Group LASSO in R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# group_lasso_fns.R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "library(gglasso)\n",
    "library(MASS)\n",
    "\n",
    "solve_problem = function(X, y, groups, lambda, penalty_factor, loss=\"ls\"){\n",
    "  if (is.null(lambda)){\n",
    "    cv <- cv.gglasso(x=X, y=y, group=groups, loss=loss, pf=penalty_factor, intercept=FALSE, eps=1e-12)\n",
    "    beta_hat = coef(cv, s=\"lambda.1se\")\n",
    "  }\n",
    "  else {\n",
    "    m <- gglasso(x=X,y=y,group=groups,loss=loss, pf=penalty_factor, intercept=FALSE,eps=1e-12)\n",
    "    beta_hat = coef(m,s=lambda)\n",
    "  }\n",
    "  return(beta_hat[-1])\n",
    "}\n",
    "\n",
    "truncation_set = function(X, y, Qbeta_bar, Q, target_cov, group, target_stat,\n",
    "                          groups, lambda, penalty_factor){\n",
    "\n",
    "  penalty_factor_rest = 1 * penalty_factor\n",
    "  penalty_factor_rest[group]=10^10  # HERE\n",
    "  restricted_soln = solve_problem(X, y, groups, lambda, penalty_factor=penalty_factor_rest)\n",
    "  p=ncol(X)\n",
    "  n=nrow(X)\n",
    "  I=diag(p)\n",
    "  group_vars = which(groups==group)\n",
    "  nuisance = (Qbeta_bar - I[,group_vars] %*% solve(target_cov) %*% target_stat) / n  # HERE\n",
    "  center = nuisance[group_vars] - Q[group_vars,] %*% restricted_soln / n             # HERE\n",
    "  radius = penalty_factor[group]*lambda\n",
    "  # print(c(\"radius\", radius))\n",
    "  return(list(target_cov=target_cov, center=center*n, radius=radius*n))              # HERE\n",
    "\n",
    "}\n",
    "\n",
    "sample = function(target_cov, observed, center, radius, n, nsample = 5000){\n",
    "    samples = matrix(nrow=nsample, ncol=length(observed))\n",
    "    i=1\n",
    "    target_cov_inv = solve(target_cov)\n",
    "    chol = chol(target_cov)\n",
    "    p = nrow(target_cov)\n",
    "    while (i<=nsample){\n",
    "      G = chol %*% rnorm(p)  \n",
    "      V = (target_cov_inv %*% G) + center\n",
    "      if (sqrt(sum(V^2))>=radius){\n",
    "\tsamples[i,]=G\n",
    "\ti=i+1\n",
    "      }\n",
    "    }\n",
    "    return(samples)\n",
    "}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# test_group_lasso.R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$pvalues</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>0.0813999999999999</li>\n",
       "\t<li>0.9872</li>\n",
       "\t<li>0.7782</li>\n",
       "\t<li>0.62</li>\n",
       "\t<li>0.3588</li>\n",
       "\t<li>0.191</li>\n",
       "\t<li>0.815</li>\n",
       "\t<li>0.0980000000000001</li>\n",
       "\t<li>0.126</li>\n",
       "\t<li>0.384</li>\n",
       "\t<li>0.9402</li>\n",
       "\t<li>0.2586</li>\n",
       "\t<li>0.7618</li>\n",
       "\t<li>0.7138</li>\n",
       "\t<li>0.208</li>\n",
       "\t<li>0.2242</li>\n",
       "\t<li>0.3704</li>\n",
       "\t<li>0.524</li>\n",
       "\t<li>0.9828</li>\n",
       "\t<li>0.8554</li>\n",
       "\t<li>0.0691999999999999</li>\n",
       "\t<li>0.7412</li>\n",
       "\t<li>0.1234</li>\n",
       "\t<li>0.9212</li>\n",
       "\t<li>0.8154</li>\n",
