test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def change_order(theta):\n",
    "    order = np.argsort(theta[1,:])\n",
    "    new_theta = np.zeros(theta.shape)\n",
    "    for i in range(m):\n",
    "        new_theta[0,i] = theta[0,order[i]]\n",
    "        new_theta[1,i] = theta[1,order[i]]\n",
    "    return new_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating data set...\n",
      "Data set created!\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from mixture_poisson import poisson_random_param, sample_poisson, poisson_s_bar, poisson_theta_bar\n",
    "from online_EM import online_EM,online_EM2\n",
    "from batch_EM import batch_EM\n",
    "n = 5000  # Size of the data set\n",
    "m = 3\n",
    "max_l = 100\n",
    "l = [10, 40, 80]\n",
    "p = [0.4, 0.35, 0.25]\n",
    "theta_true = np.array([p, l])\n",
    "print('Creating data set...')\n",
    "Y, W = sample_poisson(n, l, p)\n",
    "print('Data set created!\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_true.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.distplot(Y,kde=True,bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize data set \n",
    "data = pd.DataFrame({'Y':Y,'W':W})\n",
    "colors = ['g','r','b']\n",
    "\n",
    "plt.figure(figsize=(7,4))\n",
    "for i in range(m):\n",
    "    ax = sns.distplot(data[data['W']==i]['Y'],kde=False,norm_hist=False,\\\n",
    "                      color = colors[i%len(colors)],label='Group{}'.format(i))\n",
    "plt.ylabel('Count')\n",
    "plt.savefig('poisson-data-dist.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Online EM [Test 1]\n",
    "alpha = [1.,0.6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial Theta:\n",
      "[[ 0.32837651  0.27375606  0.39786743]\n",
      " [22.26518886 13.06477171 47.52336423]]\n"
     ]
    }
   ],
   "source": [
    "# Initialization\n",
    "p_init, l_init = poisson_random_param(m, max_l)\n",
    "# p_init = np.ones(m)/m\n",
    "# l_init = max_l/2 * np.ones(m) + np.random.rand(3)\n",
    "theta_init = np.array([p_init, l_init])\n",
    "print(f\"Initial Theta:\\n{theta_init}\")\n",
    "\n",
    "# Stochastic Parameters\n",
    "gamma_0 = [1, 1]\n",
    "alphas = [1.,0.6]\n",
    "gamma1 = np.array([gamma_0[0] * np.power(l, -alphas[0]) for l in range(1, n+1)])\n",
    "gamma2 = np.array([gamma_0[1] * np.power(l, -alphas[1]) for l in range(1, n+1)])\n",
    "#gamma3 = np.array([gamma_0 * np.power(l, -alphas[2]) for l in range(1, n+1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "===============\n",
      "Final results \n",
      "===============\n",
      "Truth:\n",
      "[[ 0.4   0.35  0.25]\n",
      " [20.   40.   60.  ]]\n",
      "Online EM with alpha 1.0 after 20000 iterations:\n",
      "[[2.90834972e-02 3.78264602e-01 5.92651901e-01]\n",
      " [4.00595561e+01 1.99821613e+01 4.76934836e+01]]\n",
      "Online EM with alpha 0.6 after 20000 iterations:\n",
      "[[ 0.27182793  0.38562111  0.34255097]\n",
      " [59.48650965 19.3707946  40.85614588]]\n"
     ]
    }
   ],
   "source": [
    "s_g1, theta_g1, all_theta_g1 = online_EM(Y, theta_init, gamma1, \\\n",
    "                                         poisson_s_bar, poisson_theta_bar, save_iter_theta = True)\n",
    "s_g2, theta_g2, all_theta_g2 = online_EM(Y, theta_init, gamma2, \\\n",
    "                                         poisson_s_bar, poisson_theta_bar, save_iter_theta = True)\n",
    "#s_g3, theta_g3, all_theta_g3 = online_EM(Y, theta_init, gamma3, \\\n",
    "                                         #poisson_s_bar, poisson_theta_bar, save_iter_theta = True)\n",
    "print(\"\\n===============\\nFinal results \\n===============\")\n",
    "print(f\"Truth:\\n{theta_true}\")\n",
    "print(f\"Online EM with alpha {alphas[0]} after {n} iterations:\\n{theta_g1}\")\n",
    "print(f\"Online EM with alpha {alphas[1]} after {n} iterations:\\n{theta_g2}\")\n",
    "#print(f\"Online EM with alpha {alphas[2]} after {n} iterations:\\n{theta_g3}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "cannot import name 'multi_online_EM' from 'online_EM' (/home/leon/Documents/X4A-MVA/Computational-Statistics/Online-EM/online_EM.py)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-155-7e1e89c5b32c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0monline_EM\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmulti_online_EM\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;31m# Step size for EM algo\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mgamma_0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0malphas\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1.\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malphas\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mImportError\u001b[0m: cannot import name 'multi_online_EM' from 'online_EM' (/home/leon/Documents/X4A-MVA/Computational-Statistics/Online-EM/online_EM.py)"
     ]
    }
   ],
   "source": [
    "# Step size for EM algo\n",
