Truth_Trunk_Marron.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys, os\n",
    "from joblib import Parallel, delayed\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import scipy\n",
    "from scipy.integrate import quad, nquad\n",
    "from sklearn.preprocessing import normalize\n",
    "from sktree.tree import DecisionTreeClassifier\n",
    "from sktree.ensemble import HonestForestClassifier\n",
    "from sktree.stats import FeatureImportanceForestClassifier\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from scipy.stats import entropy\n",
    "\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import multivariate_normal\n",
    "from scipy.integrate import simps\n",
    "from scipy.stats import entropy\n",
    "from scipy.stats import gamma\n",
    "from simulations import *\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hyppo import make_trunk_classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "SIMULATIONS = {\n",
    "    \"1\" : {},\n",
    "    \"2\" : {\"m_factor\" : 1},\n",
    "    \"3\" : {\"band_type\" : \"ar\", \"rho\" : 0.5},\n",
    "    \"4\" : {\"band_type\" : \"ar\", \"m_factor\" : 1, \"rho\" : 0.5},\n",
    "    \"5\" : {\"mix\" : 0.5}\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TRUNK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "Dimension256\n",
      "entropy0.018205466547358797\n",
      "MI0.6749417140125865\n",
      "pAUC 0.9987425157894736\n",
      "[0.e+00 2.e-05 4.e-05 ... 1.e+00 1.e+00 1.e+00]\n",
      "S@98 0.99808\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x1500 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100000\n",
    "\n",
    "DIMENSIONS = [2**i for i in range(8, 9)]\n",
    "# DIMENSIONS = [i for i in range(2, 100,2)]\n",
    "plt.rcParams[\"font.size\"] = 10\n",
    "fig, axs = plt.subplots(4, 3,figsize=(15, 15))\n",
    "for i in [\"1\"]:\n",
    "    print(int(i))\n",
    "    MIs = []\n",
    "    pAUCs = []\n",
    "    tprs = []\n",
    "    for p in DIMENSIONS:\n",
    "        print(\"Dimension\" + str(p))\n",
    "        ### sample from TRUNK\n",
    "        x,y,mu,cov = make_trunk_classification(n_samples=n, n_dim=p, **SIMULATIONS[i],return_params = True)\n",
    "        p_class0 = 0.5\n",
    "        p_class1 = 0.5\n",
    "        x = np.float32(x)\n",
    "        y = np.float32(y)\n",
    "        ## Get the pdf for class one and class two\n",
    "        pdf_class0 = multivariate_normal(mean = mu[0], cov = cov[0],allow_singular=True)\n",
    "        pdf_class1 = multivariate_normal(mean = mu[1], cov = cov[1],allow_singular=True)\n",
    "        \n",
    "        p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "        p_x_given_class1 = np.nan_to_num(pdf_class1.pdf(x))\n",
    "\n",
    "\n",
    "        p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "        # pos_class0 = p_x_given_class0*p_class0/p_x\n",
    "\n",
    "        pos_class0 = (np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1))\n",
    "        pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "        posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "        # print(posterior.shape)\n",
    "        # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "        stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "        prior_y = np.array([p_class0,p_class1])\n",
    "        entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "        print('entropy'+str(stats_conen))\n",
    "        MI = entropy_y - stats_conen\n",
    "        print(\"MI\"+str(MI))\n",
    "        MIs.append(MI)\n",
    "        # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "        # plt.show()\n",
    "        pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "        print('pAUC '+ str(pauc))\n",
    "        pAUCs.append(pauc)\n",
    "\n",
    "        fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "        print(tpr)\n",
    "        # plt.plot(fpr,tpr)\n",
    "        if len(tpr) == len(fpr) == 2:\n",
    "            tprs.append(0.02)\n",
    "        elif len(tpr[np.round(fpr, 3)==0.02]) == 0:\n",
    "            tpr_s = np.max(tpr[fpr<=0.02])\n",
    "            print('S@98 '+ str(tpr_s))\n",
    "            tprs.append(tpr_s)\n",
    "        \n",
    "        else:\n",
    "            tpr_s = np.max(tpr[fpr<=0.02])\n",
    "            print('S@98 '+ str(tpr_s))\n",
    "            tprs.append(tpr_s)\n",
    "    np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Trunk_{}.csv\".format(i), tprs, delimiter=\",\")\n",
    "\n",
    "    axs[int(i)-1,0].plot(DIMENSIONS,tprs,\n",
    "                        'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "    axs[int(i)-1,0].set_ylabel('Simulation '+ str(i)+ '\\n \\n Sensitivity at 98% Specificity')\n",
    "    axs[int(i)-1,0].set_xlabel('Dimension')\n",
    "    axs[int(i)-1,0].set_ylim((-0.01,1.01))\n",
    "    axs[int(i)-1,0].set_yticks((0,0.5,1))\n",
    "    axs[int(i)-1,0].set_xticks((4,100,200))\n",
    "\n",
    "    axs[int(i)-1,1].plot(DIMENSIONS,MIs,\n",
    "                        'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "    axs[int(i)-1,1].set_ylabel('Mutual Information')\n",
    "    axs[int(i)-1,1].set_xlabel('Dimension')\n",
    "    axs[int(i)-1,1].set_ylim((-0.01,0.71))\n",
    "    axs[int(i)-1,1].set_yticks((0,0.7))\n",
    "    axs[int(i)-1,1].set_xticks((4,100,200))\n",
    "\n",
    "    axs[int(i)-1,2].plot(DIMENSIONS,pAUCs,\n",
    "                        'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "    axs[int(i)-1,2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "    axs[int(i)-1,2].set_xlabel('Dimension')\n",
    "    axs[int(i)-1,2].set_ylim((0.49,1.01))\n",
    "    axs[int(i)-1,2].set_yticks((0.5,1))\n",
    "    axs[int(i)-1,2].set_xticks((4,100,200))\n",
    "\n",
    "    axs[int(i)-1,2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.10043861936391474\n",
      "pAUC 0.6231504947368421\n",
      "S@98 0.19224\n",
      "MI0.14266059928168273\n",
      "pAUC 0.6599032405263158\n",
      "S@98 0.25137\n",