       "\t<li>0.7982</li>\n",
       "\t<li>0.068</li>\n",
       "\t<li>0.1322</li>\n",
       "\t<li>0.9564</li>\n",
       "\t<li>0.309</li>\n",
       "\t<li>0.8362</li>\n",
       "\t<li>0.1188</li>\n",
       "\t<li>0.2652</li>\n",
       "\t<li>0.596</li>\n",
       "\t<li>0.0458000000000001</li>\n",
       "\t<li>0.7118</li>\n",
       "\t<li>0.6538</li>\n",
       "\t<li>0.7484</li>\n",
       "\t<li>0.5854</li>\n",
       "\t<li>0.628</li>\n",
       "\t<li>0.3338</li>\n",
       "\t<li>0.581</li>\n",
       "\t<li>0.6524</li>\n",
       "\t<li>0.1318</li>\n",
       "\t<li>0.0551999999999999</li>\n",
       "\t<li>0.7246</li>\n",
       "\t<li>0.1306</li>\n",
       "\t<li>0.7216</li>\n",
       "\t<li>0.2788</li>\n",
       "\t<li>0.8</li>\n",
       "\t<li>0.1818</li>\n",
       "\t<li>0.3324</li>\n",
       "\t<li>0.4346</li>\n",
       "\t<li>0.3782</li>\n",
       "\t<li>0.806</li>\n",
       "\t<li>0.0884</li>\n",
       "\t<li>0.055</li>\n",
       "\t<li>0.4084</li>\n",
       "\t<li>0.8416</li>\n",
       "\t<li>0.6198</li>\n",
       "\t<li>0.34</li>\n",
       "\t<li>0.5054</li>\n",
       "\t<li>0.6948</li>\n",
       "\t<li>0.1112</li>\n",
       "\t<li>0.8192</li>\n",
       "\t<li>0.9376</li>\n",
       "\t<li>0.3236</li>\n",
       "\t<li>0.7272</li>\n",
       "\t<li>0.293</li>\n",
       "\t<li>0.0568</li>\n",
       "\t<li>0.2698</li>\n",
       "\t<li>0.3638</li>\n",
       "\t<li>0.3146</li>\n",
       "\t<li>0.0548</li>\n",
       "\t<li>0.1246</li>\n",
       "\t<li>0.0024</li>\n",
       "\t<li>0.6266</li>\n",
       "\t<li>0.4348</li>\n",
       "\t<li>0.4518</li>\n",
       "\t<li>0.785</li>\n",
       "\t<li>0.9814</li>\n",
       "\t<li>0.6796</li>\n",
       "\t<li>0.7448</li>\n",
       "\t<li>0.5548</li>\n",
       "\t<li>0.432</li>\n",
       "\t<li>0.2584</li>\n",
       "\t<li>0.543</li>\n",
       "\t<li>0.0992</li>\n",
       "\t<li>0.943</li>\n",
       "\t<li>0.6328</li>\n",
       "\t<li>0.6418</li>\n",
       "\t<li>0.9254</li>\n",
       "\t<li>0.3476</li>\n",
       "\t<li>0.712</li>\n",
       "\t<li>0.549</li>\n",
       "</ol>\n",
       "</dd>\n",
       "\t<dt>$naive_pvalues</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>0.0149999999999999</li>\n",
       "\t<li>0.1874</li>\n",
       "\t<li>0.3822</li>\n",
       "\t<li>0.11</li>\n",
       "\t<li>0.301</li>\n",
       "\t<li>0.5004</li>\n",
       "\t<li>0.366</li>\n",
       "\t<li>0.0189999999999999</li>\n",
       "\t<li>0.0258</li>\n",
       "\t<li>0.0702</li>\n",
       "\t<li>0.1928</li>\n",
       "\t<li>0.046</li>\n",
       "\t<li>0.141</li>\n",
       "\t<li>0.1332</li>\n",
       "\t<li>0.0344</li>\n",
       "\t<li>0.0316000000000001</li>\n",
       "\t<li>0.0708</li>\n",
       "\t<li>0.2198</li>\n",
       "\t<li>0.1614</li>\n",
       "\t<li>0.1372</li>\n",
       "\t<li>0.0118</li>\n",
       "\t<li>0.1336</li>\n",
       "\t<li>0.4328</li>\n",
       "\t<li>0.2164</li>\n",
       "\t<li>0.133</li>\n",
       "\t<li>0.1988</li>\n",
       "\t<li>0.5762</li>\n",
       "\t<li>0.357</li>\n",
       "\t<li>0.155</li>\n",
