osue_markov_exercise_tofix.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8QCb5Lh6UQ44"
   },
   "source": [
    "# Prerequisites"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 119
    },
    "colab_type": "code",
    "id": "6Gf6k9zNSyOt",
    "outputId": "f7b85712-2bd4-4fdf-9324-bd1515431271"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6Fet57psSyOz"
   },
   "source": [
    "# Data and utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 581
    },
    "colab_type": "code",
    "id": "0xp80l-9SyO0",
    "outputId": "ab63efea-3f3f-445b-9655-5838b0239b02"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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b7uZNz9/oPe37PtX+bS4F1g7jM0r7JpIkdUpnuvgkSeplgZIkdZIFSpLUSRYo\nSVInWaAkSZ1kgZIkdZIFSpLUSRYoSVIn/X8EF8Ly34TFnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b6cb1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b700fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "users = [\"A\", \"B\", \"C\"]  # the three users we are interested in\n",
    "states = {\"work\": 0, \"pause\": 1, \"game\": 2, \"browse\": 3, \"stream\": 4}   # their states (activities)\n",
    "states_inv = {v: k for k, v in states.items()}\n",
    "observations = {\"none\": 0, \"very_low\": 1, \"low\": 2, \"medium\": 3, \"high\": 4, \"very_high\": 5}   # our observations (LED blinking frequency)\n",
    "observations_inv = {v: k for k, v in observations.items()}\n",
    "\n",
    "def convert_state(state):\n",
    "    return states[state]\n",
    "\n",
    "\n",
    "def convert_observation(observation):\n",
    "    return observations[observation]\n",
    "\n",
    "def convert_state_observation(state_observation, sep=','):\n",
    "    state, observation = state_observation.split(sep)\n",
    "    return (convert_state(state), convert_observation(observation))\n",
    "\n",
    "\n",
    "def load_activities(users):\n",
    "    \"\"\" Loads activities for all users from file \"\"\"\n",
    "    activities_data = {}   # map user -> activties_data\n",
    "    for u in users:\n",
    "        # load activities CSV\n",
    "        path = os.path.join(\"data\", u + \"_activities.csv\")\n",
    "        data = np.genfromtxt(path, dtype='unicode', delimiter='|')\n",
    "        # we are only interested in the second column\n",
    "        # and map the activity names to indices\n",
    "        activities_data[u] = [list(map(convert_state, d.split())) for d in data[:, 1]]\n",
    "    return activities_data\n",
    "\n",
    "\n",
    "def load_observations():\n",
    "    \"\"\" Loads observations from file \"\"\"\n",
    "    # load observations CSV\n",
    "    path = os.path.join(\"data\", \"observations.csv\")\n",
    "    data = np.genfromtxt(path, dtype='unicode', delimiter='|')\n",
    "    \n",
    "    # full matrix\n",
    "    full_data = np.vstack((\n",
    "              np.vectorize(states.get)(data[:, 0]),\n",
    "              np.vectorize(observations.get)(data[:, 1]))).T\n",
    "    \n",
    "    # counts per activity, matrix activity x observation\n",
    "    # dictionary with keys activity, values arrays \n",
    "    # as arr[observation] == count\n",
    "    observation_counts = np.ones((len(states), len(observations)))\n",
    "    for row in full_data:\n",
    "        activity, observation = row\n",
    "        observation_counts[activity][observation] += 1.0\n",
    "    return (full_data, observation_counts)\n",
    "\n",
    "\n",
    "def load_testsets(users):\n",
    "    \"\"\" Load testsets from the files. \"\"\"\n",
    "    activities_data = {}   # map user -> activties_data\n",
    "    for u in users:\n",
    "        # load activities CSV\n",
    "        path = os.path.join(\"data\", u + \"_testset.csv\")\n",
    "        data = np.genfromtxt(path, dtype='unicode', delimiter='|')\n",
    "        # we are only interested in the second column\n",
    "        # and map the activity/observation names to tuples of indices\n",
    "        activities_data[u] = [list(map(convert_state_observation, d.split())) for d in data[:, 1]]\n",
    "    return activities_data\n",
    "    \n",
    "    \n",
    "def split_testset(activities_data, test_set_size=3):\n",
    "    \"\"\" Splits activities data in training and test set \"\"\"\n",