      "MI0.186135995049458\n",
      "pAUC 0.6922189215789474\n",
      "S@98 0.30747\n",
      "MI0.22914032581595256\n",
      "pAUC 0.7306741168421053\n",
      "S@98 0.37319\n",
      "MI0.2700314080514234\n",
      "pAUC 0.761531107368421\n",
      "S@98 0.44178\n",
      "MI0.3082623374198656\n",
      "pAUC 0.788302225263158\n",
      "S@98 0.49677\n",
      "MI0.34406402765006877\n",
      "pAUC 0.8176725431578947\n",
      "S@98 0.55933\n"
     ]
    }
   ],
   "source": [
    "#### Mixture Gaussian\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    mu_class1 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    sig = np.identity(p)\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1, cov = sig,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = -mu_class1, cov = sig,allow_singular=True)\n",
    "\n",
    "    n1 = np.random.binomial(n, 0.5)\n",
    "    n2 = n - n1\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n2)\n",
    "    x = np.vstack((x_0,x_1_1,x_1_2))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2.pdf(x))\n",
    "    p_x_given_class1 = 0.5*p_x_given_class1_1+0.5*p_x_given_class1_2\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Mixture_Gaussian.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Mixture Gaussian')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3,figsize=(15, 5))\n",
    "axs[0].plot(DIMENSIONS,tprs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[0].set_ylabel('Sensitivity at 98% Specificity')\n",
    "axs[0].set_xlabel('Dimension')\n",
    "axs[0].set_ylim((-0.01,1.01))\n",
    "axs[0].set_yticks((0,0.5,1))\n",
    "axs[0].set_xticks((2,100,200))\n",
    "\n",
    "axs[1].plot(DIMENSIONS,MIs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[1].set_ylabel('Mutual Information')\n",
    "axs[1].set_xlabel('Dimension')\n",
    "axs[1].set_ylim((-0.01,0.71))\n",
    "axs[1].set_yticks((0,0.7))\n",
    "axs[1].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].plot(DIMENSIONS,pAUCs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "axs[2].set_xlabel('Dimension')\n",
    "axs[2].set_ylim((0.49,1.01))\n",
    "axs[2].set_yticks((0.5,1))\n",
    "axs[2].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n",
    "\n",
    "plt.suptitle('Mixture Gaussian')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Skewed Unimodal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.2370302300727838\n",
      "pAUC 0.6970173536842106\n",
      "S@98 0.27194\n",
      "MI0.3241472997667929\n",
      "pAUC 0.780820062631579\n",
      "S@98 0.45876\n",
      "MI0.3998355536940342\n",
      "pAUC 0.8418148610526316\n",
      "S@98 0.60874\n",
      "MI0.46099262149445674\n",
      "pAUC 0.8892458894736842\n",
      "S@98 0.71813\n",
      "MI0.5078103181980063\n",
      "pAUC 0.92251629\n",
      "S@98 0.80243\n",
      "MI0.5461465742928849\n",
      "pAUC 0.9473388473684211\n",
      "S@98 0.86445\n",
      "MI0.5739532184063624\n",
      "pAUC 0.9640251294736841\n",
      "S@98 0.90422\n"
     ]
    }
   ],
   "source": [
    "#### Skewed Unimodal\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "    mu_class1_1 = np.array([0 for i in range(p)])\n",
    "    mu_class1_2 = np.array([1/2 for i in range(p)])\n",
    "    mu_class1_3 = np.array([12/13 for i in range(p)])\n",
    "    sig_1_1 = np.identity(p)\n",
    "    sig_1_2 = (4/9)*np.identity(p)\n",
    "    sig_1_3 = (25/81)*np.identity(p)\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1_1, cov = sig_1_1,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = mu_class1_2, cov =sig_1_2,allow_singular=True)\n",
    "    pdf_class1_3 = multivariate_normal(mean = mu_class1_3, cov =sig_1_3,allow_singular=True)\n",
    "    \n",
    "    n1_1 = np.random.binomial(n, 0.2)\n",
    "    n1_2 = np.random.binomial(n, 0.2)\n",
    "    n1_3 = n - n1_1-n1_2\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1_1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n1_2)\n",
    "    x_1_3 = pdf_class1_3.rvs(size = n1_3)\n",
    "    z_2 = np.vstack((x_1_1,x_1_2,x_1_3))\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "    mu_class1_1_weighted  = mu_class1_1*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_2_weighted  = mu_class1_2*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_3_weighted  = mu_class1_3*coeff_z2+mu_class0*coeff_z1\n",
    "    sig_1_1_weighted  = sig_1_1*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_2_weighted  = sig_1_2*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_3_weighted  = sig_1_3*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "\n",
    "\n",
    "    pdf_class1_1_weighted = multivariate_normal(mean = mu_class1_1_weighted, cov = sig_1_1_weighted,allow_singular=True)\n",
    "    pdf_class1_2_weighted = multivariate_normal(mean = mu_class1_2_weighted, cov =sig_1_2_weighted,allow_singular=True)\n",
    "    pdf_class1_3_weighted = multivariate_normal(mean = mu_class1_3_weighted, cov =sig_1_3_weighted,allow_singular=True)\n",
    "    \n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1_weighted.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2_weighted.pdf(x))\n",
    "    p_x_given_class1_3 = np.nan_to_num(pdf_class1_3_weighted.pdf(x))\n",
    "\n",
    "    p_x_given_class1 = 0.2*p_x_given_class1_1+0.2*p_x_given_class1_2+0.6*p_x_given_class1_3\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Skewed_Unimodal.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Mixture Gaussian')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3,figsize=(15, 5))\n",
    "axs[0].plot(DIMENSIONS,tprs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[0].set_ylabel('Sensitivity at 98% Specificity')\n",
    "axs[0].set_xlabel('Dimension')\n",
    "axs[0].set_ylim((-0.01,1.01))\n",
    "axs[0].set_yticks((0,0.5,1))\n",
    "axs[0].set_xticks((2,100,200))\n",
    "\n",
    "axs[1].plot(DIMENSIONS,MIs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[1].set_ylabel('Mutual Information')\n",
    "axs[1].set_xlabel('Dimension')\n",
    "axs[1].set_ylim((-0.01,0.71))\n",
    "axs[1].set_yticks((0,0.7))\n",