       "\t<li>0.357</li>\n",
       "\t<li>0.1344</li>\n",
       "\t<li>0.4056</li>\n",
       "\t<li>0.556</li>\n",
       "\t<li>0.2552</li>\n",
       "\t<li>0.00639999999999996</li>\n",
       "\t<li>0.1782</li>\n",
       "\t<li>0.127</li>\n",
       "\t<li>0.1138</li>\n",
       "\t<li>0.0768</li>\n",
       "\t<li>0.2628</li>\n",
       "\t<li>0.0644</li>\n",
       "\t<li>0.3658</li>\n",
       "\t<li>0.1274</li>\n",
       "\t<li>0.6484</li>\n",
       "\t<li>0.00760000000000005</li>\n",
       "\t<li>0.246</li>\n",
       "\t<li>0.3712</li>\n",
       "\t<li>0.1514</li>\n",
       "\t<li>0.046</li>\n",
       "\t<li>0.1336</li>\n",
       "\t<li>0.4842</li>\n",
       "\t<li>0.5128</li>\n",
       "\t<li>0.294</li>\n",
       "\t<li>0.5844</li>\n",
       "\t<li>0.1324</li>\n",
       "\t<li>0.747</li>\n",
       "\t<li>0.8532</li>\n",
       "\t<li>0.0684</li>\n",
       "\t<li>0.2786</li>\n",
       "\t<li>0.1078</li>\n",
       "\t<li>0.3256</li>\n",
       "\t<li>0.2694</li>\n",
       "\t<li>0.1628</li>\n",
       "\t<li>0.0167999999999999</li>\n",
       "\t<li>0.1754</li>\n",
       "\t<li>0.199</li>\n",
       "\t<li>0.0686</li>\n",
       "\t<li>0.1284</li>\n",
       "\t<li>0.3126</li>\n",
       "\t<li>0.0072000000000001</li>\n",
       "\t<li>0.0387999999999999</li>\n",
       "\t<li>0.0482</li>\n",
       "\t<li>0.3346</li>\n",
       "\t<li>0.5584</li>\n",
       "\t<li>0.4412</li>\n",
       "\t<li>0.7022</li>\n",
       "\t<li>0.2124</li>\n",
       "\t<li>0.0691999999999999</li>\n",
       "\t<li>0.0698000000000001</li>\n",
       "\t<li>0.144</li>\n",
       "\t<li>0.153</li>\n",
       "\t<li>0.2514</li>\n",
       "\t<li>0.164</li>\n",
       "\t<li>0.2754</li>\n",
       "\t<li>0.2632</li>\n",
       "\t<li>0.0508</li>\n",
       "\t<li>0.2356</li>\n",
       "\t<li>0.0176000000000001</li>\n",
       "\t<li>0.1888</li>\n",
       "\t<li>0.102</li>\n",
       "\t<li>0.0908</li>\n",
       "\t<li>0.193</li>\n",
       "\t<li>0.0624</li>\n",
       "\t<li>0.2176</li>\n",
       "\t<li>0.318</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$pvalues] \\begin{enumerate*}\n",
       "\\item 0.0813999999999999\n",
       "\\item 0.9872\n",
       "\\item 0.7782\n",
       "\\item 0.62\n",
       "\\item 0.3588\n",
       "\\item 0.191\n",
       "\\item 0.815\n",
       "\\item 0.0980000000000001\n",
       "\\item 0.126\n",
       "\\item 0.384\n",
       "\\item 0.9402\n",
       "\\item 0.2586\n",
       "\\item 0.7618\n",
       "\\item 0.7138\n",
       "\\item 0.208\n",
       "\\item 0.2242\n",
       "\\item 0.3704\n",
       "\\item 0.524\n",
       "\\item 0.9828\n",
       "\\item 0.8554\n",
       "\\item 0.0691999999999999\n",
       "\\item 0.7412\n",
       "\\item 0.1234\n",
       "\\item 0.9212\n",
       "\\item 0.8154\n",
       "\\item 0.7982\n",
       "\\item 0.068\n",
       "\\item 0.1322\n",
       "\\item 0.9564\n",
       "\\item 0.309\n",
       "\\item 0.8362\n",
       "\\item 0.1188\n",
       "\\item 0.2652\n",
       "\\item 0.596\n",
       "\\item 0.0458000000000001\n",
       "\\item 0.7118\n",
       "\\item 0.6538\n",