    "    random.seed(1234)\n",
    "    random.shuffle(activities_data)\n",
    "    return (activities_data[test_set_size:],\n",
    "            activities_data[:test_set_size])\n",
    "    \n",
    "\n",
    "def plot_transition_matrices(models):\n",
    "    \"\"\" Plots transition matrices for the provided models \"\"\"\n",
    "    fig, axarr = plt.subplots(1, len(models))\n",
    "    plt_num = 0\n",
    "    for user in models:\n",
    "        A = models[user][0]\n",
    "        axarr[plt_num].matshow(A)\n",
    "        axarr[plt_num].set_title(\"Transition matrix \" + user, y=-0.3)\n",
    "        plt_num += 1\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    plt.close(fig)\n",
    "    \n",
    "    \n",
    "def plot_graphs(models):\n",
    "    \"\"\" Plots graphs for the provided models \"\"\"\n",
    "    import networkx as nx\n",
    "    fig, axarr = plt.subplots(1, len(models))\n",
    "    plt_num = 0\n",
    "    for user in models:\n",
    "        A = models[user][0]\n",
    "        G = nx.from_numpy_matrix(A)\n",
    "        nx.draw(G)\n",
    "        axarr[plt_num].set_title(\"Transition matrix \" + user, y=-0.3)\n",
    "        plt_num += 1\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    plt.close(fig)\n",
    "\n",
    "\n",
    "def plot_results(results_matrix):\n",
    "    \"\"\" Plots classification results \"\"\"\n",
    "    fig = plt.figure(figsize=(100,100))\n",
    "    plt.matshow(results_matrix)\n",
    "    plt.show()\n",
    "    plt.close(fig)\n",
    "\n",
    "\n",
    "def plot_models(models):\n",
    "    # chain model\n",
    "    # if (len(model) == 2):\n",
    "    plot_transition_matrices(models)\n",
    "    #plot_graphs(models)\n",
    "\n",
    "    \n",
    "def plot_observation_counts(observation_counts):\n",
    "    \"\"\" Plots transition matrices for the provided models \"\"\"\n",
    "    fig, axarr = plt.subplots(1, len(observation_counts))\n",
    "    plt_num = 0\n",
    "    for idx, row in enumerate(observation_counts):\n",
    "        counts = [int(c) for c in row]\n",
    "        axarr[plt_num].bar(range(len(counts)), counts)\n",
    "        axarr[plt_num].set_title(states_inv[idx], y=-0.15)\n",
    "        plt_num += 1\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    plt.close(fig)\n",
    "\n",
    "\n",
    "def plot_activities(activities_data):\n",
    "    fig, axarr = plt.subplots(1, len(activities_data))\n",
    "    plt_num = 0\n",
    "    for user in activities_data:\n",
    "        user_activities = activities_data[user]\n",
    "        flat_activites = [i for sl in user_activities for i in sl]\n",
    "        bins = sorted(states.values())\n",
    "        bins.append(len(states))\n",
    "        axarr[plt_num].hist(flat_activites, bins=bins)\n",
    "        axarr[plt_num].set_xticks(bins)\n",
    "        axarr[plt_num].set_title(\"State counts \" + user, y=-0.2)\n",
    "        plt_num += 1\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    plt.close(fig)\n",
    "\n",
    "\n",
    "# load data into global variables\n",
    "activities_data = load_activities(users)\n",
    "testset_data = load_testsets(users)\n",
    "observations_data, observations_counts = load_observations()\n",
    "\n",
    "plot_activities(activities_data)\n",
    "plot_observation_counts(observations_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ug-e8PIWSyO5"
   },
   "source": [
    "# Task 1: Markov chain model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "Rp7yIbiHSyO6"
   },
   "outputs": [],
   "source": [
    "def init_chain_model(states):\n",
    "    \"\"\" Initialize an empy Markov chain model \"\"\"\n",
    "    # transition probability matrix\n",
    "    A = np.zeros((len(states), len(states)))\n",
    "    \n",
    "    # initial state probability vector\n",
    "    I = np.zeros((1, len(states)))\n",
    "    \n",
    "    return (A, I)\n",
    "\n",
    "\n",
    "def train_chain_model(model, activities_data):\n",
    "    \"\"\" Trains a Markov chain model given activities_data \"\"\"\n",
    "    # get transition matrix and initial transition vector from model tuple\n",
    "    A, I = model # transition matrix (previous, current), initial probabilities\n",
    "    \n",
    "    # get a counts matrix of same size as A\n",