    "axs[1].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].plot(DIMENSIONS,pAUCs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "axs[2].set_xlabel('Dimension')\n",
    "axs[2].set_ylim((0.49,1.01))\n",
    "axs[2].set_yticks((0.5,1))\n",
    "axs[2].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n",
    "\n",
    "plt.suptitle('Skewed Unimodal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strongly Skewed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kurtotic Unimodal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.14888712701406215\n",
      "pAUC 0.6586952505263157\n",
      "S@98 0.28645\n",
      "MI0.22469933369581974\n",
      "pAUC 0.7008524226315789\n",
      "S@98 0.34955\n",
      "MI0.3046265243140798\n",
      "pAUC 0.7541760463157895\n",
      "S@98 0.4234\n",
      "MI0.37595968473183716\n",
      "pAUC 0.8129794721052631\n",
      "S@98 0.53531\n",
      "MI0.4345032853709957\n",
      "pAUC 0.8606846468421052\n",
      "S@98 0.64008\n",
      "MI0.48369959808085405\n",
      "pAUC 0.899846807368421\n",
      "S@98 0.73544\n",
      "MI0.5219711624859653\n",
      "pAUC 0.9293670447368421\n",
      "S@98 0.812\n"
     ]
    }
   ],
   "source": [
    "### Kurtotic Unimodal\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "    mu_class1_1 = np.array([0 for i in range(p)])\n",
    "    mu_class1_2 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    sig_1_1 = np.identity(p)\n",
    "    sig_1_2 = (1/100)*np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1_1, cov = sig_1_1,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = mu_class1_2, cov =sig_1_2,allow_singular=True)\n",
    "    \n",
    "    n1_1 = np.random.binomial(n, 2/3)\n",
    "    # print(n1_1)\n",
    "    n1_2 = n - n1_1\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1_1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n1_2)\n",
    "    z_2 = np.vstack((x_1_1,x_1_2))\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "    mu_class1_1_weighted  = mu_class1_1*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_2_weighted  = mu_class1_2*coeff_z2+mu_class0*coeff_z1\n",
    "\n",
    "    sig_1_1_weighted  = sig_1_1*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_2_weighted  = sig_1_2*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "\n",
    "\n",
    "\n",
    "    pdf_class1_1_weighted = multivariate_normal(mean = mu_class1_1_weighted, cov = sig_1_1_weighted,allow_singular=True)\n",
    "    pdf_class1_2_weighted = multivariate_normal(mean = mu_class1_2_weighted, cov =sig_1_2_weighted,allow_singular=True)\n",
    "    \n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1_weighted.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2_weighted.pdf(x))\n",
    "\n",
    "\n",
    "    p_x_given_class1 = (2/3)*p_x_given_class1_1+(1/3)*p_x_given_class1_2\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Kurtotic_Unimodal.csv\", tprs, delimiter=\",\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Kurtotic Unimodal')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3,figsize=(15, 5))\n",
    "axs[0].plot(DIMENSIONS,tprs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[0].set_ylabel('Sensitivity at 98% Specificity')\n",
    "axs[0].set_xlabel('Dimension')\n",
    "axs[0].set_ylim((-0.01,1.01))\n",
    "axs[0].set_yticks((0,0.5,1))\n",
    "axs[0].set_xticks((2,100,200))\n",
    "\n",
    "axs[1].plot(DIMENSIONS,MIs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[1].set_ylabel('Mutual Information')\n",
    "axs[1].set_xlabel('Dimension')\n",
    "axs[1].set_ylim((-0.01,0.71))\n",
    "axs[1].set_yticks((0,0.7))\n",
    "axs[1].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].plot(DIMENSIONS,pAUCs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "axs[2].set_xlabel('Dimension')\n",
    "axs[2].set_ylim((0.49,1.01))\n",
    "axs[2].set_yticks((0.5,1))\n",
    "axs[2].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n",
    "\n",
    "plt.suptitle('Kurtotic Unimodal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outlier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.44092182015069853\n",
      "pAUC 0.8855386189473684\n",
      "S@98 0.69941\n",
      "MI0.4847862364046617\n",
      "pAUC 0.9201224184210526\n",
      "S@98 0.82451\n",
      "MI0.5203473896942746\n",
      "pAUC 0.9402474621052632\n",
      "S@98 0.87008\n",
      "MI0.5512351418120499\n",
      "pAUC 0.9549659810526315\n",
      "S@98 0.8956\n",
      "MI0.5773686045279468\n",
      "pAUC 0.9672830905263157\n",
      "S@98 0.92307\n",
      "MI0.5980512710899101\n",
      "pAUC 0.9770488852631579\n",
      "S@98 0.94417\n",
      "MI0.6152972839222376\n",
      "pAUC 0.9834058242105261\n",
      "S@98 0.96053\n"
     ]
    }
   ],
   "source": [
    "### Outlier\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "    mu_class1_1 = np.array([0 for i in range(p)])\n",
    "    mu_class1_2 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    sig_1_1 = np.identity(p)\n",
    "    sig_1_2 = (1/100)*np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1_1, cov = sig_1_1,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = mu_class1_2, cov =sig_1_2,allow_singular=True)\n",
    "    \n",
    "    n1_1 = np.random.binomial(n, 1/10)\n",
    "    # print(n1_1)\n",
    "    n1_2 = n - n1_1\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1_1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n1_2)\n",
    "    z_2 = np.vstack((x_1_1,x_1_2))\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "    mu_class1_1_weighted  = mu_class1_1*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_2_weighted  = mu_class1_2*coeff_z2+mu_class0*coeff_z1\n",
    "\n",
    "    sig_1_1_weighted  = sig_1_1*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_2_weighted  = sig_1_2*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "\n",
    "\n",
    "\n",
    "    pdf_class1_1_weighted = multivariate_normal(mean = mu_class1_1_weighted, cov = sig_1_1_weighted,allow_singular=True)\n",
    "    pdf_class1_2_weighted = multivariate_normal(mean = mu_class1_2_weighted, cov =sig_1_2_weighted,allow_singular=True)\n",