       "\\item 0.7484\n",
       "\\item 0.5854\n",
       "\\item 0.628\n",
       "\\item 0.3338\n",
       "\\item 0.581\n",
       "\\item 0.6524\n",
       "\\item 0.1318\n",
       "\\item 0.0551999999999999\n",
       "\\item 0.7246\n",
       "\\item 0.1306\n",
       "\\item 0.7216\n",
       "\\item 0.2788\n",
       "\\item 0.8\n",
       "\\item 0.1818\n",
       "\\item 0.3324\n",
       "\\item 0.4346\n",
       "\\item 0.3782\n",
       "\\item 0.806\n",
       "\\item 0.0884\n",
       "\\item 0.055\n",
       "\\item 0.4084\n",
       "\\item 0.8416\n",
       "\\item 0.6198\n",
       "\\item 0.34\n",
       "\\item 0.5054\n",
       "\\item 0.6948\n",
       "\\item 0.1112\n",
       "\\item 0.8192\n",
       "\\item 0.9376\n",
       "\\item 0.3236\n",
       "\\item 0.7272\n",
       "\\item 0.293\n",
       "\\item 0.0568\n",
       "\\item 0.2698\n",
       "\\item 0.3638\n",
       "\\item 0.3146\n",
       "\\item 0.0548\n",
       "\\item 0.1246\n",
       "\\item 0.0024\n",
       "\\item 0.6266\n",
       "\\item 0.4348\n",
       "\\item 0.4518\n",
       "\\item 0.785\n",
       "\\item 0.9814\n",
       "\\item 0.6796\n",
       "\\item 0.7448\n",
       "\\item 0.5548\n",
       "\\item 0.432\n",
       "\\item 0.2584\n",
       "\\item 0.543\n",
       "\\item 0.0992\n",
       "\\item 0.943\n",
       "\\item 0.6328\n",
       "\\item 0.6418\n",
       "\\item 0.9254\n",
       "\\item 0.3476\n",
       "\\item 0.712\n",
       "\\item 0.549\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\item[\\$naive\\_pvalues] \\begin{enumerate*}\n",
       "\\item 0.0149999999999999\n",
       "\\item 0.1874\n",
       "\\item 0.3822\n",
       "\\item 0.11\n",
       "\\item 0.301\n",
       "\\item 0.5004\n",
       "\\item 0.366\n",
       "\\item 0.0189999999999999\n",
       "\\item 0.0258\n",
       "\\item 0.0702\n",
       "\\item 0.1928\n",
       "\\item 0.046\n",
       "\\item 0.141\n",
       "\\item 0.1332\n",
       "\\item 0.0344\n",
       "\\item 0.0316000000000001\n",
       "\\item 0.0708\n",
       "\\item 0.2198\n",
       "\\item 0.1614\n",
       "\\item 0.1372\n",
       "\\item 0.0118\n",
       "\\item 0.1336\n",
       "\\item 0.4328\n",
       "\\item 0.2164\n",
       "\\item 0.133\n",
       "\\item 0.1988\n",
       "\\item 0.5762\n",
       "\\item 0.357\n",
       "\\item 0.155\n",
       "\\item 0.357\n",
       "\\item 0.1344\n",
       "\\item 0.4056\n",
       "\\item 0.556\n",
       "\\item 0.2552\n",
       "\\item 0.00639999999999996\n",
       "\\item 0.1782\n",
       "\\item 0.127\n",
       "\\item 0.1138\n",
       "\\item 0.0768\n",
       "\\item 0.2628\n",
       "\\item 0.0644\n",
       "\\item 0.3658\n",
       "\\item 0.1274\n",
       "\\item 0.6484\n",
       "\\item 0.00760000000000005\n",
       "\\item 0.246\n",
       "\\item 0.3712\n",
       "\\item 0.1514\n",
       "\\item 0.046\n",
       "\\item 0.1336\n",
       "\\item 0.4842\n",
       "\\item 0.5128\n",
       "\\item 0.294\n",
       "\\item 0.5844\n",
       "\\item 0.1324\n",
       "\\item 0.747\n",
       "\\item 0.8532\n",