    "    # we use \"ones_like\" instead of \"zeroes_like\" so that\n",
    "    # when normalizing we don't get divisions by zero\n",
    "    # at the same time achieves Laplace smoothing\n",
    "    # https://en.wikipedia.org/wiki/Additive_smoothing\n",
    "    A_counts = np.ones_like(A)\n",
    "    I_counts = np.ones_like(I)\n",
    "    \n",
    "    # loop over sequences (one sequence per day)\n",
    "    for seq in activities_data:\n",
    "        # get initial activity for this dy\n",
    "        I_counts[0, seq[0]] += 1\n",
    "        \n",
    "        # loop activities in this day\n",
    "        for idx in range(1, len(seq)):\n",
    "            # ========================================\n",
    "            # TASK TODO: get current and last activity\n",
    "            # from sequence \"seq\"\n",
    "            # and increase the respective entry in the \n",
    "            # transition count matrix A_counts\n",
    "            # ========================================\n",
    "            curr = 0 # TO FIX\n",
    "            last = 0 # TO FIX\n",
    "            A_counts[last, curr] += 0 # TO FIX\n",
    "            \n",
    "    # normalize matrix rows to get probabilites\n",
    "    # (so that the sum of each row is 1.0)\n",
    "    # sum up rows, and then divide using broadcasting\n",
    "    # https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html\n",
    "    A = A_counts / A_counts.sum(axis=1, keepdims=True)\n",
    "    I = I_counts / I_counts.sum(axis=1, keepdims=True)\n",
    "    return (A, I)\n",
    "\n",
    "\n",
    "def predict_chain_model(model, activities_data):\n",
    "    \"\"\" Run prediction on a Markov Chain model \"\"\"\n",
    "    A, I = model   # transition matrix (previous, current), initial probabilities\n",
    "    \n",
    "    predictions = []\n",
    "    # loop sequences (daily activities)\n",
    "    for seq_idx, seq in enumerate(activities_data):\n",
    "        # get initial property for first state\n",
    "        seq_prob = I[0, seq[0]]\n",
    "        \n",
    "        # loop activities per day\n",
    "        for idx in range(1, len(seq)):\n",
    "            # ===========================================\n",
    "            # TASK TODO: get current and last activity\n",
    "            # get the transition probability P(curr|last)\n",
    "            # multiply transition probabilities up for \n",
    "            # the entire sequence\n",
    "            # ===========================================\n",
    "            curr = 0 # TO FIX\n",
    "            last = 0 # TO FIX\n",
    "            seq_prob = 1.0 # TO FIX \n",
    "        predictions.append(seq_prob)\n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AxRkZoAASyO-"
   },
   "source": [
    "## 1.1 Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 185
    },
    "colab_type": "code",
    "id": "OczEScdHSyO-",
    "outputId": "4b70e140-82bc-4ef1-e09e-c48fabe14cb5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PAJdR7SIrhXmpFZCXHwG/HxF9re9eo/oc0u5U+6Cfi4i3Ux1c7EtEHFefUgjVAcvk1VNA\nez3J9s/ouAj4YkTsFRGLgS9Q7RMetN2p9h2vp3oXdgbVu5dJTwJLm7yY9To8g2p3wPHAn23nDKgT\nqP44D+q5fBg4JiLe0OSJDJmZGV1mpj52L+D3gLv7Xd4ImJfR5eWvqbbG/n7yM1sRsSQivh4R79je\nckbVkE6jeke+ieqdzCUNHnsYcHNEPEf1Lu3TmfmzaeY7F/j1iHg6Ir4/zf1nAndQvYu6k+qA45cb\n1LGjrqB6B/HfVAcRN/La/a2XUG2xbIiIm2YaLCImqEL+l5n508y8j6rhfDciFkyZ991UuxG+mZlP\nTF6odtutpWpMpTIzI8hMj/fUHwrdDNxTL//UHXw+w2BeRpSXzFxPdZYjVOtxE9VnHtczw3HHWX8w\nVpKkNozNVwdJkrrNhiRJKoINSZJUBBuSJKkINiRJUhFsSJKkItiQJElFsCFJkopgQ5IkFeH/AaAX\nGLc4CGsJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b421940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train our models\n",
    "chain_models = {}\n",
    "test_data = {}\n",
    "for user in activities_data:\n",
    "    user_activities_data = activities_data[user]\n",
    "    user_train_data, user_test_data = split_testset(user_activities_data, 5)\n",
    "    \n",
    "    # store test data\n",
    "    test_data[user] = user_test_data\n",
    "    \n",
    "    # initialize and then train model\n",
    "    chain_model = init_chain_model(states)\n",
    "    chain_model = train_chain_model(chain_model, user_train_data)\n",
    "    chain_models[user] = chain_model\n",
    "    \n",
    "# plot our trained models\n",
