02.3_Sampling_H.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dddcff16",
   "metadata": {},
   "outputs": [],
   "source": [
    "# GLOBAL VARIABLES. BE SURE NOT TO OVERWRITE THEM\n",
    "D = 8 # Amount of documents\n",
    "V = 12 # Size of the vocabulary\n",
    "\n",
    "# (Approximate) Maximum allowed amount of same word repetition in a document (it may be lower in practise due to the data generation strategy)\n",
    "# To get the actual maximum amount, call Simulator.get_M\n",
    "M = 10 \n",
    "\n",
    "\n",
    "k = 5 # Amount of topics\n",
    "gamma = 0.2  #"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e4645073",
   "metadata": {},
   "outputs": [],
   "source": [
    "# GLOBAL VARIABLES. BE SURE NOT TO OVERWRITE THEM\n",
    "D = 100 # Amount of documents\n",
    "V = 18 # Size of the vocabulary\n",
    "\n",
    "# (Approximate) Maximum allowed amount of same word repetition in a document (it may be lower in practise due to the data generation strategy)\n",
    "# To get the actual maximum amount, call Simulator.get_M\n",
    "M = 5 \n",
    "\n",
    "k = 6 # Amount of topics\n",
    "gamma = 0.2\n",
    "\n",
    "# FA: Since we're testing so much, lets agree on using just 1 small set of global variables for now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "36c0a59c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a62dba4b",
   "metadata": {},
   "source": [
    "From now on let's use the following simulated data for further testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "93f83bf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from simulator import Simulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d4918be0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: Sigma transformed from K\n",
      "Success: G transformed from K\n",
      "Success: W and Z generated\n",
      "Success: E transformed from Z\n",
      "Success: C transformed from Z\n",
      "Success: G transformed from K\n",
      "Success: W and Z generated\n",
      "Success: E transformed from Z\n",
      "Success: C transformed from Z\n"
     ]
    }
   ],
   "source": [
    "test_data = Simulator(D, V, M, k, gamma, seed=1967)  # Man on the moon\n",
    "test_data.generate_all_data()\n",
    "\n",
    "random_initial_data = Simulator(D, V, M, k, gamma, seed=1969)  # Woodstock Music Festival\n",
    "random_initial_data.generate_non_informative()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6e2cab4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f11663e520>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(test_data.G, cmap='Blues')\n",
    "plt.matshow(random_initial_data.G, cmap='Blues')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "818eaada",
   "metadata": {},
   "source": [
    "# 2. MC SAMPLER"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "923cc838",
   "metadata": {},
   "source": [
    "## 2.3.1 Sampling H (Metropolis-Hastings MC Sampling)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dcaa27d",
   "metadata": {},
   "source": [
    "### Task:\n",
    "\n",
    "You must implement a function that receives matrices $E_i$, $K_i$ and vector $\\mu$ and generates the next $H_{i+1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15e510dc",
   "metadata": {},
   "source": [
    "\n",
    ". $E$ matrix of $D \\times k$ where $E_d$ is the $k$-dim vector of counts of sampled drawings for the $z$-th topic over all words for each document\n",
    "\n",
    ". $K$ matrix of $k \\times k$ representing the precision matrix associated to the graph $G$\n",
    "\n",
    ". $\\mu = 0$\n",
    "\n",
    ". $H$ matrix of $D \\times k$ where $H_d = \\eta_d$ is the $k$-dim vector of the topic prevalences over document $d$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1d632883",
   "metadata": {},
   "outputs": [],
   "source": [
    "from samplers import MC_sample_H"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd1d2e8d",
   "metadata": {},
   "source": [
    "## 2.3.2 H Sampling Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f89702ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "step_size = 0.25\n",
    "E_copy = test_data.E.copy()\n",
    "Sigma_copy = test_data.Sigma.copy()\n",
    "K_copy = test_data.K.copy()\n",
    "G_copy=test_data.G.copy()\n",
    "\n",
    "H_sample, step_size = MC_sample_H(E_copy, Sigma_copy, K_copy, step_size=step_size,\n",
    "                                 adaptive_step_ratio=1.5, adaptive_step_threshold=0.55, max_step=0.5)\n",
    "\n",
    "assert np.all(E_copy == test_data.E)\n",
    "assert np.all(Sigma_copy == test_data.Sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "67ce85b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 2min 44s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Check that the Sampler works properly (This will take... forever)\n",
    "errors = []\n",
    "matrix_changes = []\n",
    "burn_in = 1000\n",
    "step_size = 0.5\n",
    "steps = []\n",
    "\n",
    "for i in range(5000):\n",
    "    H_sample_old = H_sample.copy()\n",
    "    H_sample, step_size = MC_sample_H(E=E_copy, Sigma=Sigma_copy, K=K_copy, H_current=H_sample_old, step_size=step_size,\n",
    "                                 adaptive_step_ratio=1.5, adaptive_step_threshold=0.55, max_step=0.5)\n",
    "    matrix_changes.append(~np.all(H_sample_old == H_sample))\n",
    "    if i >= burn_in:\n",
    "        errors.append(np.linalg.norm(H_sample - test_data.H))  # Computing error wrt the target matrix\n",
    "        steps.append(step_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b0ba906f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix changes (1 = changed, 0 = same)\n",
      "count    5000.0\n",
      "mean        0.0\n",
      "std         0.0\n",
      "min         0.0\n",
      "25%         0.0\n",
      "50%         0.0\n",
      "75%         0.0\n",