    "    \n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1_weighted.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2_weighted.pdf(x))\n",
    "\n",
    "\n",
    "    p_x_given_class1 = (1/10)*p_x_given_class1_1+(9/10)*p_x_given_class1_2\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Outlier.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Outlier')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3,figsize=(15, 5))\n",
    "axs[0].plot(DIMENSIONS,tprs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[0].set_ylabel('Sensitivity at 98% Specificity')\n",
    "axs[0].set_xlabel('Dimension')\n",
    "axs[0].set_ylim((-0.01,1.01))\n",
    "axs[0].set_yticks((0,0.5,1))\n",
    "axs[0].set_xticks((2,100,200))\n",
    "\n",
    "axs[1].plot(DIMENSIONS,MIs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[1].set_ylabel('Mutual Information')\n",
    "axs[1].set_xlabel('Dimension')\n",
    "axs[1].set_ylim((-0.01,0.71))\n",
    "axs[1].set_yticks((0,0.7))\n",
    "axs[1].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].plot(DIMENSIONS,pAUCs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "axs[2].set_xlabel('Dimension')\n",
    "axs[2].set_ylim((0.49,1.01))\n",
    "axs[2].set_yticks((0.5,1))\n",
    "axs[2].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n",
    "\n",
    "plt.suptitle('Outlier')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bimodal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.2610885637707866\n",
      "pAUC 0.67935941\n",
      "S@98 0.2328\n",
      "MI0.38482262111068605\n",
      "pAUC 0.7937391210526317\n",
      "S@98 0.45828\n",
      "MI0.4745362418146924\n",
      "pAUC 0.8814157484210526\n",
      "S@98 0.67849\n",
      "MI0.5380037947219697\n",
      "pAUC 0.9316331889473684\n",
      "S@98 0.81512\n",
      "MI0.5807553934862785\n",
      "pAUC 0.9620659442105264\n",
      "S@98 0.90289\n",
      "MI0.6114296913261951\n",
      "pAUC 0.9797050652631578\n",
      "S@98 0.95279\n",
      "MI0.6337291158473524\n",
      "pAUC 0.9884816626315789\n",
      "S@98 0.97513\n"
     ]
    }
   ],
   "source": [
    "### Bimodal\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "    mu_class1_1 = np.array([-1 for i in range(p)])\n",
    "    mu_class1_2 = np.array([1 for i in range(p)])\n",
    "    \n",
    "    sig_1_1 = (4/9)*np.identity(p)\n",
    "    sig_1_2 = (4/9)*np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1_1, cov = sig_1_1,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = mu_class1_2, cov =sig_1_2,allow_singular=True)\n",
    "    \n",
    "    p = 1/2\n",
    "    n1_1 = np.random.binomial(n, p)\n",
    "    # print(n1_1)\n",
    "    n1_2 = n - n1_1\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1_1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n1_2)\n",
    "    z_2 = np.vstack((x_1_1,x_1_2))\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "    mu_class1_1_weighted  = mu_class1_1*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_2_weighted  = mu_class1_2*coeff_z2+mu_class0*coeff_z1\n",
    "\n",
    "    sig_1_1_weighted  = sig_1_1*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_2_weighted  = sig_1_2*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "\n",
    "\n",
    "\n",
    "    pdf_class1_1_weighted = multivariate_normal(mean = mu_class1_1_weighted, cov = sig_1_1_weighted,allow_singular=True)\n",
    "    pdf_class1_2_weighted = multivariate_normal(mean = mu_class1_2_weighted, cov =sig_1_2_weighted,allow_singular=True)\n",
    "    \n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1_weighted.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2_weighted.pdf(x))\n",
    "\n",
    "\n",
    "    p_x_given_class1 = p*p_x_given_class1_1+(1-p)*p_x_given_class1_2\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Bimodal.csv\", tprs, delimiter=\",\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Bimodal')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3,figsize=(15, 5))\n",
    "axs[0].plot(DIMENSIONS,tprs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[0].set_ylabel('Sensitivity at 98% Specificity')\n",
    "axs[0].set_xlabel('Dimension')\n",
    "axs[0].set_ylim((-0.01,1.01))\n",
    "axs[0].set_yticks((0,0.5,1))\n",
    "axs[0].set_xticks((2,100,200))\n",
    "\n",
    "axs[1].plot(DIMENSIONS,MIs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[1].set_ylabel('Mutual Information')\n",
    "axs[1].set_xlabel('Dimension')\n",
    "axs[1].set_ylim((-0.01,0.71))\n",
    "axs[1].set_yticks((0,0.7))\n",
    "axs[1].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].plot(DIMENSIONS,pAUCs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "axs[2].set_xlabel('Dimension')\n",
    "axs[2].set_ylim((0.49,1.01))\n",
    "axs[2].set_yticks((0.5,1))\n",
    "axs[2].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n",
    "\n",
    "plt.suptitle('Bimodal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Separated Bimodal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.5080176225583501\n",
      "pAUC 0.8892351731578947\n",
      "S@98 0.67624\n",
      "MI0.5864794933233697\n",
      "pAUC 0.9593202831578947\n",
      "S@98 0.89622\n",
      "MI0.6294483713143608\n",
      "pAUC 0.9844980931578947\n",
      "S@98 0.97016\n",
      "MI0.654437236801647\n",
      "pAUC 0.9945920894736842\n",
      "S@98 0.99221\n",
      "MI0.6686819355748189\n",
      "pAUC 0.9977318289473684\n",
      "S@98 0.99773\n",
      "MI0.6773848981286941\n",
      "pAUC 0.9989742778947368\n",
      "S@98 0.99924\n",
      "MI0.6830957745449959\n",
      "pAUC 0.9995409394736843\n",
      "S@98 0.99982\n"
     ]
    }
   ],
   "source": [
    "### Bimodal\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "    mu_class1_1 = np.array([-3/2 for i in range(p)])\n",
    "    mu_class1_2 = np.array([3/2 for i in range(p)])\n",
    "    \n",
    "    sig_1_1 = (1/4)*np.identity(p)\n",
    "    sig_1_2 = (1/4)*np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1_1, cov = sig_1_1,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = mu_class1_2, cov =sig_1_2,allow_singular=True)\n",