       "\\item 0.0684\n",
       "\\item 0.2786\n",
       "\\item 0.1078\n",
       "\\item 0.3256\n",
       "\\item 0.2694\n",
       "\\item 0.1628\n",
       "\\item 0.0167999999999999\n",
       "\\item 0.1754\n",
       "\\item 0.199\n",
       "\\item 0.0686\n",
       "\\item 0.1284\n",
       "\\item 0.3126\n",
       "\\item 0.0072000000000001\n",
       "\\item 0.0387999999999999\n",
       "\\item 0.0482\n",
       "\\item 0.3346\n",
       "\\item 0.5584\n",
       "\\item 0.4412\n",
       "\\item 0.7022\n",
       "\\item 0.2124\n",
       "\\item 0.0691999999999999\n",
       "\\item 0.0698000000000001\n",
       "\\item 0.144\n",
       "\\item 0.153\n",
       "\\item 0.2514\n",
       "\\item 0.164\n",
       "\\item 0.2754\n",
       "\\item 0.2632\n",
       "\\item 0.0508\n",
       "\\item 0.2356\n",
       "\\item 0.0176000000000001\n",
       "\\item 0.1888\n",
       "\\item 0.102\n",
       "\\item 0.0908\n",
       "\\item 0.193\n",
       "\\item 0.0624\n",
       "\\item 0.2176\n",
       "\\item 0.318\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$pvalues\n",
       ":   1. 0.0813999999999999\n",
       "2. 0.9872\n",
       "3. 0.7782\n",
       "4. 0.62\n",
       "5. 0.3588\n",
       "6. 0.191\n",
       "7. 0.815\n",
       "8. 0.0980000000000001\n",
       "9. 0.126\n",
       "10. 0.384\n",
       "11. 0.9402\n",
       "12. 0.2586\n",
       "13. 0.7618\n",
       "14. 0.7138\n",
       "15. 0.208\n",
       "16. 0.2242\n",
       "17. 0.3704\n",
       "18. 0.524\n",
       "19. 0.9828\n",
       "20. 0.8554\n",
       "21. 0.0691999999999999\n",
       "22. 0.7412\n",
       "23. 0.1234\n",
       "24. 0.9212\n",
       "25. 0.8154\n",
       "26. 0.7982\n",
       "27. 0.068\n",
       "28. 0.1322\n",
       "29. 0.9564\n",
       "30. 0.309\n",
       "31. 0.8362\n",
       "32. 0.1188\n",
       "33. 0.2652\n",
       "34. 0.596\n",
       "35. 0.0458000000000001\n",
       "36. 0.7118\n",
       "37. 0.6538\n",
       "38. 0.7484\n",
       "39. 0.5854\n",
       "40. 0.628\n",
       "41. 0.3338\n",
       "42. 0.581\n",
       "43. 0.6524\n",
       "44. 0.1318\n",
       "45. 0.0551999999999999\n",
       "46. 0.7246\n",
       "47. 0.1306\n",
       "48. 0.7216\n",
       "49. 0.2788\n",
       "50. 0.8\n",
       "51. 0.1818\n",
       "52. 0.3324\n",
       "53. 0.4346\n",
       "54. 0.3782\n",
       "55. 0.806\n",
       "56. 0.0884\n",
       "57. 0.055\n",
       "58. 0.4084\n",
       "59. 0.8416\n",
       "60. 0.6198\n",
       "61. 0.34\n",
       "62. 0.5054\n",
       "63. 0.6948\n",
       "64. 0.1112\n",
       "65. 0.8192\n",
       "66. 0.9376\n",
       "67. 0.3236\n",
       "68. 0.7272\n",
       "69. 0.293\n",
       "70. 0.0568\n",
       "71. 0.2698\n",
       "72. 0.3638\n",
       "73. 0.3146\n",
       "74. 0.0548\n",
       "75. 0.1246\n",
       "76. 0.0024\n",
       "77. 0.6266\n",
       "78. 0.4348\n",
       "79. 0.4518\n",
       "80. 0.785\n",
       "81. 0.9814\n",
       "82. 0.6796\n",
       "83. 0.7448\n",
       "84. 0.5548\n",
       "85. 0.432\n",
       "86. 0.2584\n",