      "max         0.0\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Matrix should change\n",
    "matrix_changes = pd.Series(matrix_changes).astype(int)\n",
    "print(\"Matrix changes (1 = changed, 0 = same)\")\n",
    "\n",
    "print(matrix_changes.describe())\n",
    "matrix_changes.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b4302d72",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H L2-error metrics\n",
      "count    4000.000000\n",
      "mean      259.189200\n",
      "std         1.296858\n",
      "min       255.182547\n",
      "25%       258.318835\n",
      "50%       259.259300\n",
      "75%       260.097031\n",
      "max       263.022491\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Error should be distributed close to 0 (I guess...)  # BUG https://trello.com/c/9k2e8PQz/33-mcsampleh-is-not-close-to-expected-target\n",
    "errors = pd.Series(errors)\n",
    "print(\"H L2-error metrics\")\n",
    "print(errors.describe())\n",
    "errors.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f9d2bb20",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H L2-error series\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "errors.plot()\n",
    "print(\"H L2-error series\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7707c472",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steps\n",
      "count    4000.000000\n",
      "mean        0.188452\n",
      "std         0.060993\n",
      "min         0.065844\n",
      "25%         0.148148\n",
      "50%         0.148148\n",
      "75%         0.222222\n",
      "max         0.333333\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Matrix should change\n",
    "steps = pd.Series(steps)\n",
    "print(\"Steps\")\n",
    "\n",
    "print(steps.describe())\n",
    "steps.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "92e979a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steps\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps.plot()\n",
    "print(\"Steps\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb369073",
   "metadata": {},
   "source": [
    "As you can see, the true (left) and the last sampled (center) $\\Theta$ are quite similar. The right heatmap represents the difference of the first two. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "154f4d48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "5.100873201148261"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import seaborn as sn\n",
    "from transformation_functions import update_Theta\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1,3, figsize=(15, 5))\n",
    "\n",
    "last_Theta = update_Theta(np.zeros(H_sample.shape), H_sample)\n",
    "true_Theta = update_Theta(np.zeros(H_sample.shape), test_data.H)\n",
    "\n",
    "sn.heatmap(true_Theta, cmap='Blues',ax=ax[0])\n",
    "sn.heatmap(last_Theta, cmap='Blues',ax=ax[1])\n",
    "sn.heatmap(abs(true_Theta - last_Theta),cmap='Blues',ax=ax[2],center=0)\n",
    "plt.show()\n",
    "\n",
    "np.linalg.norm(true_Theta-last_Theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96b84cf5",
   "metadata": {},
   "source": [
    "# OLD CODE, JUST KEEPING IT HERE FOR REFERENCE (for now)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "305cba08",
   "metadata": {},
   "source": [
    "## 2.3.2 H Sampling Tests (burn-in 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1f6cb20f",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_copy = test_data.E.copy()\n",
    "Sigma_copy = test_data.Sigma.copy()\n",
    "K_copy = test_data.K.copy()\n",
    "\n",
    "H_sample = MC_sample_H(E_copy, Sigma_copy, K_copy)\n",
    "\n",
    "assert np.all(E_copy == test_data.E)\n",
    "assert np.all(Sigma_copy == test_data.Sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1bd64de4",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'tuple' object has no attribute 'copy'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<timed exec>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'tuple' object has no attribute 'copy'"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Check that the Sampler works properly (This will take... forever)\n",
    "errors = []\n",
    "matrix_changes = []\n",
    "burn_in = 100\n",
    "\n",
    "for i in range(500):\n",
    "    H_sample_old = H_sample.copy()\n",
    "    H_sample = MC_sample_H(E_copy, Sigma_copy, K_copy, H_sample_old, burn_in=10)\n",
    "    matrix_changes.append(~np.all(H_sample_old == H_sample))\n",
    "    if i >= burn_in:\n",
    "        errors.append(np.linalg.norm(H_sample - test_data.H))  # Computing error wrt the target matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "35d6ddc5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix changes (1 = changed, 0 = same)\n",
      "count    0.0\n",
      "mean     NaN\n",
      "std      NaN\n",
      "min      NaN\n",
      "25%      NaN\n",
      "50%      NaN\n",
      "75%      NaN\n",
      "max      NaN\n",
      "dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-18-78c0c5618887>:2: DeprecationWarning: The default dtype for empty Series will be 'object' instead of 'float64' in a future version. Specify a dtype explicitly to silence this warning.\n",
      "  matrix_changes = pd.Series(matrix_changes).astype(int)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Matrix should change\n",
    "matrix_changes = pd.Series(matrix_changes).astype(int)\n",
    "print(\"Matrix changes (1 = changed, 0 = same)\")\n",
    "\n",
    "print(matrix_changes.describe())\n",
    "matrix_changes.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6b1fda6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H L2-error metrics\n",
      "count    0.0\n",
      "mean     NaN\n",
      "std      NaN\n",
      "min      NaN\n",
      "25%      NaN\n",
      "50%      NaN\n",
      "75%      NaN\n",
