SIGLE_statistics_motivation.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5ec17856",
   "metadata": {},
   "outputs": [],
   "source": [
    "import PSILOGIT\n",
    "import numpy as np\n",
    "from PSILOGIT.tools import *\n",
    "from sklearn.linear_model import LogisticRegression, LogisticRegressionCV\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def linear_temperature(t):\n",
    "    return 0.2/np.log(t+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fce5f35e",
   "metadata": {},
   "source": [
    "# Run only one cell below depending on the setting you want to use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "82db5637",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  9\n"
     ]
    }
   ],
   "source": [
    "################### SETTING 1 Localized\n",
    "nu = 0.4\n",
    "\n",
    "n,p = 100,10\n",
    "\n",
    "## CHOOSE THE MODE (LOCALIZED OR DISSEMINATED)\n",
    "modes = ['disseminated-signal' ,'localized-signal']\n",
    "mode = modes[1]\n",
    "\n",
    "## CHOOSE THE NUMBER OF STEP FOR THE REJECTION SAMPLING METHOD \n",
    "nb_ite = 10000 # 400000\n",
    "\n",
    "lamb = 5\n",
    "\n",
    "if mode=='localized-signal':\n",
    "    vartheta = np.zeros(p)\n",
    "    vartheta[0] = nu\n",
    "else:\n",
    "    vartheta = nu*np.ones(p)\n",
    "    \n",
    "\n",
    "model = PSILOGIT.PSILOGIT(truetheta=vartheta, regularization=1/lamb, n=n, p=p)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "model.sampling_algorithm = 'RS'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "83c47f2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  5\n"
     ]
    }
   ],
   "source": [
    "################### SETTING 2 Localized\n",
    "nu = 3\n",
    "\n",
    "n,p = 20, 15\n",
    "\n",
    "## CHOOSE THE MODE (LOCALIZED OR DISSEMINATED)\n",
    "modes = ['disseminated-signal' ,'localized-signal']\n",
    "mode = modes[1]\n",
    "\n",
    "## CHOOSE THE NUMBER OF STEP FOR THE REJECTION SAMPLING METHOD \n",
    "nb_ite = 10000 # 400000\n",
    "\n",
    "lamb = 3\n",
    "\n",
    "if mode=='localized-signal':\n",
    "    vartheta = np.zeros(p)\n",
    "    vartheta[0] = nu\n",
    "else:\n",
    "    vartheta = nu*np.ones(p)\n",
    "    \n",
    "\n",
    "model = PSILOGIT.PSILOGIT(truetheta=vartheta, regularization=1/lamb, n=n, p=p)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "model.sampling_algorithm = 'SA'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7a7dcda3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  11\n"
     ]
    }
   ],
   "source": [
    "################### SETTING 3 Localized\n",
    "nu = 3\n",
    "\n",
    "n,p = 20, 30\n",
    "\n",
    "## CHOOSE THE MODE (LOCALIZED OR DISSEMINATED)\n",
    "modes = ['disseminated-signal' ,'localized-signal']\n",
    "mode = modes[1]\n",
    "\n",
    "## CHOOSE THE NUMBER OF STEP FOR THE REJECTION SAMPLING METHOD \n",
    "nb_ite = 10000 # 400000\n",
    "\n",
    "lamb = 3\n",
    "\n",
    "if mode=='localized-signal':\n",
    "    vartheta = np.zeros(p)\n",
    "    vartheta[0] = nu\n",
    "else:\n",
    "    vartheta = nu*np.ones(p)\n",
    "    \n",
    "    \n",
    "model = PSILOGIT.PSILOGIT(truetheta=vartheta, regularization=1/lamb, n=n, p=p)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "model.sampling_algorithm = 'SA'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c772a18",
   "metadata": {},
   "source": [
    "# Sampling states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "74a846fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "model_id": "4243272b60664513b4dd116976bfb3a7",
       "version_major": 2,
       "version_minor": 0
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     "data": {
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   ],
   "source": [
    "thetanull = np.zeros(model.X.shape[1])\n",
    "signull = sigmoid(model.X @ thetanull)\n",
    "if model.sampling_algorithm !='SA':\n",
    "    states = model.SEI_by_sampling(model.sig, nb_ite=nb_ite)\n",
    "    if np.max(np.abs(signull-model.sig))<1e-3:\n",
    "        statesnull = np.copy(states)\n",
    "    else:\n",
    "        statesnull = model.SEI_by_sampling(signull, nb_ite=nb_ite)\n",
    "else:\n",
    "    states, ls_FNR, energies = model.SEI_SLR(total_length_SEISLR_path=50000, backup_start_time=2000, temperature=linear_temperature, repulsing_force=True, random_start=True, conditioning_signs=False, seed=0)\n",
    "    if np.max(np.abs(signull-model.sig))<1e-3:\n",
    "        statesnull = np.copy(states)\n",
    "    else:\n",