    "plot_models(chain_models)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "z0HpvrpjSyPC"
   },
   "source": [
    "## 1.2 Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1046
    },
    "colab_type": "code",
    "id": "7VinCC42SyPD",
    "outputId": "438fe73d-941c-4e1b-aafe-76518a9d84f8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user A\n",
      "[[0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]\n",
      " [0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]\n",
      " [0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b421400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAECCAYAAAA7JjqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc1e630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user B\n",
      "[[0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]\n",
      " [0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]\n",
      " [0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd799e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAECCAYAAAA7JjqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd2b9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user C\n",
      "[[0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]\n",
      " [0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]\n",
      " [0.33333333 0.33333333 0.33333333 0.33333333 0.33333333]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c2b1240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAECCAYAAAA7JjqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c1a4198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# test on held-out data \n",
    "for user_data in test_data:\n",
    "    print (\"Testing on data for user \" + user_data)\n",
    "    # Calculate predictions for all models\n",
    "    predictions = [predict_chain_model(chain_models[user_model], test_data[user_data]) \n",
    "                   for user_model in chain_models]\n",
    "    \n",
    "    # Now we have a matrix of the form (users, test_activities)\n",
    "    results = np.array(predictions)\n",
    "    \n",
    "    # Normalize\n",
    "    results /= results.sum(axis=0, keepdims=True)\n",
    "    \n",
    "    # Show normalized results\n",
    "    print (results)\n",
    "    plot_results(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_voR8M-BSyPG"
   },
   "source": [
    "# Task 2: Hidden Markov model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "5XfWKGFOSyPH"
   },
   "outputs": [],
   "source": [
    "def init_hidden_markov_model(states, observations):\n",
    "    \"\"\"Initialize an empy hidden Markov model\n",
    "    \n",
    "    Zero-initializes the model parameters for a hidden Markov model.\n",
    "    \n",
    "    # Returns\n",
    "        Model as tuple (A, I, O) with transition matrix, initial state vector and \n",
    "        observation probabilities matrix respectively.\n",
    "    \"\"\"\n",
    "    # transition probability matrix (States x States)\n",
    "    # access transitions from previous_state to current_state\n",
    "    # by A[previous_state, current_state]\n",
    "    A = np.zeros((len(states), len(states)))\n",
    "    \n",
    "    # initial state probability vector (1 x States)\n",
    "    I = np.zeros((1, len(states)))\n",
    "    \n",
    "    # observation probabilities matrix (States x Observations)\n",
    "    # Access observation probabilities as O[observation, current_state]\n",
    "    O = np.zeros((len(states), len(observations)))\n",
    "    \n",
    "    return (A, I, O)\n",
    "\n",
    "\n",
    "def train_hidden_markov_model(model, activities_data, observations_counts):\n",
    "    \"\"\"Trains a hidden Markov model.\n",
    "    \n",
    "    Given activities data and observation counts, trains a hidden Markov model.\n",
    "    As we do have activities data available, training becomes simple counting and normalizing.\n",
    "    If we only had observations, we would have to use an algorithm like Baum-Welch.\n",
    "    (see for example http://www.sfs.uni-tuebingen.de/resources/em.pdf)\n",
    "    \n",
    "    # Arguments\n",
    "        model: Model generated by init_hidden_markov_model\n",
    "        activities_data: Data on user activities\n",
    "        observations_counts: Counts per observation\n",