      "max      NaN\n",
      "dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-19-d7e8127eacc3>:2: DeprecationWarning: The default dtype for empty Series will be 'object' instead of 'float64' in a future version. Specify a dtype explicitly to silence this warning.\n",
      "  errors = pd.Series(errors)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Error should be distributed close to 0 (I guess...)  # BUG https://trello.com/c/9k2e8PQz/33-mcsampleh-is-not-close-to-expected-target\n",
    "errors = pd.Series(errors)\n",
    "print(\"H L2-error metrics\")\n",
    "print(errors.describe())\n",
    "errors.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4fe28e54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H L2-error series\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "errors.plot()\n",
    "print(\"H L2-error series\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6eb1ec34",
   "metadata": {},
   "source": [
    "As you can see, the true (left) and the last sampled (center) $\\Theta$ are quite similar. The right heatmap represents the difference of the first two. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4a761bc9",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'tuple' object has no attribute 'shape'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-21-0f0972b57612>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfigsize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m15\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mlast_Theta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mupdate_Theta\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mH_sample\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mH_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[0mtrue_Theta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mupdate_Theta\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mH_sample\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtest_data\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mH\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'tuple' object has no attribute 'shape'"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sn\n",
    "from transformation_functions import update_Theta\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1,3, figsize=(15, 5))\n",
    "\n",
    "last_Theta = update_Theta(np.zeros(H_sample.shape), H_sample)\n",
    "true_Theta = update_Theta(np.zeros(H_sample.shape), test_data.H)\n",
    "\n",
    "sn.heatmap(true_Theta, cmap='Blues',ax=ax[0])\n",
    "sn.heatmap(last_Theta, cmap='Blues',ax=ax[1])\n",
    "sn.heatmap(abs(true_Theta - last_Theta),cmap='Blues',ax=ax[2],center=0)\n",
    "plt.show()\n",
    "\n",
    "np.linalg.norm(true_Theta-last_Theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65860db7",
   "metadata": {},
   "source": [
    "## 2.3.2 H Sampling Tests (burn-in 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c223814",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_copy = test_data.E.copy()\n",
    "Sigma_copy = test_data.Sigma.copy()\n",
    "K_copy = test_data.K.copy()\n",
    "\n",
    "H_sample = MC_sample_H(E_copy, Sigma_copy, K_copy)\n",
    "\n",
    "assert np.all(E_copy == test_data.E)\n",
    "assert np.all(Sigma_copy == test_data.Sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8d418e81",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "# Check that the Sampler works properly (This will take... forever)\n",
    "errors = []\n",
    "matrix_changes = []\n",
    "burn_in = 100\n",
    "\n",
    "for i in range(500):\n",
    "    H_sample_old = H_sample.copy()\n",
    "    H_sample = MC_sample_H(E_copy, Sigma_copy, K_copy, H_sample_old, burn_in=100)\n",
    "    matrix_changes.append(~np.all(H_sample_old == H_sample))\n",
    "    if i >= burn_in:\n",
    "        errors.append(np.linalg.norm(H_sample - test_data.H))  # Computing error wrt the target matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69227ca7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Matrix should change\n",
    "matrix_changes = pd.Series(matrix_changes).astype(int)\n",
    "print(\"Matrix changes (1 = changed, 0 = same)\")\n",
    "\n",
    "print(matrix_changes.describe())\n",
    "matrix_changes.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5baf85fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Error should be distributed close to 0 (I guess...)  # BUG https://trello.com/c/9k2e8PQz/33-mcsampleh-is-not-close-to-expected-target\n",
    "errors = pd.Series(errors)\n",
    "print(\"H L2-error metrics\")\n",
    "print(errors.describe())\n",
    "errors.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa7b3ca8",
   "metadata": {},
   "outputs": [],
   "source": [
    "errors.plot()\n",
    "print(\"H L2-error series\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f55559b",
   "metadata": {},
   "source": [
    "As you can see, the true (left) and the last sampled (center) $\\Theta$ are quite similar. The right heatmap represents the difference of the first two. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d531bfee",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sn\n",
    "from transformation_functions import update_Theta\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1,3, figsize=(15, 5))\n",
    "\n",
    "last_Theta = update_Theta(np.zeros(H_sample.shape), H_sample)\n",
    "true_Theta = update_Theta(np.zeros(H_sample.shape), test_data.H)\n",
    "\n",
    "sn.heatmap(true_Theta, cmap='Blues',ax=ax[0])\n",
    "sn.heatmap(last_Theta, cmap='Blues',ax=ax[1])\n",
    "sn.heatmap(abs(true_Theta - last_Theta),cmap='Blues',ax=ax[2],center=0)\n",
    "plt.show()\n",
    "\n",
    "np.linalg.norm(true_Theta-last_Theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3d920cbe",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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