    "gamma_0 = 1\n",
    "alphas = [1., 0.6]\n",
    "N = len(alphas)\n",
    "gamma_list = [np.array([gamma_0 * np.power(l, -alphas[j]) for l in range(1, n + 1)]) for j in range(N)]\n",
    "\n",
    "# Online EM algo\n",
    "print('Online EM algorithm for Poisson mixture...')\n",
    "s_list, theta_list, all_theta_list = multi_online_EM(Y, theta_init, gamma_list, poisson_s_bar, poisson_theta_bar)\n",
    "print('\\n============Results============')\n",
    "print(f\"Truth:\\n{theta_true}\")\n",
    "for j in range(N):\n",
    "    print(f\"Online EM with alpha {alphas[j]} after {n} iterations:\\n{theta_list[j]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 2]\n",
      "[1 0 2 4 3 5]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1440 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the process of parameter convergence \n",
    "names = ['omega 1','omega 2','omega 3','lambda 1','lambda 2','lambda 3']\n",
    "truth = change_order(theta_true).reshape((1,-1))[0]\n",
    "\n",
    "order1 = np.argsort(theta_g1[1,:])\n",
    "order1 = np.concatenate([order1,order1+3])\n",
    "\n",
    "order2 = np.argsort(theta_g2[1,:])\n",
    "order2 = np.concatenate([order2,order2+3])\n",
    "\n",
    "plt.figure(figsize=(10,20))\n",
    "for i in range(6):\n",
    "    plt.subplot(6,1,i+1).set_title(names[i])\n",
    "    plt.plot(all_theta_g1[1:,order1[i]],label='alpha=1.0')\n",
    "    plt.plot(all_theta_g2[1:,order2[i]],label='alpha=0.6')\n",
    "    plt.plot([1,n],[truth[i],truth[i]],'r--',label='Truth')\n",
    "#     if i<3:\n",
    "#         plt.ylim(0.,1.)\n",
    "#     else:\n",
    "#         plt.ylim(0,max_l+10)\n",
    "    #plt.plot(all_theta_g3[1:,0],label='alpha=0.3')\n",
    "#     plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Online EM [Test 2]\n",
    "Initialization sensitivity "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_iter = 100\n",
    "gamma = np.array([gamma_0 * np.power(l, -1.0) for l in range(1, n+1)])\n",
    "all_theta =[]\n",
    "for i in range(num_iter):\n",
    "    p_init, l_init = poisson_random_param(m, max_l)\n",
    "    theta_init = np.array([p_init, l_init])\n",
    "    s, theta = online_EM(Y, theta_init, gamma, poisson_s_bar, poisson_theta_bar)\n",
    "    #print(theta)\n",
    "    theta = change_order(theta)\n",
    "    all_theta.append(theta.reshape(1,-1)[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.58237906e-09 3.89281609e-01 6.10718388e-01 8.02078090e-01\n",
      "  1.03504193e+00 3.26338253e+01]\n",
      " [3.89572554e-01 2.64748880e-01 3.45678566e-01 1.07714227e+00\n",
      "  1.91550345e+01 4.29361333e+01]\n",
      " [3.86952150e-01 3.53701678e-01 2.59346172e-01 1.01870407e+00\n",
      "  2.00938721e+01 4.94766278e+01]\n",
      " [3.85514530e-01 3.60243090e-01 2.54242380e-01 1.02014254e+00\n",
      "  1.99779799e+01 5.01206409e+01]\n",
      " [3.85739742e-01 2.82433593e-01 3.31826666e-01 1.02066903e+00\n",
      "  1.94338264e+01 4.35484048e+01]\n",
      " [3.86324924e-01 3.60306079e-01 2.53368997e-01 1.01966186e+00\n",
      "  2.00726607e+01 5.01512721e+01]\n",
      " [3.87075297e-01 2.39822855e-01 3.73101848e-01 1.01799770e+00\n",
      "  1.88475629e+01 4.13262008e+01]\n",
      " [3.89002678e-01 3.61018768e-01 2.49978554e-01 1.02288492e+00\n",
      "  2.04246126e+01 5.02500169e+01]\n",
      " [4.54175790e-06 3.88864847e-01 6.11130612e-01 9.71218900e-01\n",
      "  1.03603796e+00 3.26118778e+01]\n",
      " [7.03130386e-01 2.96664659e-01 2.04955685e-04 9.16808138e+00\n",
      "  4.67738603e+01 5.11921075e+01]\n",
      " [3.89909821e-01 3.57596395e-01 2.52493784e-01 1.02110099e+00\n",
      "  2.02990707e+01 5.02031694e+01]\n",
      " [4.73726081e-01 2.74614026e-01 2.51659893e-01 4.09563811e+00\n",
      "  2.10436342e+01 5.01228548e+01]\n",
      " [3.87423649e-01 3.61849376e-01 2.50726975e-01 1.01849006e+00\n",
      "  2.03039883e+01 5.02196757e+01]\n",
      " [5.92083251e-01 1.53347642e-01 2.54569107e-01 7.14607895e+00\n",
      "  2.22539067e+01 4.98463555e+01]\n",
      " [2.86394470e-02 3.61560914e-01 6.09799639e-01 1.87761020e-01\n",
      "  1.11451734e+00 3.26741038e+01]\n",
      " [6.93560516e-01 2.32776671e-01 7.36628130e-02 9.00590945e+00\n",
      "  4.30265857e+01 5.52690191e+01]\n",
      " [3.90605767e-01 3.57931988e-01 2.51462244e-01 1.13901134e+00\n",
      "  2.02903629e+01 5.02084346e+01]\n",
      " [3.76854854e-01 3.68727281e-01 2.54417865e-01 1.09388437e+00\n",
      "  1.94929000e+01 5.00483735e+01]\n",
      " [4.01064052e-01 3.29166595e-01 2.69769354e-01 1.43772102e+00\n",
      "  2.02272076e+01 4.85535535e+01]\n",
      " [3.90170646e-01 3.15354475e-01 2.94474879e-01 1.02125121e+00\n",
      "  1.97313361e+01 4.65648297e+01]\n",
      " [5.03885830e-01 6.83062165e-02 4.27807954e-01 4.65225685e+00\n",
      "  1.86817081e+01 3.90659331e+01]\n",
      " [5.12956873e-01 2.33975729e-01 2.53067398e-01 5.25889736e+00\n",
      "  2.11815526e+01 5.01030292e+01]\n",