    "        statesnull, ls_FNR, energies = model.SEI_SLR(total_length_SEISLR_path=50000, backup_start_time=2000, temperature=linear_temperature, repulsing_force=True, random_start=True, conditioning_signs=False, seed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "599b300e",
   "metadata": {},
   "source": [
    "# Computing covariance matrices and centering parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "baf3b255",
   "metadata": {},
   "outputs": [
    {
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       "version_minor": 0
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   ],
   "source": [
    "##### COMPUTING COVARIANCE MATRICES\n",
    "n,p = (model.X).shape\n",
    "matXtrue = model.X[:,model.M]\n",
    "\n",
    "tildeGN12, barpi = model.params_saturated(signull, statesnull)\n",
    "tildetheta, gaps = model.compute_theta_bar(barpi, grad_descent={'lr':0.01,'return_gaps':True,'max_ite':10000})\n",
    "GN = matXtrue.T @ np.diag(barpi*(np.ones(n)-barpi)) @ matXtrue\n",
    "HN = matXtrue.T @ np.diag(sigmoid1(matXtrue @ tildetheta)) @ matXtrue\n",
    "\n",
    "\n",
    "if model.sampling_algorithm != 'SA':\n",
    "    # Linear conditional covariance statistic (SATURATED)\n",
    "    Gammabar = np.zeros((n,n))\n",
    "    for y in statesnull:\n",
    "        Gammabar += np.reshape(y-barpi, (-1,1)) @ np.reshape(y-barpi, (1,-1)) / len(statesnull)\n",
    "    usvd,s,vt = np.linalg.svd(Gammabar)\n",
    "    Gammabar_12 = usvd @ np.diag(1/np.sqrt(s)) @ vt\n",
    "else:\n",
    "    # Linear conditional covariance statistic (SATURATED)\n",
    "    Gammabar = np.zeros((n,n))\n",
    "    normalization = 0\n",
    "    for y in statesnull:\n",
    "        proba = compute_proba(y,signull)\n",
    "        Gammabar += np.reshape(y-barpi, (-1,1)) @ np.reshape(y-barpi, (1,-1)) * proba\n",
    "        normalization += proba\n",
    "    Gammabar /= normalization\n",
    "    usvd,s,vt = np.linalg.svd(Gammabar)\n",
    "    Gammabar_12 = usvd @ np.diag(1/np.sqrt(s)) @ vt\n",
    "\n",
    "# Linear unconditional covariance statistic (SATURATED)\n",
    "Gamma = np.diag(signull *(np.ones(n)-signull))\n",
    "usvd,s,vt = np.linalg.svd(Gamma)\n",
    "Gamma_12 = usvd @ np.diag(1/np.sqrt(s)) @ vt\n",
    "\n",
    "\n",
    "# SIGLE (SELECTED)\n",
    "usvd,s,vt = np.linalg.svd(GN)\n",
    "GN_12 = usvd @ np.diag(1/np.sqrt(s)) @ vt\n",
    "VN = GN_12 @ HN\n",
    "\n",
    "# Logistic unconditional Fisher statistic (SELECTED)\n",
    "HN_uncondi = matXtrue.T @ np.diag(sigmoid1(model.X @ vartheta)) @ matXtrue\n",
    "GN_uncondi = matXtrue.T @ Gamma @ matXtrue\n",
    "usvd,s,vt = np.linalg.svd(GN_uncondi)\n",
    "GN_uncondi_12 = usvd @ np.diag(1/np.sqrt(s)) @ vt\n",
    "VN_fisher = GN_uncondi_12 @ HN_uncondi\n",
    "\n",
    "# SIGLE correlated (SELECTED)\n",
    "GNbar_misspe = matXtrue.T @ Gammabar @ matXtrue\n",
    "usvd,s,vt = np.linalg.svd(GNbar_misspe)\n",
    "GNbar_misspe_12 = usvd @ np.diag(1/np.sqrt(s)) @ vt\n",
    "VN_misspe = GNbar_misspe_12 @ HN\n",
    "    \n",
    "covariances = {'saturated' : {'SIGLE'        : GN_12 @ matXtrue.T,\n",
    "                              'SIGLE correlated': GNbar_misspe_12 @ matXtrue.T,\n",
    "                              'Logistic unconditional Fisher statistic':  GN_uncondi_12 @ matXtrue.T,\n",
    "                              'Linear conditional covariance statistic'  : Gammabar_12,\n",
    "                              'Linear unconditional covariance statistic': Gamma_12\n",
    "                             },\n",
    "               'selected'  : {'SIGLE'        : VN,\n",
    "                              'SIGLE correlated': VN_misspe ,\n",
    "                              'Logistic unconditional Fisher statistic' :  VN_fisher\n",
    "                              }\n",
    "              }\n",
    "centers =     {'saturated' : {'SIGLE'        : barpi,\n",
    "                              'SIGLE correlated': barpi,\n",
    "                              'Logistic unconditional Fisher statistic' : signull,\n",
    "                              'Linear conditional covariance statistic'  : barpi,\n",
    "                              'Linear unconditional covariance statistic': signull\n",
    "                             },\n",
    "               'selected'  : {'SIGLE'  : tildetheta,\n",
    "                              'SIGLE correlated': tildetheta,\n",
    "                              'Logistic unconditional Fisher statistic':  thetanull[model.M]\n",
    "                             }\n",
    "              }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80d7dbcd",
   "metadata": {},
   "source": [
    "# Saturated model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b641fae3",