    "    \"\"\"\n",
    "    # get transition matrix, initial transition vector and observations matrix from model tuple\n",
    "    A, I, O = model\n",
    "    \n",
    "    # get a counts matrix of same size as A\n",
    "    # we use \"ones_like\" instead of \"zeroes_like\" so that\n",
    "    # when normalizing we don't get divisions by zero\n",
    "    # at the same time achieves Laplace smoothing\n",
    "    # https://en.wikipedia.org/wiki/Additive_smoothing\n",
    "    A_counts = np.ones_like(A)\n",
    "    I_counts = np.ones_like(I)\n",
    "    \n",
    "    # loop over sequences (one sequence per day)\n",
    "    for seq in activities_data:\n",
    "        # get initial activity for this dy\n",
    "        I_counts[0, seq[0]] += 1\n",
    "        \n",
    "        # loop activities in this day\n",
    "        for idx in range(1, len(seq)):\n",
    "            # ========================================\n",
    "            # TASK TODO: get current and last activity\n",
    "            # and increase the according entry in the \n",
    "            # transition count matrix\n",
    "            #=========================================\n",
    "            curr = 0 # TO FIX\n",
    "            last = 0 # TO FIX\n",
    "            A_counts[last, curr] += 0 # TO FIX\n",
    "            \n",
    "    # normalize matrix rows to get probabilites\n",
    "    # (so that the sum of each row is 1.0)\n",
    "    # sum up rows, and then divide using broadcasting\n",
    "    # https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html\n",
    "    A_norm = A_counts / A_counts.sum(axis=1, keepdims=True)\n",
    "    I_norm = I_counts / I_counts.sum(axis=1, keepdims=True)\n",
    "    O_norm = observations_counts / observations_counts.sum(axis=1, keepdims=True)\n",
    "    return (A_norm, I_norm, O_norm)\n",
    "\n",
    "\n",
    "def _predict_forward_algorithm(model, test_data):\n",
    "    \"\"\" Forward algorithm for the evaluation problem in HMMs. \n",
    "    \n",
    "    Calculates the probabilty of observation sequences in test_data given model.\n",
    "    https://en.wikipedia.org/wiki/Forward_algorithm\n",
    "    \n",
    "    # Arguments:\n",
    "        model: A trained hidden Markov model\n",
    "        test_data: Sequence of tuples of (_, observation)\n",
    "    \"\"\"\n",
    "    A, I, O = model   # transition matrix, initial probabilities, observation probabilities matrix\n",
    "    num_states = I.shape[1]\n",
    "    predictions = []\n",
    "    # loop sequences (one sequence per day)\n",
    "    for seq_idx, seq in enumerate(test_data):\n",
    "        # forward alpha matrix of shape state_num x max_seq_len\n",
    "        F = np.zeros((num_states, len(seq)))\n",
    "        \n",
    "        # get a sequence of observations from the sequence of (state, observation)\n",
    "        observations = [x for (_, x) in seq]\n",
    "\n",
    "        # initial probabilities\n",
    "        for i in range(0, num_states):\n",
    "            # probability for starting with state i: transition * emission probability\n",
    "            F[i, 0] = I[0, i] * O[i, observations[0]]\n",
    "    \n",
    "        # loop the rest of observations in sequence along time t\n",
    "        for t in range(1, len(observations)):\n",
    "            curr_obs = observations[t]\n",
    "\n",
    "            # all possible transitions k -> i at time t\n",
    "            for i in range(0, num_states):\n",
    "                p_sum = 0\n",
    "                for k in range(0, num_states):\n",
    "                    p_sum += F[k, t-1] * A[k, i] * O[i, curr_obs]\n",
    "                F[i, t] = p_sum\n",
    "                \n",
    "        p_ret = 0.0\n",
    "        for k in range(0, num_states):\n",
    "            p_ret += F[k, -1]\n",
    "            \n",
    "        predictions.append(p_ret)\n",
    "    return predictions\n",
    "\n",
    "    \n",
    "def predict_hidden_markov_model(model, test_data, use_states=True):\n",
    "    \"\"\"Run prediction on a hidden Markov model. \n",
    "    \n",
    "    Predict the probability of a given sequence of activities or observations.\n",
    "    \n",
    "    If use_states is True, state (activity) information can be used - we can easily calculate\n",