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      "  1.85366169e+01 3.97890900e+01]\n",
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      "  2.03062599e+01 4.96173274e+01]\n",
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      "  1.85366159e+01 3.97878162e+01]\n",
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      "  2.02592978e+01 5.01640337e+01]\n",
      " [3.90469353e-01 3.05451800e-01 3.04078847e-01 1.02601450e+00\n",
      "  1.97663842e+01 4.56943825e+01]\n",
      " [3.87730245e-01 3.67659483e-01 2.44610273e-01 1.01945494e+00\n",
      "  2.07359313e+01 5.03411593e+01]\n",
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      "  2.06395896e+01 5.01507390e+01]\n",
      " [3.87872259e-01 3.42175687e-01 2.69952054e-01 1.01864674e+00\n",
      "  1.98254621e+01 4.87275569e+01]\n",
      " [2.88091795e-01 1.03863994e-01 6.08044212e-01 7.84753270e-01\n",
      "  1.92486316e+00 3.27393875e+01]\n",
      " [3.90179713e-01 1.67893035e-01 4.41927251e-01 1.02096451e+00\n",
      "  1.81284068e+01 3.82212391e+01]\n",
      " [3.90921146e-01 1.01196782e-01 5.07882072e-01 1.03761287e+00\n",
      "  1.71961918e+01 3.58098403e+01]\n",
      " [3.87796181e-01 3.64707698e-01 2.47496121e-01 1.01817832e+00\n",
      "  2.05377167e+01 5.02952972e+01]\n",
      " [5.69635200e-01 1.69834671e-01 2.60530129e-01 6.64546205e+00\n",
      "  2.14349911e+01 4.95417029e+01]\n",
      " [4.77123292e-01 3.23681396e-01 1.99195312e-01 3.88110997e+00\n",
      "  2.52461661e+01 5.17558251e+01]\n",
      " [5.57247299e-01 1.83614463e-01 2.59138238e-01 6.34412373e+00\n",
      "  2.13498216e+01 4.96940099e+01]\n",
      " [3.88978287e-01 2.68077948e-01 3.42943766e-01 1.01441891e+00\n",
      "  1.89956364e+01 4.32901932e+01]\n",
      " [6.30827672e-01 9.98121652e-02 2.69360163e-01 7.88290555e+00\n",
      "  2.20229469e+01 4.88642674e+01]\n",
      " [5.52968854e-01 1.88579519e-01 2.58451628e-01 6.25710947e+00\n",
      "  2.13082373e+01 4.97374163e+01]\n",
      " [7.02994131e-01 2.97005869e-01 7.89632246e-12 9.16458013e+00\n",
      "  4.67679443e+01 4.79663543e+01]\n",
      " [3.95697736e-01 3.55510142e-01 2.48792123e-01 1.28526350e+00\n",
      "  2.05687316e+01 5.02911078e+01]\n",
      " [4.11256738e-01 1.87502349e-01 4.01240912e-01 1.76538995e+00\n",
      "  1.87039738e+01 4.01253511e+01]\n",
      " [6.68329894e-01 5.37725987e-02 2.77897508e-01 8.50933343e+00\n",
      "  2.42916300e+01 4.80023521e+01]\n",
      " [4.00874291e-01 2.33878751e-01 3.65246958e-01 1.39451762e+00\n",
      "  1.90326424e+01 4.19514599e+01]\n",
      " [3.87152171e-01 2.99640264e-01 3.13207566e-01 1.01324021e+00\n",
      "  1.92003471e+01 4.52975163e+01]\n",
      " [3.86009772e-01 3.61180513e-01 2.52809715e-01 1.10442474e+00\n",
      "  2.00101896e+01 5.01538903e+01]\n",
      " [3.51899663e-01 3.87192078e-02 6.09381129e-01 9.59964028e-01\n",
      "  1.92454243e+00 3.26900051e+01]\n",
      " [5.05383741e-01 2.33915177e-01 2.60701082e-01 4.96903384e+00\n",
      "  2.09411426e+01 4.95712558e+01]\n",
      " [4.16382302e-01 3.07693589e-01 2.75924108e-01 2.02593463e+00\n",
      "  2.00921328e+01 4.82278126e+01]\n",
      " [3.90344212e-01 2.70442194e-01 3.39213593e-01 1.02418253e+00\n",
      "  1.91930796e+01 4.34611053e+01]\n",
      " [3.89353532e-01 2.07295745e-01 4.03350723e-01 1.03625341e+00\n",
      "  1.85583212e+01 3.98721736e+01]\n",
      " [3.87640433e-01 2.70060509e-01 3.42299058e-01 1.01821348e+00\n",
      "  1.91762131e+01 4.31189075e+01]\n",
      " [4.83952543e-01 2.63475320e-01 2.52572137e-01 4.41667219e+00\n",
      "  2.09573773e+01 5.01788865e+01]\n",
      " [3.86552442e-01 3.59130015e-01 2.54317543e-01 1.01898266e+00\n",
      "  2.00238033e+01 5.01261565e+01]\n",
      " [3.86887451e-01 3.61398938e-01 2.51713611e-01 1.01887239e+00\n",
      "  2.02114697e+01 5.01935803e+01]\n",
      " [3.92278161e-01 3.54891467e-01 2.52830372e-01 1.10347529e+00\n",
      "  2.03135267e+01 5.01958422e+01]\n",
      " [4.98533429e-01 2.46404866e-01 2.55061706e-01 4.79813333e+00\n",
      "  2.09952707e+01 5.00570372e+01]\n",
      " [3.88078879e-01 3.65871012e-01 2.46050110e-01 1.02065378e+00\n",
      "  2.06524387e+01 5.03181128e+01]\n",
      " [3.90316777e-01 3.63459671e-01 2.46223552e-01 1.02400583e+00\n",
      "  2.07350381e+01 5.03484054e+01]\n",
      " [3.88102133e-01 2.32951568e-01 3.78946299e-01 1.01801394e+00\n",
      "  1.88121622e+01 4.10495735e+01]\n",
      " [3.85144144e-01 3.64146674e-01 2.50709182e-01 1.01988975e+00\n",
      "  2.01962322e+01 5.02008126e+01]\n",
      " [3.82543766e-01 3.65714528e-01 2.51741707e-01 1.01993328e+00\n",
      "  2.00051073e+01 5.01572532e+01]\n",
      " [4.65871750e-01 2.81470899e-01 2.52657351e-01 3.79839824e+00\n",
      "  2.09116222e+01 5.01763373e+01]\n",
      " [3.88026122e-01 3.62388903e-01 2.49584975e-01 1.01989438e+00\n",
      "  2.04047638e+01 5.02546051e+01]\n",