    "    \n",
    "    p = 1/2\n",
    "    n1_1 = np.random.binomial(n, p)\n",
    "    # print(n1_1)\n",
    "    n1_2 = n - n1_1\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1_1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n1_2)\n",
    "    z_2 = np.vstack((x_1_1,x_1_2))\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "    mu_class1_1_weighted  = mu_class1_1*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_2_weighted  = mu_class1_2*coeff_z2+mu_class0*coeff_z1\n",
    "\n",
    "    sig_1_1_weighted  = sig_1_1*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_2_weighted  = sig_1_2*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "\n",
    "\n",
    "\n",
    "    pdf_class1_1_weighted = multivariate_normal(mean = mu_class1_1_weighted, cov = sig_1_1_weighted,allow_singular=True)\n",
    "    pdf_class1_2_weighted = multivariate_normal(mean = mu_class1_2_weighted, cov =sig_1_2_weighted,allow_singular=True)\n",
    "    \n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1_weighted.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2_weighted.pdf(x))\n",
    "\n",
    "\n",
    "    p_x_given_class1 = p*p_x_given_class1_1+(1-p)*p_x_given_class1_2\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Separated_Bimodal.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Separate Bimodal')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3,figsize=(15, 5))\n",
    "axs[0].plot(DIMENSIONS,tprs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[0].set_ylabel('Sensitivity at 98% Specificity')\n",
    "axs[0].set_xlabel('Dimension')\n",
    "axs[0].set_ylim((-0.01,1.01))\n",
    "axs[0].set_yticks((0,0.5,1))\n",
    "axs[0].set_xticks((2,100,200))\n",
    "\n",
    "axs[1].plot(DIMENSIONS,MIs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[1].set_ylabel('Mutual Information')\n",
    "axs[1].set_xlabel('Dimension')\n",
    "axs[1].set_ylim((-0.01,0.71))\n",
    "axs[1].set_yticks((0,0.7))\n",
    "axs[1].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].plot(DIMENSIONS,pAUCs,\n",
    "                    'black',marker='o', markersize=2,label = 'Truth',linewidth =2)\n",
    "axs[2].set_ylabel('Partial AUC (90% Specificity)')\n",
    "axs[2].set_xlabel('Dimension')\n",
    "axs[2].set_ylim((0.49,1.01))\n",
    "axs[2].set_yticks((0.5,1))\n",
    "axs[2].set_xticks((2,100,200))\n",
    "\n",
    "axs[2].legend(bbox_to_anchor = (1.8,1),loc = 'upper right')\n",
    "\n",
    "plt.suptitle('Separate Bimodal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Skewed Bimodal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.1265832839347698\n",
      "pAUC 0.6293415105263158\n",
      "S@98 0.24813\n",
      "MI0.20676300916602436\n",
      "pAUC 0.6779637384210526\n",
      "S@98 0.30191\n",
      "MI0.2908017261711566\n",
      "pAUC 0.7413222168421052\n",
      "S@98 0.39578\n",
      "MI0.36465172917408833\n",
      "pAUC 0.8031772221052631\n",
      "S@98 0.51402\n",
      "MI0.42609894634802065\n",
      "pAUC 0.8525838168421052\n",
      "S@98 0.61837\n",
      "MI0.4773722087434241\n",
      "pAUC 0.8959142415789474\n",
      "S@98 0.72512\n",
      "MI0.5173812437721691\n",
      "pAUC 0.9242926868421052\n",
      "S@98 0.8\n"
     ]
    }
   ],
   "source": [
    "### Skewed Bimodal\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "    mu_class1_1 = np.array([0 for i in range(p)])\n",
    "    mu_class1_2 = np.array([3/2 for i in range(p)])\n",
    "    \n",
    "    sig_1_1 = np.identity(p)\n",
    "    sig_1_2 = np.square(1/3)*np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "    pdf_class1_1 = multivariate_normal(mean = mu_class1_1, cov = sig_1_1,allow_singular=True)\n",
    "    pdf_class1_2 = multivariate_normal(mean = mu_class1_2, cov =sig_1_2,allow_singular=True)\n",
    "    \n",
    "    p = 3/4\n",
    "    n1_1 = np.random.binomial(n, p)\n",
    "    # print(n1_1)\n",
    "    n1_2 = n - n1_1\n",
    "    # print(n1,n2)\n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    x_1_1 = pdf_class1_1.rvs(size = n1_1)\n",
    "    x_1_2 = pdf_class1_2.rvs(size = n1_2)\n",
    "    z_2 = np.vstack((x_1_1,x_1_2))\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "    mu_class1_1_weighted  = mu_class1_1*coeff_z2+mu_class0*coeff_z1\n",
    "    mu_class1_2_weighted  = mu_class1_2*coeff_z2+mu_class0*coeff_z1\n",
    "\n",
    "    sig_1_1_weighted  = sig_1_1*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "    sig_1_2_weighted  = sig_1_2*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "\n",
    "\n",
    "\n",
    "    pdf_class1_1_weighted = multivariate_normal(mean = mu_class1_1_weighted, cov = sig_1_1_weighted,allow_singular=True)\n",
    "    pdf_class1_2_weighted = multivariate_normal(mean = mu_class1_2_weighted, cov =sig_1_2_weighted,allow_singular=True)\n",
    "    \n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "    p_x_given_class1_1 = np.nan_to_num(pdf_class1_1_weighted.pdf(x))\n",
    "    p_x_given_class1_2 = np.nan_to_num(pdf_class1_2_weighted.pdf(x))\n",
    "\n",
    "\n",
    "    p_x_given_class1 = p*p_x_given_class1_1+(1-p)*p_x_given_class1_2\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Skewed_Bimodal.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trimodal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "MI0.2885248797252763\n",
      "pAUC 0.7134464068421053\n",
      "S@98 0.3037\n",
      "1.0\n",
      "MI0.3948840415616861\n",
      "pAUC 0.8316854805263159\n",
      "S@98 0.55194\n",
      "1.0\n",
      "MI0.4828046542222914\n",
      "pAUC 0.9099149363157895\n",
      "S@98 0.7483\n",
      "1.0\n",
      "MI0.5439290997837068\n",
      "pAUC 0.9511351805263158\n",
      "S@98 0.86924\n",
      "1.0\n",
      "MI0.5870911559052401\n",
      "pAUC 0.9737534142105262\n",
      "S@98 0.93285\n",
      "1.0\n",
      "MI0.6162942642629795\n",
      "pAUC 0.9857972031578945\n",
      "S@98 0.96587\n",
      "1.0\n",
      "MI0.636870371828872\n",