       "87. 0.543\n",
       "88. 0.0992\n",
       "89. 0.943\n",
       "90. 0.6328\n",
       "91. 0.6418\n",
       "92. 0.9254\n",
       "93. 0.3476\n",
       "94. 0.712\n",
       "95. 0.549\n",
       "\n",
       "\n",
       "\n",
       "$naive_pvalues\n",
       ":   1. 0.0149999999999999\n",
       "2. 0.1874\n",
       "3. 0.3822\n",
       "4. 0.11\n",
       "5. 0.301\n",
       "6. 0.5004\n",
       "7. 0.366\n",
       "8. 0.0189999999999999\n",
       "9. 0.0258\n",
       "10. 0.0702\n",
       "11. 0.1928\n",
       "12. 0.046\n",
       "13. 0.141\n",
       "14. 0.1332\n",
       "15. 0.0344\n",
       "16. 0.0316000000000001\n",
       "17. 0.0708\n",
       "18. 0.2198\n",
       "19. 0.1614\n",
       "20. 0.1372\n",
       "21. 0.0118\n",
       "22. 0.1336\n",
       "23. 0.4328\n",
       "24. 0.2164\n",
       "25. 0.133\n",
       "26. 0.1988\n",
       "27. 0.5762\n",
       "28. 0.357\n",
       "29. 0.155\n",
       "30. 0.357\n",
       "31. 0.1344\n",
       "32. 0.4056\n",
       "33. 0.556\n",
       "34. 0.2552\n",
       "35. 0.00639999999999996\n",
       "36. 0.1782\n",
       "37. 0.127\n",
       "38. 0.1138\n",
       "39. 0.0768\n",
       "40. 0.2628\n",
       "41. 0.0644\n",
       "42. 0.3658\n",
       "43. 0.1274\n",
       "44. 0.6484\n",
       "45. 0.00760000000000005\n",
       "46. 0.246\n",
       "47. 0.3712\n",
       "48. 0.1514\n",
       "49. 0.046\n",
       "50. 0.1336\n",
       "51. 0.4842\n",
       "52. 0.5128\n",
       "53. 0.294\n",
       "54. 0.5844\n",
       "55. 0.1324\n",
       "56. 0.747\n",
       "57. 0.8532\n",
       "58. 0.0684\n",
       "59. 0.2786\n",
       "60. 0.1078\n",
       "61. 0.3256\n",
       "62. 0.2694\n",
       "63. 0.1628\n",
       "64. 0.0167999999999999\n",
       "65. 0.1754\n",
       "66. 0.199\n",
       "67. 0.0686\n",
       "68. 0.1284\n",
       "69. 0.3126\n",
       "70. 0.0072000000000001\n",
       "71. 0.0387999999999999\n",
       "72. 0.0482\n",
       "73. 0.3346\n",
       "74. 0.5584\n",
       "75. 0.4412\n",
       "76. 0.7022\n",
       "77. 0.2124\n",
       "78. 0.0691999999999999\n",
       "79. 0.0698000000000001\n",
       "80. 0.144\n",
       "81. 0.153\n",
       "82. 0.2514\n",
       "83. 0.164\n",
       "84. 0.2754\n",
       "85. 0.2632\n",
       "86. 0.0508\n",
       "87. 0.2356\n",
       "88. 0.0176000000000001\n",
       "89. 0.1888\n",
       "90. 0.102\n",
       "91. 0.0908\n",
       "92. 0.193\n",
       "93. 0.0624\n",
       "94. 0.2176\n",
       "95. 0.318\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$pvalues\n",
       " [1] 0.0814 0.9872 0.7782 0.6200 0.3588 0.1910 0.8150 0.0980 0.1260 0.3840\n",
       "[11] 0.9402 0.2586 0.7618 0.7138 0.2080 0.2242 0.3704 0.5240 0.9828 0.8554\n",
       "[21] 0.0692 0.7412 0.1234 0.9212 0.8154 0.7982 0.0680 0.1322 0.9564 0.3090\n",
       "[31] 0.8362 0.1188 0.2652 0.5960 0.0458 0.7118 0.6538 0.7484 0.5854 0.6280\n",
       "[41] 0.3338 0.5810 0.6524 0.1318 0.0552 0.7246 0.1306 0.7216 0.2788 0.8000\n",
       "[51] 0.1818 0.3324 0.4346 0.3782 0.8060 0.0884 0.0550 0.4084 0.8416 0.6198\n",