    "    the total probability with the product of the individual probabilities of the sequence.\n",
    "    This is then a Markov chain model with observations, as the states (activities) are not hidden.\n",
    "    \n",
    "    If use_states is False, the states (activities) are hidden and we have to find the most likely sequence\n",
    "    in a hidden Markov model.\n",
    "    \n",
    "    # Arguments:\n",
    "        model: A trained hidden Markov model\n",
    "        test_data: Sequence of tuples of (state, observation)\n",
    "        use_states: Use given state information or ignore and predict it\n",
    "    \"\"\"    \n",
    "    # allowed to use state information in the test data, just multiply probabilites\n",
    "    if use_states:\n",
    "        # transition matrix, initial probabilities, observation probabilities matrix\n",
    "        A, I, O = model  \n",
    "        predictions = []\n",
    "        # loop sequences (one sequence per day)\n",
    "        for seq_idx, seq in enumerate(test_data):\n",
    "            # get initial property for first state\n",
    "            seq_prob = I[0, seq[0][0]] * O[0, seq[0][1]]\n",
    "\n",
    "            # loop activities/observations for this day\n",
    "            for idx in range(1, len(seq)):\n",
    "                # =======================================================\n",
    "                # TASK TODO: get current and last activity\n",
    "                # get the transition probability P(curr_state|last_state)\n",
    "                # get the observation probability P(curr_obs|last_obs)\n",
    "                # =======================================================\n",
    "                curr_state, curr_obs = seq[idx]\n",
    "                last_state, _ = seq[idx-1]\n",
    "                seq_prob = seq_prob * 1.0 # TO FIX\n",
    "                \n",
    "            predictions.append(seq_prob)\n",
    "        return predictions\n",
    "    # states are hidden, use forward algorithm\n",
    "    else:\n",
    "        return _predict_forward_algorithm(model, test_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xvNi9cGJSyPJ"
   },
   "source": [
    "## 2.1 Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 185
    },
    "colab_type": "code",
    "id": "ac567f-2SyPK",
    "outputId": "0cde3c12-72a9-4b7b-f0f7-183c03171249"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PAJdR7SIrhXmpFZCXHwG/HxF9re9eo/oc0u5U+6Cfi4i3Ux1c7EtEHFefUgjVAcvk1VNA\nez3J9s/ouAj4YkTsFRGLgS9Q7RMetN2p9h2vp3oXdgbVu5dJTwJLm7yY9To8g2p3wPHAn23nDKgT\nqP44D+q5fBg4JiLe0OSJDJmZGV1mpj52L+D3gLv7Xd4ImJfR5eWvqbbG/n7yM1sRsSQivh4R79je\nckbVkE6jeke+ieqdzCUNHnsYcHNEPEf1Lu3TmfmzaeY7F/j1iHg6Ir4/zf1nAndQvYu6k+qA45cb\n1LGjrqB6B/HfVAcRN/La/a2XUG2xbIiIm2YaLCImqEL+l5n508y8j6rhfDciFkyZ991UuxG+mZlP\nTF6odtutpWpMpTIzI8hMj/fUHwrdDNxTL//UHXw+w2BeRpSXzFxPdZYjVOtxE9VnHtczw3HHWX8w\nVpKkNozNVwdJkrrNhiRJKoINSZJUBBuSJKkINiRJUhFsSJKkItiQJElFsCFJkopgQ5IkFeH/AaAX\nGLc4CGsJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c3a8d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train our models\n",
    "models = {}\n",
    "for user in activities_data:\n",
    "    user_activities_data = activities_data[user]\n",
    "    \n",
    "    # initialize and then train model\n",
    "    model = init_hidden_markov_model(states, observations)\n",
    "    model = train_hidden_markov_model(model, user_activities_data, observations_counts)\n",
    "    models[user] = model\n",
    "    \n",
    "# plot our trained models\n",
    "plot_models(models)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "wHn6edOpSyPO"
   },
   "source": [
    "## 2.2 Evaluation (observable states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1097
    },
    "colab_type": "code",
    "id": "WwdtQwKYSyPP",
    "outputId": "57e558ab-0b7c-435b-9d65-02da8b36869e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user A\n",
      "[[0.3059126  0.67613636 0.24843424 0.3059126  0.3059126 ]\n",
      " [0.49164524 0.14488636 0.15970772 0.49164524 0.49164524]\n",
      " [0.20244216 0.17897727 0.59185804 0.20244216 0.20244216]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b7e46d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAECCAYAAAA7JjqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnlvpkQkAWyImAIyJCQBjYgLAmJgAMPZ/cPaSWKJ966AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c2adb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user B\n",
