "    SD = sqrt(sum((y - beta * Py)^2) / (n-1))\n",
    "    T = N / (D * SD)\n",
    "    return(T)\n",
    "    \n",
    "}\n",
    "\n",
    "null_distribution = function(P, nsim=1000) {\n",
    "    n = nrow(P)\n",
    "    null_sample = rep(NA, nsim)\n",
    "    for (i in 1:nsim) {\n",
    "        noise = rnorm(n)\n",
    "        Pnoise = P %*% noise\n",
    "        null_sample[i] = sum(noise * Pnoise) / sqrt(sum(Pnoise^2))\n",
    "    }\n",
    "    return(null_sample)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using the full fit "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loaded lars 1.2\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "0.716"
      ],
      "text/latex": [
       "0.716"
      ],
      "text/markdown": [
       "0.716"
      ],
      "text/plain": [
       "[1] 0.716"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "library(lars)\n",
    "data(diabetes)\n",
    "X = diabetes$x\n",
    "\n",
    "simulate_full_fit = function(X, sigma=2) {\n",
    "    n = nrow(X)\n",
    "    H = X %*% solve(t(X) %*% X) %*% t(X)\n",
    "    Y = rnorm(n) * sigma\n",
    "    T = prevalidation_test(Y, H)\n",
    "    null_ = null_distribution(H)\n",
    "    pval = mean(null_ > T)\n",
    "    return(pval)\n",
    "}\n",
    "\n",
    "simulate_full_fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "P = c()\n",
    "X = diabetes$x\n",
    "for (i in 1:200) {\n",
    "    P = c(P, simulate_full_fit(X))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Plot with title “ecdf(P)”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(ecdf(P))\n",
    "abline(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using leave-one-out matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.102"
      ],
      "text/latex": [
       "0.102"
      ],
      "text/markdown": [
       "0.102"
      ],
      "text/plain": [
       "[1] 0.102"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "simulate_leave1out = function(X, sigma=2) {\n",
    "    n = nrow(X)\n",
    "    H = X %*% solve(t(X) %*% X) %*% t(X)\n",
    "    I = rep(1, n)\n",
    "    D = diag(H)\n",
    "    M2 = diag(I - D) %*% (H-D)\n",
    "    Y = rnorm(n) * sigma\n",
    "    T = prevalidation_test(Y, H)\n",
    "    null_ = null_distribution(H)\n",
    "    pval = mean(null_ > T)\n",
    "    return(pval)\n",
    "}\n",
    "\n",
    "simulate_leave1out(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "P = c()\n",
    "X = diabetes$x\n",
    "for (i in 1:200) {\n",
    "    P = c(P, simulate_leave1out(X))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title “ecdf(P)”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(ecdf(P))\n",
    "abline(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.2.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}