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls_modes_sat = [key for key in covariances['saturated'].keys()]\n",
    "\n",
    "lists_pvalues_sat = []\n",
    "for mode in ls_modes_sat:\n",
    "    center_sat = centers['saturated'][mode]\n",
    "    cov_sat = covariances['saturated'][mode]\n",
    "    lspvals_sat = model.pval_alt_SIGLE_sat(states, center_sat, cov_sat, l2_regularization=100000, statesnull=statesnull, signull=signull)\n",
    "    lists_pvalues_sat += [lspvals_sat]\n",
    "\n",
    "model.plot_cdf_pvalues(lists_pvalues_sat, ls_modes_sat, states = states, legend_outfig=True, sigalt=model.sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59af0f35",
   "metadata": {},
   "source": [
    "# Selected model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ee025012",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e6c2ee6bfcc94170b3ec887ea5f1dd20",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/264 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "82db8e7c9e6c4fca998ee1a7622c5fe2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/228 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "06ee4a681ce84a299857136ca8821f0c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/264 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "71e0e472b70d42f4ba460bae43f5fa24",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/228 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "506947971762490f96f5473f50390fa1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/264 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "65a0f0eb0d0c4928b0b9db9b988c5f14",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/228 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls_modes_sel = [key for key in covariances['selected'].keys()]\n",
    "\n",
    "lists_pvalues_sel = []\n",
    "for mode in ls_modes_sel:\n",
    "    center_sel = centers['selected'][mode]\n",
    "    cov_sel = covariances['selected'][mode]\n",
    "    lspvals_sel = model.pval_alt_SIGLE_sel(states, center_sel, cov_sel, l2_regularization=100000, statesnull=statesnull, signull=signull)\n",
    "    lists_pvalues_sel += [lspvals_sel]\n",
    "\n",
    "model.plot_cdf_pvalues(lists_pvalues_sel, ls_modes_sel, states = states, legend_outfig=True, sigalt=model.sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51225b01",
   "metadata": {},
   "source": [
    "# Comparison with the $\\chi^2$ distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a6a1b36d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_11480/1037124601.py:14: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  mini = np.float('inf')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pylab\n",
    "import scipy.stats as stats\n",
    "mode = 'SIGLE'\n",
    "center_sat = centers['saturated'][mode]\n",
    "cov_sat = covariances['saturated'][mode]\n",
    "\n",
    "lsstatnull_sat = []\n",
    "for i in range(len(statesnull)):\n",
    "    y = np.array(statesnull[i])\n",
    "    stat = np.linalg.norm( cov_sat @ (y-center_sat))**2\n",
    "    lsstatnull_sat.append(stat)\n",
    "\n",
    "mini = np.float('inf')\n",
    "optdf = 0\n",
    "for df in np.arange(2,50,1):\n",
    "    qq = stats.probplot(lsstatnull_sat, dist=stats.chi2, sparams=(df,))\n",
    "    norm = np.linalg.norm(qq[0][0]-qq[0][1])\n",
    "    if norm<mini:\n",
    "        optdf = df\n",
    "        mini = norm\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "#df = np.mean(lsstatnull_sat) #len(model.M)\n",
    "#print(df, model.M)\n",
    "qq = stats.probplot(lsstatnull_sat, dist=stats.chi2, sparams=(optdf,), plot=ax)\n",
    "#plt.axis('square')\n",
    "ax.set_xlim([1, 27])\n",
    "ax.set_ylim([1, 27])\n",
    "\n",
    "#plt.savefig('quantiles_sat_'+mode+'.png', dpi=250)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "481d6f4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/duchemin/anaconda3/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/home/duchemin/anaconda3/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.distplot(lsstatnull_sat, hist = False, kde = True,\n",
    "                 kde_kws = {'linewidth': 3},\n",
    "                 label = 'SIGLE statistic pdf')\n",
    "chi2 = stats.chi2.rvs(optdf, size=10000)\n",
    "sns.distplot(chi2, hist = False, kde = True,\n",
    "                 kde_kws = {'linewidth': 3, 'linestyle':'--'},\n",
    "                 label = '$\\chi^2({0})$ pdf'.format(optdf))\n",
    "plt.legend(fontsize=13)\n",
    "plt.ylabel('Density', fontsize=13)\n",
    "plt.savefig('PDFs_sigle_vs_chi2_nu04.png', dpi=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81730da8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}