      "pAUC 0.9917256689473684\n",
      "S@98 0.98244\n"
     ]
    }
   ],
   "source": [
    "## Trimodal\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([9/20 if k <= 1 else 1/10 for k in range(3)])\n",
    "    print(sum(prior_p))\n",
    "    for i in range(3):\n",
    "        if i==0:\n",
    "            mu_class1_i = np.array([-6/5 for _ in range(p)])\n",
    "            sig_1_i = np.square(3/5)*np.identity(p)\n",
    "        elif i==1:\n",
    "            mu_class1_i = np.array([6/5 for _ in range(p)])\n",
    "            sig_1_i = np.square(3/5)*np.identity(p)\n",
    "        else:\n",
    "            mu_class1_i = np.array([0 for _ in range(p)])\n",
    "            sig_1_i = np.square(1/4)*np.identity(p)\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <2:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(3):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Trimodal.csv\", tprs, delimiter=\",\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Strongly Skewed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.3552425515479054\n",
      "pAUC 0.7603989226315789\n",
      "S@98 0.41628\n",
      "MI0.4474280197779684\n",
      "pAUC 0.8500283794736843\n",
      "S@98 0.60059\n",
      "MI0.5139940571893992\n",
      "pAUC 0.9111997384210526\n",
      "S@98 0.75236\n",
      "MI0.5582254118974681\n",
      "pAUC 0.9461372078947368\n",
      "S@98 0.85106\n",
      "MI0.5903941627798487\n",
      "pAUC 0.9679167757894737\n",
      "S@98 0.91588\n",
      "MI0.6133499709760484\n",
      "pAUC 0.9802383147368421\n",
      "S@98 0.95009\n",
      "MI0.6311661789690123\n",
      "pAUC 0.9871721842105263\n",
      "S@98 0.97059\n"
     ]
    }
   ],
   "source": [
    "### Strongly Skewed\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([1/8 for p in range(8)])\n",
    "    for i in range(8):\n",
    "        mu_class1_i = np.array([3*(2/3)**i-1 for _ in range(p)])\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1_i = (2/3)**(2*i)*np.identity(p)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <7:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(8):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Strongly_Skewed.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Claw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.3152242656880713\n",
      "pAUC 0.6728769431578947\n",
      "S@98 0.26358\n",
      "MI0.36901706469134177\n",
      "pAUC 0.7303908005263158\n",
      "S@98 0.39978\n",
      "MI0.4106605282582527\n",
      "pAUC 0.7851657889473684\n",
      "S@98 0.49545\n",
      "MI0.4487446484212332\n",
      "pAUC 0.8373758010526315\n",
      "S@98 0.59359\n",
      "MI0.48416886805991804\n",
      "pAUC 0.8793242626315789\n",
      "S@98 0.68669\n",
      "MI0.5172639648319874\n",
      "pAUC 0.9154542968421053\n",
      "S@98 0.7752\n",
      "MI0.5450968149012112\n",
      "pAUC 0.9390211231578947\n",
      "S@98 0.8388\n"
     ]
    }
   ],
   "source": [
    "## Claw\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([1/2 if k == 0 else 1/10 for k in range(5)])\n",
    "    for i in range(5):\n",
    "        if i==0:\n",
    "            mu_class1_i = np.array([0 for _ in range(p)])\n",
    "            sig_1_i = np.identity(p)\n",
    "        else:\n",
    "            mu_class1_i = np.array([((i-1)/2)-1 for _ in range(p)])\n",
    "            sig_1_i = (1/100)*np.identity(p)\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <4:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(5):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Claw.csv\", tprs, delimiter=\",\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Double Claw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n",
      "MI0.5708892558926152\n",
      "pAUC 0.5683835736842106\n",
      "S@98 0.08947\n",
      "1.0000000000000002\n",
      "MI0.5509996250566777\n",
      "pAUC 0.6539862968421053\n",
      "S@98 0.19685\n",
      "1.0000000000000002\n",
      "MI0.5212758821966929\n",
      "pAUC 0.7551510115789474\n",
      "S@98 0.3759\n",
      "1.0000000000000002\n",
      "MI0.5006338272883493\n",
      "pAUC 0.8417263547368421\n",
      "S@98 0.58225\n",
      "1.0000000000000002\n",
      "MI0.4960244043582769\n",
      "pAUC 0.9013807168421053\n",
      "S@98 0.7347\n",
      "1.0000000000000002\n",
      "MI0.508698711813077\n",
      "pAUC 0.9376727526315789\n",
      "S@98 0.83456\n",
      "1.0000000000000002\n",
      "MI0.5297943471715688\n",
      "pAUC 0.9641879168421053\n",
      "S@98 0.9059\n"
     ]
    }
   ],
   "source": [
    "## Double Claw\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([49/100 if k <= 1 else 1/350 for k in range(9)])\n",
    "    print(sum(prior_p))\n",
    "    for i in range(9):\n",
    "        if i == 0:\n",
    "            mu_class1_i = np.array([-1 for _ in range(p)])\n",
    "            sig_1_i = np.identity(p)\n",
    "        elif i == 1:\n",
    "            mu_class1_i = np.array([1 for _ in range(p)])\n",
    "            sig_1_i = np.identity(p)\n",
    "        else:\n",
    "            mu_class1_i = np.array([(i-5)/2 for _ in range(p)])\n",
    "            sig_1_i = (1/100)*np.identity(p)\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <8:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(9):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Double_Claw.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Asymmetric Claw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MI0.39716615064877503\n",
      "pAUC 0.6798530994736842\n",
      "S@98 0.28689\n",
      "MI0.44142338455073826\n",
      "pAUC 0.7391842184210526\n",
      "S@98 0.42518\n",
      "MI0.47159580787924044\n",
      "pAUC 0.7936764010526316\n",
      "S@98 0.5158\n",
      "MI0.4912799378433852\n",
      "pAUC 0.8461726015789475\n",
      "S@98 0.61266\n",
      "MI0.509546284839362\n",
      "pAUC 0.8873908363157894\n",
      "S@98 0.70646\n",
      "MI0.5293529366853866\n",
      "pAUC 0.9184799042105263\n",
      "S@98 0.78369\n",
      "MI0.548908532193414\n",
      "pAUC 0.9435630205263157\n",