      "[[0.3059126  0.3059126  0.3059126 ]\n",
      " [0.49164524 0.49164524 0.49164524]\n",
      " [0.20244216 0.20244216 0.20244216]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c197940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxwf+Z9KJD2wRPgwkfBhI+DCQ8GGg/wJvjDUrfD4RcQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8856a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user C\n",
      "[[0.24843424 0.24843424 0.3059126  0.24843424]\n",
      " [0.15970772 0.15970772 0.49164524 0.15970772]\n",
      " [0.59185804 0.59185804 0.20244216 0.59185804]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8c26a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUgAAAECCAYAAACc1045AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npjtIgIsikAADgQQYCCTAQCABBv8FR4p7E+fgnAoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c18b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# test on extra testsets\n",
    "for user_data in testset_data:\n",
    "    print (\"Testing on data for user \" + user_data)\n",
    "    # Calculate predictions for all models\n",
    "    predictions = [predict_hidden_markov_model(models[user_model], testset_data[user_data], use_states=True) \n",
    "                   for user_model in models]\n",
    "    \n",
    "    # Now we have a matrix of the form (users, test_activities)\n",
    "    results = np.array(predictions)\n",
    "    \n",
    "    # Normalize\n",
    "    results /= results.sum(axis=0, keepdims=True)\n",
    "    \n",
    "    # Show normalized results\n",
    "    print (results)\n",
    "    plot_results(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "R027wtymSyPU"
   },
   "source": [
    "## 2.2 Evaluation (hidden states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1046
    },
    "colab_type": "code",
    "id": "A-Z0hPagSyPV",
    "outputId": "582baeda-decf-40e3-f81e-03f905675d9a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user A\n",
      "[[0.31864514 0.50394988 0.2724072  0.35254521 0.31864514]\n",
      " [0.40601109 0.24353564 0.27329326 0.38620644 0.40601109]\n",
      " [0.27534377 0.25251448 0.45429955 0.26124835 0.27534377]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8c9f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAECCAYAAAA7JjqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMCYmAIz9H+0kmGEijKQsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc88ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user B\n",
      "[[0.31864514 0.31864514 0.31864514]\n",
      " [0.40601109 0.40601109 0.40601109]\n",
      " [0.27534377 0.27534377 0.27534377]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c398048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b7caef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing on data for user C\n",
      "[[0.2724072  0.2724072  0.31864514 0.2724072 ]\n",
      " [0.27329326 0.27329326 0.40601109 0.27329326]\n",
      " [0.45429955 0.45429955 0.27534377 0.45429955]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b71c908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUgAAAECCAYAAACc1045AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkACD/wIhIW6LnyzKYgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c399438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# test on extra testsets\n",
    "for user_data in testset_data:\n",
    "    print (\"Testing on data for user \" + user_data)\n",
    "    # Calculate predictions for all models\n",
    "    predictions = [predict_hidden_markov_model(models[user_model], testset_data[user_data], use_states=False) \n",
    "                   for user_model in models]\n",
    "    \n",
    "    # Now we have a matrix of the form (users, test_activities)\n",
    "    results = np.array(predictions)\n",
    "    \n",
    "    # Normalize\n",
    "    results /= results.sum(axis=0, keepdims=True)\n",
    "    \n",
    "    # Show normalized results\n",
    "    print (results)\n",
    "    plot_results(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "osue_markov_exercise_tofix.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}