      " [3.82324158e-01 3.65015747e-01 2.52660096e-01 1.01866963e+00\n",
      "  1.99353432e+01 5.01338519e+01]\n",
      " [3.87794253e-01 3.61881832e-01 2.50323915e-01 1.01799234e+00\n",
      "  2.03494463e+01 5.02314512e+01]\n",
      " [4.25373760e-01 2.83999610e-01 2.90626630e-01 2.34302915e+00\n",
      "  1.99832589e+01 4.70056689e+01]\n",
      " [3.84133024e-01 3.63222553e-01 2.52644423e-01 1.02061431e+00\n",
      "  2.00213288e+01 5.01445867e+01]\n",
      " [5.33800561e-01 2.09465767e-01 2.56733673e-01 5.78753251e+00\n",
      "  2.12554721e+01 4.98232975e+01]\n",
      " [3.88871783e-01 2.32410387e-01 3.78717830e-01 1.02093429e+00\n",
      "  1.88112729e+01 4.10966979e+01]\n",
      " [3.90144424e-01 3.21072086e-01 2.88783490e-01 1.02111385e+00\n",
      "  1.98156316e+01 4.69984345e+01]\n",
      " [3.90316881e-01 3.52556043e-01 2.57127077e-01 1.02213780e+00\n",
      "  2.02959527e+01 4.96975339e+01]\n",
      " [3.91043872e-01 3.59828625e-01 2.49127504e-01 1.09853033e+00\n",
      "  2.05026132e+01 5.02794720e+01]\n",
      " [3.89003885e-01 3.59485102e-01 2.51511013e-01 1.02528794e+00\n",
      "  2.03179399e+01 5.02171343e+01]\n",
      " [3.89415707e-01 1.48904109e-01 4.61680184e-01 1.06985461e+00\n",
      "  1.78527452e+01 3.73809301e+01]\n",
      " [3.81329878e-01 3.64598328e-01 2.54071795e-01 1.01776373e+00\n",
      "  1.97934795e+01 5.00969687e+01]\n",
      " [3.98337063e-01 3.49725849e-01 2.51937088e-01 1.34037018e+00\n",
      "  2.04272579e+01 5.02313530e+01]\n",
      " [7.09984105e-01 2.88057155e-01 1.95873985e-03 9.37445856e+00\n",
      "  4.71604614e+01 4.71604659e+01]\n",
      " [3.87066235e-01 3.24984835e-01 2.87948930e-01 1.01620618e+00\n",
      "  1.95191969e+01 4.72174629e+01]\n",
      " [7.05898658e-01 2.96448768e-04 2.93804893e-01 9.24617059e+00\n",
      "  4.69433221e+01 4.69434806e+01]\n",
      " [4.77135821e-01 2.17313305e-01 3.05550874e-01 4.11468382e+00\n",
      "  2.01553364e+01 4.57852206e+01]\n",
      " [3.88861573e-01 3.61765693e-01 2.49372734e-01 1.02278220e+00\n",
      "  2.04551845e+01 5.02673052e+01]\n",
      " [4.51207700e-01 3.16124225e-01 2.32668075e-01 3.20613402e+00\n",
      "  2.22992776e+01 5.08751610e+01]\n",
      " [4.03130057e-01 3.13004063e-01 2.83865880e-01 1.55115665e+00\n",
      "  1.98606729e+01 4.75267080e+01]\n",
      " [7.03824230e-01 5.64323100e-02 2.39743460e-01 9.18741597e+00\n",
      "  4.64509742e+01 4.69057144e+01]\n",
      " [3.99962153e-01 3.50050490e-01 2.49987356e-01 1.39546284e+00\n",
      "  2.05918364e+01 5.02692833e+01]\n",
      " [5.20489728e-01 2.25502975e-01 2.54007298e-01 5.44097703e+00\n",
      "  2.12111659e+01 5.00688227e+01]\n",
      " [3.90052097e-01 3.65157003e-01 2.44790899e-01 1.02223421e+00\n",
      "  2.09980891e+01 5.01108340e+01]\n",
      " [3.88378867e-01 3.31623880e-01 2.79997253e-01 1.01790731e+00\n",
      "  1.97115495e+01 4.78606331e+01]\n",
      " [3.82890741e-01 3.63913393e-01 2.53195866e-01 1.01930442e+00\n",
      "  1.99363891e+01 5.01098180e+01]\n",
      " [3.90104356e-01 2.51465185e-01 3.58430459e-01 1.02065367e+00\n",
      "  1.90038384e+01 4.22844500e+01]\n",
      " [3.89604480e-01 3.59775383e-01 2.50620138e-01 1.02008775e+00\n",
      "  2.04214966e+01 5.02290742e+01]\n",
      " [3.90904888e-01 2.68095091e-01 3.41000020e-01 1.09629064e+00\n",
      "  1.92185444e+01 4.32611622e+01]\n",
      " [3.90134735e-01 2.77871603e-01 3.31993662e-01 1.02091140e+00\n",
      "  1.92964042e+01 4.38947664e+01]\n",
      " [4.99958155e-01 2.47151295e-01 2.52890551e-01 4.87771406e+00\n",
      "  2.10848622e+01 5.01529063e+01]\n",
      " [3.80179680e-01 3.67980438e-01 2.51839882e-01 1.01966384e+00\n",
      "  1.98886295e+01 5.01378807e+01]\n",
      " [3.82521839e-01 3.66157043e-01 2.51321117e-01 1.01895713e+00\n",
      "  2.00332703e+01 5.01665111e+01]\n",
      " [3.90364325e-01 1.38857335e-01 4.70778340e-01 1.02424137e+00\n",
      "  1.77462285e+01 3.71065897e+01]]\n"
     ]
    }
   ],
   "source": [
    "all_theta = np.stack(all_theta,axis=0)\n",
    "print(all_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.42273505  0.28335954  0.2939054   2.42277613 20.75553016 46.87174813]\n",
      "[0.1159159  0.09073125 0.10732504 2.47839576 7.69709181 5.07038617]\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(all_theta,axis=0))\n",