      "S@98 0.85034\n"
     ]
    }
   ],
   "source": [
    "## Asymmetric Claw\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([1/2 if k == 0 else 2**(4-k)/31 for k in range(5)])\n",
    "    for i in range(5):\n",
    "        if i==0:\n",
    "            mu_class1_i = np.array([0 for _ in range(p)])\n",
    "            sig_1_i = np.identity(p)\n",
    "        else:\n",
    "            mu_class1_i = np.array([i-5/2 for _ in range(p)])\n",
    "            sig_1_i = np.square(2**(3-i)/10)*np.identity(p)\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <4:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(5):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Asymmetric_Claw.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Asymmetric Double Claw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999999999999999\n",
      "MI0.4297192583834661\n",
      "pAUC 0.6122746778947369\n",
      "S@98 0.1321\n",
      "0.9999999999999999\n",
      "MI0.42673826738857706\n",
      "pAUC 0.6994459026315789\n",
      "S@98 0.27421\n",
      "0.9999999999999999\n",
      "MI0.43301098800006554\n",
      "pAUC 0.7898771968421052\n",
      "S@98 0.46118\n",
      "0.9999999999999999\n",
      "MI0.4582868794009243\n",
      "pAUC 0.8657037089473685\n",
      "S@98 0.64098\n",
      "0.9999999999999999\n",
      "MI0.49526876820856347\n",
      "pAUC 0.9178848826315789\n",
      "S@98 0.77846\n",
      "0.9999999999999999\n",
      "MI0.532426683635904\n",
      "pAUC 0.9503728247368421\n",
      "S@98 0.87028\n",
      "0.9999999999999999\n",
      "MI0.5646132114728338\n",
      "pAUC 0.9703146199999999\n",
      "S@98 0.92688\n"
     ]
    }
   ],
   "source": [
    "## Double Claw\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([46/100 if k <= 1 \n",
    "                        else 1/300 if 1< k <=4\n",
    "                        else 7/300 for k in range(8)])\n",
    "    print(sum(prior_p))\n",
    "    for i in range(8):\n",
    "        if i <= 1:\n",
    "            mu_class1_i = np.array([2*i-1 for _ in range(p)])\n",
    "            sig_1_i = np.identity(p)\n",
    "        elif 2<= i <= 4:\n",
    "            mu_class1_i = np.array([-(i-1)/2 for _ in range(p)])\n",
    "            sig_1_i = np.square(1/100)*np.identity(p)\n",
    "        else:\n",
    "            mu_class1_i = np.array([(i-4)/2 for _ in range(p)])\n",
    "            sig_1_i = np.square(7/100)*np.identity(p)\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <7:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(8):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Asymmetric_Double_Claw.csv\", tprs, delimiter=\",\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Smooth Comb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "MI0.4461851836370763\n",
      "pAUC 0.877667884736842\n",
      "S@98 0.64595\n",
      "1.0\n",
      "MI0.48303607425194006\n",
      "pAUC 0.9472023978947368\n",
      "S@98 0.85246\n",
      "1.0\n",
      "MI0.5378547649386578\n",
      "pAUC 0.9770120684210526\n",
      "S@98 0.94413\n",
      "1.0\n",
      "MI0.582907982330443\n",
      "pAUC 0.9892277789473685\n",
      "S@98 0.97738\n",
      "1.0\n",
      "MI0.6139761949854046\n",
      "pAUC 0.9944940305263157\n",
      "S@98 0.99066\n",
      "1.0\n",
      "MI0.6376081390845953\n",
      "pAUC 0.9970829568421052\n",
      "S@98 0.99618\n",
      "1.0\n",
      "MI0.6527329286294696\n",
      "pAUC 0.9985680952631577\n",
      "S@98 0.99833\n"
     ]
    }
   ],
   "source": [
    "## Smooth Comb\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([2**(5-k)/63 for k in range(6)])\n",
    "    print(sum(prior_p))\n",
    "    for i in range(6):\n",
    "        mu_class1_i = np.array([(65-95*(1/2)**i)/21 for _ in range(p)])\n",
    "        sig_1_i = np.square(32/63)/(2**(2*i))*np.identity(p)\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <5:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(6):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Smooth_Comb.csv\", tprs, delimiter=\",\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discrete Comb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "MI0.46636615353375344\n",
      "pAUC 0.8893669810526316\n",
      "S@98 0.69289\n",
      "1.0\n",
      "MI0.5270734143552166\n",
      "pAUC 0.9438249584210525\n",
      "S@98 0.83831\n",
      "1.0\n",
      "MI0.5716067638401479\n",
      "pAUC 0.9707331284210527\n",
      "S@98 0.91979\n",
      "1.0\n",
      "MI0.6025990803772739\n",
      "pAUC 0.9840529168421053\n",
      "S@98 0.95921\n",
      "1.0\n",
      "MI0.6247953062697285\n",
      "pAUC 0.9909247921052631\n",
      "S@98 0.97913\n",
      "1.0\n",
      "MI0.6405024896037855\n",
      "pAUC 0.9947244021052631\n",
      "S@98 0.98909\n",
      "1.0\n",
      "MI0.6520015309556348\n",
      "pAUC 0.9967479221052631\n",
      "S@98 0.99421\n"
     ]
    }
   ],
   "source": [
    "##  Discrete Comb\n",
    "\n",
    "n = 100000\n",
    "MIs = []\n",
    "pAUCs = []\n",
    "tprs = []\n",
    "DIMENSIONS = [2**i for i in range(2, 9)]\n",
    "p_class0 = 0.5\n",
    "p_class1 = 0.5\n",
    "\n",
    "for p in DIMENSIONS:\n",
    "    mu_class0 = np.array([0 for i in range(p)])\n",
    "    \n",
    "    \n",
    "    coeff_z2 = np.array([1/np.sqrt(i+1) for i in range(p)])\n",
    "    coeff_z1 = np.array([1 -i for i in coeff_z2])\n",
    "    \n",
    "    sig_0 = np.identity(p)\n",
    "\n",
    "    pdf_class0 = multivariate_normal(mean = mu_class0, cov = sig_0,allow_singular=True)\n",
    "\n",
    "\n",
    "    mu_class1 = []\n",
    "    sig_1 = []\n",
    "    pdf_class1 = []\n",
    "    prior = []\n",
    "    z_2 = np.zeros((n,p))\n",
    "    n_1_total = 0\n",
    "    prior_p = np.array([2/7 if k <=2 else 1/21 for k in range(6)])\n",
    "    print(sum(prior_p))\n",
    "    for i in range(6):\n",
    "        if i <= 5:\n",
    "            mu_class1_i = np.array([(12*i-15)/7 for _ in range(p)])\n",
    "            sig_1_i = np.square(2/7)*np.identity(p)\n",
    "        else:\n",