       "[61] 0.3400 0.5054 0.6948 0.1112 0.8192 0.9376 0.3236 0.7272 0.2930 0.0568\n",
       "[71] 0.2698 0.3638 0.3146 0.0548 0.1246 0.0024 0.6266 0.4348 0.4518 0.7850\n",
       "[81] 0.9814 0.6796 0.7448 0.5548 0.4320 0.2584 0.5430 0.0992 0.9430 0.6328\n",
       "[91] 0.6418 0.9254 0.3476 0.7120 0.5490\n",
       "\n",
       "$naive_pvalues\n",
       " [1] 0.0150 0.1874 0.3822 0.1100 0.3010 0.5004 0.3660 0.0190 0.0258 0.0702\n",
       "[11] 0.1928 0.0460 0.1410 0.1332 0.0344 0.0316 0.0708 0.2198 0.1614 0.1372\n",
       "[21] 0.0118 0.1336 0.4328 0.2164 0.1330 0.1988 0.5762 0.3570 0.1550 0.3570\n",
       "[31] 0.1344 0.4056 0.5560 0.2552 0.0064 0.1782 0.1270 0.1138 0.0768 0.2628\n",
       "[41] 0.0644 0.3658 0.1274 0.6484 0.0076 0.2460 0.3712 0.1514 0.0460 0.1336\n",
       "[51] 0.4842 0.5128 0.2940 0.5844 0.1324 0.7470 0.8532 0.0684 0.2786 0.1078\n",
       "[61] 0.3256 0.2694 0.1628 0.0168 0.1754 0.1990 0.0686 0.1284 0.3126 0.0072\n",
       "[71] 0.0388 0.0482 0.3346 0.5584 0.4412 0.7022 0.2124 0.0692 0.0698 0.1440\n",
       "[81] 0.1530 0.2514 0.1640 0.2754 0.2632 0.0508 0.2356 0.0176 0.1888 0.1020\n",
       "[91] 0.0908 0.1930 0.0624 0.2176 0.3180\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cg21spXpH9JN0oXSHYSPOQscpA8j6na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\nBAgQIECAwPYQ+DdrlzIegzmjNgAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “ecdf(pvalues)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "test_group_lasso_solver=function(){\n",
    "  n=500\n",
    "  p=30\n",
    "  set.seed(1)\n",
    "  X=matrix(rnorm(n*p), nrow=n)\n",
    "  y=rnorm(n)\n",
    "  ngroups=10\n",
    "  groups = rep(1:ngroups,each=p/ngroups)\n",
    "  group_sizes = rep(p/ngroups,ngroups)\n",
    "  penalty_factor=rep(1, length(group_sizes))\n",
    "  lambda=50/n\n",
    "  beta_hat = solve_problem(X, y, groups, lambda, penalty_factor)\n",
    "  print(beta_hat)\n",
    "  print(which(beta_hat!=0))\n",
    "}\n",
    "\n",
    "test_group_lasso_inference = function(nrep=50){\n",
    "  n=500\n",
    "  p=30\n",
    "  ngroups=10\n",
    "  groups = rep(1:ngroups,each=p/ngroups)\n",
    "  group_sizes = rep(p/ngroups,ngroups)\n",
    "  #penalty_factor = sqrt(group_sizes)\n",
    "  penalty_factor=rep(1, length(group_sizes))\n",
    "  lambda=50/n\n",
    "\n",
    "  pvalues = NULL\n",
    "  naive_pvalues=NULL\n",
    "  for (i in 1:nrep){\n",
    "    X=matrix(rnorm(n*p), n, p)\n",
    "    y=rnorm(n)\n",
    "    PVS = inference_group_lasso(X, y, groups, lambda=lambda, penalty_factor=penalty_factor)\n",
    "    pvalues = c(pvalues, PVS$pvalues)\n",
    "    naive_pvalues = c(naive_pvalues, PVS$naive_pvalues)\n",
    "  }\n",
    "  plot(ecdf(pvalues))\n",
    "  abline(0, 1)\n",
    "  lines(ecdf(naive_pvalues), col=\"red\")\n",
    "  return(list(pvalues=pvalues, naive_pvalues=naive_pvalues))\n",
    "}\n",
    "\n",
    "test_group_lasso_inference()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "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": "3.3.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}