    "print(np.std(all_theta,axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.4   0.35  0.25  1.   20.   50.  ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8re6+E0iYWcLdHyJ18XQREclD2RT+3WZWBjwC3Gpm3wLa+tlHZER79NFH09qPPPJIRJmIDFw2hX8RqS92vwjcR+qC6eeHmZTIcLdgwQIKC1O/fywsLOTcc8+NOCOR7PVb+N29yd3bSc3Jfw+pKZl7vEC6SFxUVVWRSKT++xQUFFBVVRVxRiLZy+asns+Z2Q5SP9paB6wP7kViq7y8nIULF2JmLFy4kEmTJkWdkkjWsrnm7peAE9y9MexkRPJJVVUV9fX16u1L3smm8L8I7A87EZF8U15ezooVK6JOQ2TAsin8VwN/NLPHgYMdK919SWhZiYhIaLIp/CuB3wHPAslw0xEZfNXV1dTV1Q36cbdu3QrA9OnTB/3YABUVFSxZov6VDL5sCn+bu18ZeiYieaa5uTnqFERykk3hf8jMFpM6lbPrUM8boWUlMojC6jV3HLe6ujqU44uEJZvC/7fB/dVd1jnwtsFPR0REwpbNNXePGYpERERkaPRa+M3sLHf/nZld1FPc3e8ILy2Jo7C+hA1LbW0tEN5QUlj0pbH01eOfT+psnp7m5XGgz8JvZkcB/wUcQepsoFXu/i0zmwjcDswkNbf/x9x914AzlxGnrq6Ozc89xYyy9qhTyUpxa+qH7wfqn4w4k+xt2VcQdQoyDPRa+N39X4PF69395a4xM8tm+KcN+D/u/pSZHQasN7PVwKeAB939JjNbBiwDluaUvYwoW7duxfNoFqgpo/Pv7Gb3t05DlfjK5svdXwGndlv3S2BOXzu5+3Zge7C818z+BEwjNdvnGcFmNcBa+iv8jbXwww+krzvhApj7WWjZD7d+NHOfk/8WTvkkNO2En/99Zvzd/wAnfhje3Ap3fC4z/tdfgHcsTD32PVdkxud9CY49E7ZvhPuuzoyffS3M+CvY8jg8eH1m/LyvwpEnwYsPwSP/nhk//5tQPgv+fC/88duZ8YtWwrjp8Nyv4MkfZMY/9l8wZhJsuBWe/mlm/JO/gOLR8MR3YdOdmfFP/3fq/g/VsPn+9FhRCVzyq9Tyw1+Dlx5Oj4+eAB//SWp5zXJ4tVuPeOxU+PB3U8v3LoPXngXg5OLX2DLaKMJoDd6aRbRh3eYETGK0dcZbsW6p9x9P0Eaq51tMa8Y/vb94OwnaKcCC4w88XkA7CQynqIcZzvuLt1FAkgQJnMIe44UksR7jR41upSURnJyn917ne6/TpGPhQ8FZWncvgZ0vpsePeBcsvCm1/KvPwp5t6fGj3g3nLE8t334J7O82mPG2+TD/qtTyTz4MrQfS429/H7w3GIbrXvPg0OteoK8x/uOAE4Bx3cb5xwIlvR6x52PNBE4BHgemBH8UcPftZnZ4L/ssBhYDnDS1dCAPJ3nqE8fuJXlgL9MOM95IpCY9m5jcmVG8Wihmd2ICAJOSjRSQPjR0kFG8mRgPQHmygUS33x0esBL22DgAJidfz/jD0myl7LWxABye3JGR534bzT47DPMkk70hI95kY2iyMhLeTnkPU1ztszL22xgKvI1JnnmR9r12GM02mkJvZWIPZ02/aeM4aCUUeQsTehgl3W3jabFRFPtBxvvutNgrewu4M3lcxj4SL+a9fLY2s0XABcCHgLu7hPYCt7n7H7N6gNRFXB4G/s3d7zCz3e4+vkt8l7tP6OsYlZWVvm6dJgQd6ZYsWZJXY/w79qfG+PNpyGfLvgLefuKp+u1BTJjZenev7L6+rzH+u4C7zOw0d38sxwctIjVUdGuXs4B2mNmRQW//SOD1XI4tI09FRUXUKQxIS3BWT8nMWRFnkr23k3/Pswy+bMb4LzSzTaSuwnUfMBu4wt1/0tdOZmbA94E/ufvXu4TuBqqAm4L7u3JJXEaefDvFUL/clXyVzaUXz3X3PcAHga2kOg3/N4v93gv8HXCWmT0d3N5PquAvMLNaYEHQFhGRIZJNj78ouH8/8DN3fyPVme+bu/8eMk6o6HB2dumJiMhgy6bw32NmL5Aa6vlHM5sMHOhnHxERGaayudj6MuA0oNLdW0ldjWtR2ImJiEg4ei38ZnZVl+Y57t4O4O5NQH59CyciIp36Oo//KXc/tftyT+2w6Tx+ORRhTf7WMUnbrFnhnM6pydTkUA34PH7Sv5jt/iVt/9/uioxwpaX6Rbnkp74Kv/ey3FNbZNhSr1kkXV+Ff7aZ7SHVuy8NlgnaA5qrR0REho++pmzQxN0iIiNQNr/cFRGREUSFX0QkZlT4RURiRoVfRCRmVPhFRGJGhV9EJGZU+EVEYkaFX0QkZlT4RURiRoVfRCRmVPhFRGJGhV9EJGZU+EVEYkaFX0QkZlT4RURiRoVfRCRmVPhFRGJGhV9EJGZU+EVEYia0wm9mPzCz183suS7rJprZajOrDe4nhPX4IiLSszB7/D8Czuu2bhnwoLvPAh4M2rG2efNmFi5cSF1dXdSpiEhMhFb43f0R4I1uqxcBNcFyDXBBWI+fL5YtW0ZTUxNLly6NOhURiYmhHuOf4u7bAYL7w3vb0MwWm9k6M1vX0NAwZAkOpc2bN9PY2AhAQ0ODev0iMiSG7Ze77r7K3SvdvXLy5MlRpxOKZcvSR7rU6xeRoTDUhX+HmR0JENy/PsSPP6x09PY7jNRPNiIyvAx14b8bqAqWq4C7hvjxRURiL8zTOX8GPAa8w8y2mtlngJuABWZWCywI2iIiMoQKwzqwu3+il9DZYT1mvikqKqK1tbWzXVxcHGE2IhIXw/bL3TiYNm1aWnvq1KkRZSIicaLCH6EdO3b02RYRCYMKf4TmzZuX1p4/f35EmYhInKjwi4jEjAp/hB599NG09iOPPBJRJiISJ6Gd1TOSVFdXhzKdQmlpKfv3709rL1myZNCOX1FRMajHE5GRQT3+CB1xxBGdy2aW1hYRCYt6/FkIs9d84YUXsnPnThYtWsSVV14Z2uOIiHRQ4Y/YEUccwYEDB6iqqup/YxGRQaChnogVFRUxa9YsJk2aFHUqIhITKvwiIjGjwi8iEjMq/CIiMaPCLyISMyr8IiIxo8IvIhIzKvwiIjEzon7AFdacOmGqra0Fwv118GDTHEAi+W1EFf66ujo2PPs8ydETo04la9biAKx/8bWIM8lOYv8bUacgIodoRBV+gOToiRw4/oNRpzFilTz/m6hTGDY2b97M5ZdfzooVK6ioqIg6HZGsaYxfJEc33ngjTU1NXH/99VGnIjIgKvwiOdi8eTP19fUA1NfX5913SxJvKvwiObjxxhvT2ur1Sz5R4RfJQUdvv7e2yHCmwi+SgylTpqS1dfU0ySd5cVbPSw1NfHzlY2nrPnjSkfzdaTNpbmnnUz98AoAtr7Xh7UmKnruHRFszBW3NOAnaSsZnHDPRup+C9gO4FdA2alxGvKC1iUT7QdwKaRs1NjPe0kQieZBkooj24sN6iO8jkWwhmSimvbish/heEslWklaY2t8sLV54cA/mbSQLRtFeNCZj/8KDb2LeTntBCcmi0ZnxA7sxkrQXlpIsLO0hvgvDaS8cTbKwJCNedCB12mZ70RiSBaM617e7s+61ls529YO1/KGuMW3fCaOLueXv5gBw830v8NQru9LiR44r4ZsXnwLAdfds4vlte9Lib5s8hq9edBIAV9+xkZcamtLix08dy7+efwIAV9y2ge1vHkiLn3r0BJaedxwAl/54Pbv2t6TF31tRzpKzZwFQ9YMnONDanhY/+52Hs3jesQAZ7ztIvff27NlDMlFIwzs/CkBDItG57UfmTOejlUfxRlMLn//J+oz9L3nP0Zw/eyrbdjfzxdufzoh/9vS3cc7xU3ixYR//fMezGfHLzprF38wqZ9O2N7n+nucz4led9w7mHD2R9a+8wdfu+3NG/Nrzj+eEqeP4fW0jK35XmxH/ykXv4tjJZax5fgffffSljPg3Pn4yU8eXcs8z2/jJ/7ySEf/PS+YwcUwxv1j3Kr9cvzUj/qNPz6W0uIAfP1bPbzZuz4jf/rnTAFj1yIs8+KfX02IlRQXU/MNcIL7vve51r6v+3nsdIin8ZnYe8C2gAPieu980GMctLCgkWVAAwKiiQkYVFuMk2JvI/GBTUlxIsReTtAT7rKd4EcXutFsBTT3ES0cVUuROuxX2GB89qpBChzYrZH8P8TGjiihwo6klSdIg0S3H0SVFFHiCFiviQE/7lxSR8AJarLDHeFlJMUaSg1bIwV7jzgErpKWXOECzFdDaLV5QWJSxfdw0NzdD4q3/PslkMsJsRAbG3H1oH9CsANgMLAC2Ak8Cn3D3zK5LoLKy0tetWzdEGQ6tjl/AVldXR5yJDMT73/9+9u3b19kuKyvjt7/9bYQZiWQys/XuXtl9fRQ9/rlAnbu/BGBmtwGLgF4Lf9TCnAoizCkbNLVCeJYvX86XvvSlzvYNN9wQYTYiAxPFl7vTgFe7tLcG62KptLSU0tLMMXgZ3ubOnUtZWeq7m7KyMubMmRNxRiLZi6LHbz2syxhvMrPFwGKAGTNmhJ1Tn9Rrlp4sX76cq666Sr19yTtRFP6twFFd2tOBbd03cvdVwCpIjfEPTWoi2Zs7dy5r166NOg2RAYtiqOdJYJaZHWNmxcDFwN0R5CEiEktD3uN39zYz+wJwP6nTOX/g7puGOg8RkbiK5Dx+d/8toHPfREQioCkbRERiRoVfRCRmVPhFRGJGhV9EJGaGfK6eXJhZA5A5DeDIUQ409ruVDEd67fLbSH/9jnb3yd1X5kXhH+nMbF1PEynJ8KfXLr/F9fXTUI+ISMyo8IuIxIwK//CwKuoEJGd67fJbLF8/jfGLiMSMevwiIjGjwi8iEjMq/Fkys339b5XVcZab2Zey2O5HZvaRARx3npk9ZWZtA9kvLvLg9bvSzJ43s41m9qCZHX1omY4cefDaXWpmz5rZ02b2ezM7/tAyDZ8K/8ixBfgU8NOI85DcbAAq3f0k4JfA1yLOR7L3U3d/l7ufTOp1+3rUCfVHhX+AzKws6JE9FfyVXxSsn2lmL5jZ98zsOTO71czOMbM/mFmtmc3tcpjZZva7YP1ng/3NzL4d9Pr+Gzi8y2Nea2ZPBsddZWYZl69093p33wgkQ34K8towfv0ecvf9QfN/SF2ZTroYxq/dni7NMfRwKdlhx911y+IG7AvuC4GxwXI5UEfqOsIzgTbgXaT+oK4HfhDEFgF3BvssB54BSoP9XwWmAhcBq0ldnGYqsBv4SLDPxC55/Bg4v488f9Sxn2759/oF23wb+HLUz9lwueXDawf8E/BicMxZUT9n/d3U4x84A75iZhuBNcA0YEoQe9ndn3X3JLAJeNBT74pnSb05O9zl7s3u3gg8BMwF5gE/c/d2d98G/K7L9mea2eNm9ixwFnBCiP++kW5Yv35mdglQCfy/Qfi3jjTD9rVz9/9w92OBpcCXB+nfG5pIrsCV5z4JTAbmuHurmdUDJUHsYJftkl3aSdKf6+4fBb2X9ZhZCfAdUuO/r5rZ8i6PJwM3bF8/MzsHuAaY7+4He