    "            mu_class1_i = np.array([(2*(i+5))/7 for _ in range(p)])\n",
    "            sig_1_i = np.square(1/21)*np.identity(p)\n",
    "\n",
    "        mu_class1.append(mu_class1_i)\n",
    "        sig_1.append(sig_1_i)\n",
    "        pdf_class1_i = multivariate_normal(mean = mu_class1_i, cov = sig_1_i,allow_singular=True)\n",
    "        pdf_class1.append(pdf_class1_i)\n",
    "        if i <5:\n",
    "            n_1_i = np.random.binomial(n, prior_p[i])\n",
    "            prior.append(n_1_i)\n",
    "        else:\n",
    "            n_1_i = n-np.sum(prior)\n",
    "            prior.append(n_1_i)\n",
    "        z_2[n_1_total:n_1_total+n_1_i,:] = pdf_class1_i.rvs(size = n_1_i)\n",
    "        n_1_total += n_1_i\n",
    "    \n",
    "    x_0 = pdf_class0.rvs(size = n)\n",
    "    z_1 = pdf_class0.rvs(size = n)\n",
    "    x_1 = coeff_z1*z_1 + coeff_z2*z_2\n",
    "\n",
    "    x = np.vstack((x_0,x_1))\n",
    "    y = np.array([0]*n+[1]*n).reshape(-1,1)\n",
    "    \n",
    "\n",
    "    mu_1_weighted = []\n",
    "    sig_1_weighted = []\n",
    "    pdf_class1_weighted = []\n",
    "    p_x_given_class1 = 0\n",
    "    \n",
    "    for j in range(6):\n",
    "        mu_class1_i = mu_class1[j]\n",
    "        sig_1_i = sig_1[j]\n",
    "        mu_class1_i_weighted = mu_class1_i*coeff_z2+mu_class0*coeff_z1\n",
    "        mu_1_weighted.append(mu_class1_i_weighted)\n",
    "        sig_1_i_weighted = sig_1_i*np.square(coeff_z2)+sig_0*np.square(coeff_z1)\n",
    "        sig_1_weighted.append(sig_1_i_weighted)\n",
    "        pdf_class1_i_weighted = multivariate_normal(mean = mu_class1_i_weighted, cov = sig_1_i_weighted,allow_singular=True)\n",
    "        p_x_given_class1_i = np.nan_to_num(pdf_class1_i_weighted.pdf(x))\n",
    "        p_x_given_class1 += prior_p[i]*p_x_given_class1_i\n",
    "\n",
    "    p_x_given_class0 = np.nan_to_num(pdf_class0.pdf(x))\n",
    "\n",
    "    p_x = p_x_given_class0*p_class0 + p_x_given_class1*p_class1\n",
    "\n",
    "    pos_class0 = np.array([p_x_given_class0[i]*p_class0/p_x[i] if p_x[i] != 0 else 0 for i in range(p_x.shape[0])]).reshape(-1,1)\n",
    "    pos_class1 = np.ones(pos_class0.shape) - pos_class0\n",
    "\n",
    "    posterior = np.hstack((pos_class0.reshape(-1,1),pos_class1.reshape(-1,1)))\n",
    "    # print(posterior.shape)\n",
    "    # posterior = posterior[~np.isnan(posterior)].reshape(-1,2)\n",
    "    stats_conen = np.mean(entropy(posterior, base=np.exp(1), axis=1))\n",
    "    prior_y = np.array([p_class0,p_class1])\n",
    "    entropy_y = entropy(prior_y, base=np.exp(1))\n",
    "    # print('entropy'+str(stats_conen))\n",
    "    MI = entropy_y - stats_conen\n",
    "    print(\"MI\"+str(MI))\n",
    "    MIs.append(MI)\n",
    "    # plt.scatter(x[:,0],x[:,-1],c = y,alpha = 0.3,s=2)\n",
    "    # plt.show()\n",
    "    pauc = roc_auc_score(y, posterior[:,1], max_fpr=0.1)\n",
    "    print('pAUC '+ str(pauc))\n",
    "    pAUCs.append(pauc)\n",
    "\n",
    "    fpr, tpr, thresholds = metrics.roc_curve(y, posterior[:,1], pos_label=1,drop_intermediate = False)\n",
    "    tpr_s = np.max(tpr[fpr<=0.02])\n",
    "    print('S@98 '+ str(tpr_s))\n",
    "    tprs.append(tpr_s)\n",
    "np.savetxt(\"/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/Discrete_Comb.csv\", tprs, delimiter=\",\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Trunk_1',\n",
       " 'Trunk_2',\n",
       " 'Trunk_3',\n",
       " 'Mixture_Gaussian',\n",
       " 'Skewed_Unimodal',\n",
       " 'Strongly_Skewed',\n",
       " 'Kurtotic_Unimodal',\n",
       " 'Outlier',\n",
       " 'Bimodal',\n",
       " 'Separated_Bimodal',\n",
       " 'Skewed_Bimodal',\n",
       " 'Trimodal',\n",
       " 'Claw',\n",
       " 'Double_Claw',\n",
       " 'Asymmetric_Claw',\n",
       " 'Asymmetric_Double_Claw',\n",
       " 'Smooth_Comb',\n",
       " 'Discrete_Comb']"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SIMULATIONS = {\n",
    "    \"Trunk_1\": \"Trunk\",\n",
    "    \"Trunk_2\": \"Trunk-Overlap\",\n",
    "    \"Trunk_3\": \"Trunk-Banded\",\n",
    "    \"Mixture_Gaussian\": \"Mixture Gaussian\",\n",
    "    \"Skewed_Unimodal\": \"Skewed_Unimodal\",\n",
    "    \"Strongly_Skewed\": \"Strongly Skewed\",\n",
    "    \"Kurtotic_Unimodal\": \"Kurtotic Unimodal\",\n",
    "    \"Outlier\": \"Outlier\",\n",
    "    \"Bimodal\": \"Bimodal\",\n",
    "    \"Separated_Bimodal\": \"Separated Bimodal\",\n",
    "    \"Skewed_Bimodal\": \"Skewed Bimodal\",\n",
    "    \"Trimodal\": \"Trimodal\",\n",
    "    \"Claw\": \"Claw\",\n",
    "    \"Double_Claw\": \"Double Claw\",\n",
    "    \"Asymmetric_Claw\": \"Asymmetric Claw\",\n",
    "    \"Asymmetric_Double_Claw\": \"Asymmetric Double Claw\",\n",
    "    \"Smooth_Comb\": \"Smooth Comb\",\n",
    "    \"Discrete_Comb\": \"Discrete Comb\",\n",
    "}\n",
    "sim_name = list(SIMULATIONS.keys())\n",
    "sim_name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2800x1400 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NROWS, NCOLS = 3, 6\n",
    "plt.rcParams[\"font.size\"] = 20\n",
    "fig, ax = plt.subplots(nrows=NROWS, ncols=NCOLS, figsize=(28, 14))\n",
    "# plt.axis ('off')\n",
    "for i, row in enumerate(ax):\n",
    "    for j, col in enumerate(row):\n",
    "        count = NCOLS * i + j\n",
    "        sim = sim_name[count]\n",
    "        truth = np.genfromtxt('/Users/baiyuxin/Desktop/JHU/NDD/Cancer/Truth_Calculation/{}.csv'.format(sim),delimiter=',')\n",
    "        col.plot(DIMENSIONS,truth, 'r',marker='o', markersize=2,label = 'Truth',linewidth =4)\n",
    "        if j ==0:\n",
    "            col.set_ylabel('Partial AUC (90% Specificity)')\n",
    "        if i == 2:\n",
    "            col.set_xlabel('Dimension')\n",
    "        col.set_title(SIMULATIONS[sim])\n",
    "        col.set_ylim((-0.01,1.01))\n",
    "        col.set_yticks((0,1))\n",
    "        col.set_xticks((2,100,200))\n",
    "                "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "might",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}