9om5obta9fFbcB/9rNN5NTjH7hxwOvBG+9MIJezLxaZWYmZTQLOIHUB+keAi82swMyOBM4Mtu14ozWaWRmgM3YOzbB8/czsFGAl8CF3fz2HnOJguL52s7o0PwDU5pDXkFKPf+BuBe4xs3XA08ALORzjCeC/gRnADe6+zcx+Teqj5LPAZuBhAHffbWbfDdbXk3qjZjCzdwO/BiYA55vZde6uIaFMw/L1IzW0Uwb8Ivj+cIu7fyiH3Eay4frafSH4tNYK7AKqcshrSGnKBhGRmNFQj4hIzKjwi4jEjAq/iEjMqPCLiMSMCr+ISMyo8MuIYmbtlpol8Tkz+4WZjY46JwAz++eocxDpoNM5ZUQxs33uXhYs3wqsd/esZks0swJ3bw87rwHsE1o+Em/q8ctI9ihQAWBmd5rZejPbZGaLOzYws31mdr2ZPQ6c1ttsjGa21sy+YWaPmNmfzOzdZnZHMMvjjV2Od4mZPRF86lgZ/Br0JqA0WHdrb9v1ks9N9tY8/f8+dE+djGhRzxKnm26DeSN9Jse7gM8H7YnBfSnwHDApaDvwsS779zgbI7AWuDlYvhzYBhwJjAK2ApOAdwL3AEXBdt8B/r5rXsFyX9t15gNMBP7MW5/Mx0f9/Oo2Mm6askFGmlIzez9KgfwAAAFMSURBVDpYfhT4frC8xMwuDJaPAmYBO4F24Fdd9j/TzK4CRpMqvJtIFWmAu4P7Z4FN7r4dwMxeCo75N8Ac4Mngg0Ip0NO8O2f3sV3XfPYAB4DvBfPE/ybrZ0GkDyr8MtI0e+pKSJ3M7AzgHOA0d99vZmt5awKuAx6Mo2cxG2PXGR+7zwZZSGra4Bp3v7qfHPvarjMfd2+z1EVEzgYuBr5Aak4ZkUOiMX6Jg3HArqDoHwe8p5ftDnUm1AeBj5jZ4QBmNtHeunZuq5kVZbFdpyCHce7+W+AK4OTu24jkQj1+iYP7gEuDC3j8mdSlDTN49rMx9sjdnzezLwMPmFmC1GyN/wS8AqwCNprZU+7+yT626+ow4K7gk4gBXxxIPiK90emcIiIxo6EeEZGYUeEXEYkZFX4RkZhR4RcRiRkVfhGRmFHhFxGJGRV+EZGY+V/I7ekdAIXIowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame()\n",
    "df['Estimated value'] = all_theta.reshape((-1,1))[:,0]\n",
    "df['Parameters'] = names*num_iter\n",
    "\n",
    "true_params = change_order(theta_true).reshape((1,-1))[0]\n",
    "print(true_params)\n",
    "\n",
    "df_omega =df[df['Parameters'].str.contains('omega')]\n",
    "df_lambda =df[df['Parameters'].str.contains('lambda')]\n",
    "\n",
    "plt.figure()\n",
    "sns.boxplot(x='Parameters',y='Estimated value',data=df_omega)\n",
    "for i in range(3):\n",
    "    plt.plot([-0.5,2.5],[true_params[i],true_params[i]],'--')\n",
    "    \n",
    "plt.figure()\n",
    "sns.boxplot(x='Parameters',y='Estimated value',data=df_lambda)\n",
    "for i in range(3,6):\n",
    "    plt.plot([-0.5,2.5],[true_params[i],true_params[i]],'--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Online EM [Test3]\n",
    "Compare onlie em with Titterington and batch em"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# online em (alpha =1)\n",
    "num_iter = 10\n",
    "gamma_0 = 1\n",
    "alpha = 1.\n",
    "gamma = np.array([gamma_0 * np.power(l, -alpha) for l in range(1, n+1)])\n",
    "all_theta_1 =[]\n",
    "\n",
    "for i in range(num_iter):\n",
    "    p_init, l_init = poisson_random_param(m, max_l)\n",
    "    theta_init = np.array([p_init, l_init])\n",
    "    s, theta = online_EM(Y, theta_init, gamma, poisson_s_bar, poisson_theta_bar)\n",
    "    #print(theta)\n",
    "    theta = change_order(theta)\n",
    "    all_theta_1.append(theta.reshape(1,-1)[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# online em (alpha =0.6)\n",
    "num_iter = 10\n",
    "gamma_0 = 1\n",
    "alpha = 0.6\n",
    "gamma = np.array([gamma_0 * np.power(l, -alpha) for l in range(1, n+1)])\n",
    "all_theta_06 =[]\n",
    "\n",
    "for i in range(num_iter):\n",
    "    p_init, l_init = poisson_random_param(m, max_l)\n",
    "    theta_init = np.array([p_init, l_init])\n",
    "    s, theta = online_EM(Y, theta_init, gamma, poisson_s_bar, poisson_theta_bar)\n",
    "    #print(theta)\n",
    "    theta = change_order(theta)\n",
    "    all_theta_06.append(theta.reshape(1,-1)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# online em2 \n",
    "num_iter = 100\n",
    "gamma_0 = 1\n",
    "alpha = 1.\n",
    "gamma = np.array([gamma_0 * np.power(l, -alpha) for l in range(1, n+1)])\n",
    "all_theta_2 =[]\n",
    "p_init, l_init = poisson_random_param(m, max_l)\n",
    "theta_init = np.array([p_init, l_init])\n",
    "s, theta = online_EM2(Y, theta_init, gamma)\n",
    "print(theta)\n",
    "for i in range(num_iter):\n",
    "    p_init, l_init = poisson_random_param(m, max_l)\n",
    "    theta_init = np.array([p_init, l_init])\n",
    "    s, theta = online_EM2(Y, theta_init, gamma)\n",
    "    #print(theta)\n",
    "    theta = change_order(theta)\n",
    "    all_theta_2.append(theta.reshape(1,-1)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# batch em \n",
    "num_iter = 10\n",
    "gamma_0 = 1\n",
    "alpha = 1.\n",
    "gamma = np.array([gamma_0 * np.power(l, -alpha) for l in range(1, n+1)])\n",
    "all_theta_batch =[]\n",
    "\n",
    "max_iteration =5\n",
    "for i in range(num_iter):\n",
    "    p_init, l_init = poisson_random_param(m, max_l)\n",
    "    theta_init = np.array([p_init, l_init])\n",
    "    theta = batch_EM(Y, theta_init,max_iter = max_iteration)\n",
    "    #print(theta)\n",
    "    theta = change_order(theta)\n",
    "    all_theta_batch.append(theta.reshape(1,-1)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 6)\n"
     ]
    }
   ],
   "source": [
    "all_theta_1 = np.stack(all_theta_1,axis=0)\n",
    "print(all_theta_1.shape)\n",
    "all_theta_06 = np.stack(all_theta_06,axis=0)\n",
    "all_theta_batch = np.stack(all_theta_batch,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.4   0.35  0.25 10.   30.   50.  ]\n"
     ]
    }
   ],
   "source": [
    "true_params = change_order(theta_true).reshape((1,-1))[0]\n",
    "print(true_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(30, 6)\n"
     ]
    }
   ],
   "source": [
    "all_theta =np.concatenate([all_theta_1,all_theta_06,all_theta_batch],axis=0)\n",
    "print(all_theta.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "methods = ['OL1']*num_iter + ['OL06']*num_iter +['EM5']*num_iter\n",
    "params = ['Omega 1','Omega 2','Omega 3','Lambda 1','Lambda 2','Lambda 3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(all_theta,columns=params)\n",
    "df['Methods'] = methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Omega 1   Omega 2   Omega 3   Lambda 1   Lambda 2   Lambda 3 Methods\n",
      "0   0.393135  0.360638  0.246228   9.955339  29.822031  50.029982     OL1\n",
      "1   0.390400  0.217171  0.392429   9.905212  26.978546  43.986424     OL1\n",
      "2   0.522894  0.000242  0.476865  13.667710  27.205001  41.592863     OL1\n",
      "3   0.394774  0.113140  0.492086   9.993781  25.133126  41.046969     OL1\n",
      "4   0.522810  0.000037  0.477154  13.663969  27.239367  41.585856     OL1\n",
      "5   0.398024  0.374815  0.227161  10.025838  30.583833  50.773189     OL1\n",
      "6   0.391715  0.354180  0.254106   9.931955  29.542288  49.718409     OL1\n",
      "7   0.395666  0.125302  0.479032  10.000617  25.510811  41.404409     OL1\n",
      "8   0.391410  0.020262  0.588328  10.374855  10.423868  38.610198     OL1\n",
      "9   0.445969  0.317984  0.236048  11.575182  31.342107  50.240108     OL1\n",
      "10  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "11  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "12  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "13  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "14  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "15  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "16  0.411852  0.335458  0.252689   9.839042  29.949673  49.794429    OL06\n",
      "17  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "18  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "19  0.411852  0.335458  0.252689   9.839042  29.949673  49.794430    OL06\n",
      "20  0.398398  0.345190  0.256412   9.991362  29.763764  49.657619     EM5\n",
      "21  0.354592  0.212756  0.432652   9.409377  23.526579  43.096050     EM5\n",
      "22  0.157494  0.271114  0.571392   8.374463  12.124129  39.170235     EM5\n",
      "23  0.409911  0.399604  0.190485  10.245589  32.105679  52.277876     EM5\n",
      "24  0.387180  0.299199  0.313621   9.801781  27.958894  47.277404     EM5\n",
      "25  0.402107  0.366879  0.231015  10.065484  30.594974  50.713033     EM5\n",
      "26  0.382712  0.176887  0.440402   9.757574  24.888699  42.803395     EM5\n",
      "27  0.281985  0.167466  0.550549   8.960274  15.396304  39.746650     EM5\n",
      "28  0.390194  0.280365  0.329440   9.851768  27.772790  46.615028     EM5\n",
      "29  0.399379  0.354481  0.246140  10.009889  30.068469  50.097751     EM5\n"
     ]
    }
   ],
   "source": [
    "print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fmlnfyG0EERHNkhYC9wOVwJ0RsV7SYqAmIlZ0s+96Sd8hOaHdDFzVm1cwTZs2rbe6aqeuri6XT142tCQnWEe35hNqo0ePzuGP+Utz+zmbWd/I7RxEX+vJOYi8+H4wZt27+OKLqX++HsYffls7Qs/BhOMmlHz+r1znIIYc/5E1s8HEAWFmfWbSpEnUq95XMeWo4tEKJk3snaMNvheTmZllckCYmVkmB4SZmWVyQJiZWaYjCghJN/R2IWZm1r8c6Qjio71ahZmZ9TtdXuYqqat7OwjofG9pMzMbVLr7HMRzwGsi4pmODZK2ZWxvZmaDSHeHmP4vcFoXbXfnUIuZmfUjXY4gIuL6bto+lU85ZmbWX/gyVzMzy+R7MZlZ33ouuV/QgNA202jnWU/7r+fImKD5yDggzKzPDLQ5QjZt2gTA9InTy1xJD0zsvZ9zyQEh6SXAqLbliPhzr1RgZkPGQLslflu9pc7vPNgcdpwnaYGkTcAfgV8AW4GVOddlZmZlVsoI4ibgdcDPI2KWpL8H3ptvWWZmpctrNse2Q0x5jXz6+2yOpZwpaoqIXUCFpIqIeAQ4u5TOJc2TtFFSraTrMtqvlPSkpLWSfilpZrp+iqSGdP1aSd/o0XdlZtYLRo8ezejRQ/fGEaWMIJ6TNA74L+A/JT0LNB9uJ0mVwBJgDlAHrJK0IiI2FG12d0R8I91+AfBVYF7atjkiSgoiMxva+vO78IGslBHERUAD8AngZ8Bm4MIS9psN1EbElog4BCxP+3pRRBTf72ksEKUUbWZm+TvsCCIi9hctLutB3xOB4ns21QGv7biRpKuAa4ARwJuLmqZKWgPsBa6PiMcy9r0CuALg1FNP7UFpZmZ2OKVcxfSCpL0dHtsk/UDS6d3tmrGu0wghIpZExBnAp4C223s8DZwaEbNIwuNuScdm7Ls0IgoRUZgwYcLhvhUzM+uBUs5BfBXYQXKDPgGXAi8FNgJ3Aud2sV8dMLloeVLaT1eWA18HiIhGoDF9vlrSZmAGUFNCvWZm1gtKOQcxLyLuiIgXImJvRCwFLoiIe4Dju9lvFTBd0lRJI0iCZUXxBpKKP574VmBTun5CepKbdJQyHdhS8ndlZmZHrZQRRKukdwPfS5cvKWrr8qRyRDRLWgjcD1QCd0bEekmLgZqIWAEslHQ+0ATsAarT3d8ELJbUDLQAV0bE7p58Y2ZmdnQU0f2FQ+k7+K8BrycJhMdJrmjaDpwTEb/Mu8hSFAqFqKnxESgzs56QtDoiClltpVzFtIWuL2vtF+FgZma9r5SrmGZIekjSf6fLZ0nqcjIhMzMbHEo5Sf1N4NMk5wmIiHUkJ5zNzGwQKyUgxkTEEx3WHfZWG2ZmNrCVEhA7JZ1BesWSpEtIPshmZmaDWCmXuV4FLAVeLmk7ybwQ78+1KjMzK7tSr2I6X9JYoCIiXsi/LDMzK7fDBoSk8cAHgSnAMCm5xVJE+P66ZmaDWCmHmO4j+XDck0BrvuWYmVl/UUpAjIqIa3KvxMzM+pVSrmL6tqTLJZ0s6YS2R+6VmZlZWZUygjgEfAn4LH+9OV8A3c0FYWZmA1wpAXENMC0iduZdjJmZ9R+lHGJaDxzIuxAzM+tfShlBtABrJT1COssb+DJXM7PBrpSA+GH6MDOzIaSUgLgHmEZyYnpzRBzMtyQzM+sPujwHIWmYpFuAOmAZcBewTdItkob3VYFmZlYe3Z2k/hJwAjA1Is6JiFnAGcB44MuldC5pnqSNkmolXZfRfqWkJyWtlfRLSTOL2j6d7rdR0lt69m2ZmdnR6i4g3gZcXnxzvojYC3wMuOBwHUuqBJYA84GZwHuLAyB1d0S8KiLOBm4BvpruO5NkUqIzgXnAv6b9mZlZH+kuICIiImNlC3/9wFx3ZgO1EbElIg4By4GLOvS1t2hxbFG/FwHLI6IxIv4I1Kb9mZlZH+kuIDZI+mDHlZLeD/yhhL4nAtuKluvSdR37u0rSZpIRxKIe7nuFpBpJNfX19SWUZGZmperuKqargHslfRhYTfLu/jXAaOAdJfStjHVZI5IlwBJJ7wOuB6p7sO9SksmMKBQKpYxqzMysRF0GRERsB14r6c0k5wIErIyIh0rsuw6YXLQ8CdjRzfbLga8f4b5mZtbLSplR7mHg4SPoexUwXdJUYDvJSef3FW8gaXpEbEoX3wq0PV8B3C3pq8ApwHTgiSOowczMjlApH5Q7IhHRLGkhcD9QCdwZEeslLQZqImIFsFDS+UATsIfk8BLpdt8BNgDNwFXpyXEzM+sjyrhQaUAqFApRU1NT7jLMzAYUSasjopDVVsrdXM3MhqSdO3dy9dVXs2vXrnKXUhYOCDOzLixbtox169axbNmycpdSFg4IM7MMO3fuZOXKlUQEK1euHJKjCAeEmVmGZcuW0XaOtrW1dUiOIhwQZmYZHnzwQZqamgBoamrigQceKHNFfc8BYWaWYc6cOQwfnsxsMHz4cObOnVvmivqeA8LMLEN1dTVSctefiooKqqury1xR33NAmJllqKqqYv78+Uhi/vz5nHjiieUuqc/l9klqM7OBrrq6mq1btw7J0QM4IMzMulRVVcXtt99e7jLKxoeYzMwskwPCzMwyOSDMzCyTA8LMzDI5IMzMLJMDwszMMjkgzMwskwPCzMwy5RoQkuZJ2iipVtJ1Ge3XSNogaZ2khySdVtTWImlt+liRZ51mZtZZbp+kllQJLAHmAHXAKkkrImJD0WZrgEJEHJD0MeAW4D1pW0NEnJ1XfWZm1r08RxCzgdqI2BIRh4DlwEXFG0TEIxFxIF18HJiUYz1mZtYDeQbERGBb0XJduq4rHwFWFi2PklQj6XFJb8/aQdIV6TY19fX1R1+xmZm9KM+b9SljXWRuKL0fKAB/V7T61IjYIel04GFJT0bE5nadRSwFlgIUCoXMvs3M7MjkOYKoAyYXLU8CdnTcSNL5wGeBBRHR2LY+Inak/24BHgVm5VirmZl1kGdArAKmS5oqaQRwKdDuaiRJs4A7SMLh2aL1x0samT6vAt4AFJ/cNjOznOV2iCkimiUtBO4HKoE7I2K9pMVATUSsAL4EjAO+m07t9+eIWAC8ArhDUitJiH2hw9VPZmaWM0UMjkP3hUIhampqyl2GmdmAIml1RBSy2vxJajMzy+SAMDOzTA4IMzPL5IAwM7NMDggzM8vkgDAzs0wOCDMzy+SAMDOzTA4IMzPL5IAwM7NMDggzM8vkgDAzs0wOCDMzy+SAMDOzTA4IMzPL5IAwM7NMDggzM8vkgDAzs0y5BoSkeZI2SqqVdF1G+zWSNkhaJ+khSacVtVVL2pQ+qvOs08zMOsstICRVAkuA+cBM4L2SZnbYbA1QiIizgO8Bt6T7ngB8HngtMBv4vKTj86rVzMw6y3MEMRuojYgtEXEIWA5cVLxBRDwSEQfSxceBSenztwAPRsTuiNgDPAjMy7FWMzPrIM+AmAhsK1quS9d15SPAyp7sK+kKSTWSaurr64+yXDMzK5ZnQChjXWRuKL0fKABf6sm+EbE0IgoRUZgwYcIRF2pmZp3lGRB1wOSi5UnAjo4bSTof+CywICIae7KvmZnlJ8+AWAVMlzRV0gjgUmBF8QaSZgF3kITDs0VN9wNzJR2fnpyem64zM7M+MiyvjiOiWdJCkj/slcCdEbFe0mKgJiJWkBxSGgd8VxLAnyNiQUTslnQTScgALI6I3XnVamZmnSki87TAgFMoFKKmpqbcZZiZDSiSVkdEIavNn6Q2M7NMDggzM8vkgDAzs0wOCDMzy+SAMDOzTA4IMzPL5IAwM7NMDggzM8vkgDAzs0wOCDMzy+SAMDOzTA4IMzPL5IAwM7NMDggzsy7s3LmTq6++ml27dpW7lLJwQJiZdWHZsmWsW7eOZcuWlbuUsnBAmJll2LlzJytXriQiWLly5ZAcRTggzMwyLFu2jLYJ1VpbW4fkKMIBYWaW4cEHH6SpqQmApqYmHnjggTJX1PdyDQhJ8yRtlFQr6bqM9jdJ+q2kZkmXdGhrkbQ2fazIs04zs47mzJnD8OHDARg+fDhz584tc0V9L7eAkFQJLAHmAzOB90qa2WGzPwOXAXdndNEQEWenjwV51WlmlqW6uhpJAFRUVFBdXV3mivpeniOI2UBtRGyJiEPAcuCi4g0iYmtErANac6zDzKzHqqqqmD9/PpKYP38+J554YrlL6nN5BsREYFvRcl26rlSjJNVIelzS27M2kHRFuk1NfX390dRqZtZJdXU1Z5111pAcPQAMy7FvZayLHux/akTskHQ68LCkJyNic7vOIpYCSwEKhUJP+jYzO6yqqipuv/32cpdRNnmOIOqAyUXLk4Adpe4cETvSf7cAjwKzerM4MzPrXp4BsQqYLmmqpBHApUBJVyNJOl7SyPR5FfAGYENulZqZWSe5BURENAMLgfuB3wPfiYj1khZLWgAg6TWS6oB3AXdIWp/u/gqgRtLvgEeAL0SEA8LMrA+p7ZOCA12hUIiamppyl2FmNqBIWh0Rhcy2wRIQkuqBP5W7jhxVATvLXYQdMb9+A9dgf+1Oi4gJWQ2DJiAGO0k1XaW89X9+/Qauofza+V5MZmaWyQFhZmaZHBADx9JyF2BHxa/fwDVkXzufgzAzs0weQZiZWSYHhJmZZXJA9BOSJkn6kaRNkjZL+pqkEZLOlfSTjO0XphMxRXo7EutDR/B6TZX0m3T7e9Lbz7S1vVvSBknrJWXNjWI56TAx2dq2ic0kPSrpz2qbECJZ90NJ+7rYd1BOauaA6AfSX8J7gR9GxHRgBjAO+N/d7PYr4HwG94cD+6UjfL2+CNyabr8H+Eja13Tg08AbIuJM4ON51m6dFE9MdnZEfKGo7TmS+8AhaTxwcjf7DspJzRwQ/cObgYMR8e8AEdECfAL4MDAma4eIWBMRW/usQivWo9crDZQ3A99LVy0D2uY4uRxYEhF70r6ezbd064HlJDcZBbiY5E3BkOKA6B/OBFYXr4iIvSRTsk4rS0XWnZ6+XicCz6U3sIT2k2fNAGZI+lU6Oda8nGq2bKM7HGJ6T1HbQ8Cb0umTLwXu6bDvYSc1G+jynDDISieyJ1Pqar2VV09fr+4mzxoGTAfOJZkz5TFJr4yI53qhTju8hog4u4u2FuCXwHuA0RGxteiUBJQwqdlA5xFE/7AeaHevF0nHkky4NKh+4QaJnr5eO4HxktrekBVPnlUH/CgimiLij8BGksCw/mE5cDvwnY4NQ2FSMwdE//AQMEbSBwHSIe1XgP8ADpSxLsvWo9crkk+jPgJckq6qBn6UPv8h8PdpP1Ukh5y25Fi79cxjwD8D/6945VCZ1MwB0Q+kf0DeAbxL0ibgKeAg8Jl0k/Mk1RU9Xi9pUTrZ0iRgnaR/K0/1Q8+RvF7Ap4BrJNWSnJP4Vrrt/cAuSRtIQuSTEbGrL7+fIa7jOYjiq5iIxJcjouPtvofEpGa+1YaZmWXyCMLMzDI5IMzMLJMDwszMMjkgzMwskwPCzMwyOSDMMqR3yf120fIwSfVZd2rtsN/Zki4oWr5R0rVHUcdR7W92NBwQZtn2A6+UNDpdngNsL2G/s4ELDruV2QDggDDr2krgrenz91L0aVpJYyXdKWmVpDWSLkrneFgMvKfDjd9mpvMLbJG0qKiPayT9d/r4eNH6z0raKOnnwMuK1i9K541YJ2l5jt+3GeCb9Zl1ZzlwQ3pY6SzgTuCNadtngYcj4sPpXAFPAD8HbgAKEbEQkkNEwMtJbqdxDLBR0tfT/j4EvJbkZn6/kfQLkjdtl5Lc12cY8Fv+eufY64CpEdGYfk2zXDkgzLoQEeskTSEZPdzXoXkusKDo/MAo4NQuuvppRDQCjZKeBU4C/hb4QUTsB5B0L0n4VKTrD6Tri2cqWwf8p6QfktzDySxXPsRk1r0VwJfpcLM2knf97yyaUezUiPh9F300Fj1vIXljlnUL8DZd3f/mrcAS4BxgddHdYc1y4YAw696dwOKIeLLD+vuBq9vmLJbUdqvnF0gOJR3OfwFvlzRG0liSm/89lq5/h6TRko4BLkz7rwAmR8QjwD8C40mmOTXLjd+BmHUjIuqAr2U03QT8C8mddAVsBd5GcmfP6yStJblNdFf9/lbSf5CcuwD4t4hYAyDpHlTey+8AAABKSURBVGAtyXzjj6XtlcBdko4jGX3c6kmFLG++m6uZmWXyISYzM8vkgDAzs0wOCDMzy+SAMDOzTA4IMzPL5IAwM7NMDggzM8v0/wH0x1rjNH07HwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "count = 0 \n",
    "\n",
    "for param in params:\n",
    "    plt.figure()\n",
    "    sns.boxplot(x='Methods',y=param,data=df)\n",
    "    plt.plot([-0.5,2.5],[true_params[count],true_params[count]],'--')\n",
    "    plt.title(param)\n",
    "    #if count<3:\n",
    "        #plt.ylim(0.,1.)\n",
    "    #else:\n",
    "        #plt.ylim(0,max_l+10)\n",
    "    count+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}