lab6/Lab_6_HMM_answers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 6: Hidden Markov Model\n",
    "\n",
    "\n",
    "In this lab we will look into Hidden Markov Models (HMM) to model sequential data. HMMs use Markov Chains to compute probabilities for a sequence of observed events. Moreover, HMMs are based on the Markov assumption, which states that the present state $z_n$ is sufficient to predict the future $z_{n+1}$, so the past $z_{0:n-1}$ can be discarded.\n",
    "\n",
    "<img src=\"hmm.png\" width=\"400\">\n",
    "\n",
    "Often, we are in a situation where the states we are interested in are hidden, we cannot observe them directly. As we will see in Exercise 2, the part-of-speech (POS) tags in a text are hidden and we can only observe the words. From these words we have to infer the tags. Similarly in Exercises 3 where a robot needs to be localised, we cannot observe the robot's position but rather the measurements of its sensors. Both the tags and the robot position are called hidden variables because they are not observed.\n",
    "An HMM is specified by the following components:\n",
    "\n",
    "* A set of $N$ states.\n",
    "\n",
    "* A transition probability matrix $A$ where each element $a_{ij}$ represents the probability of moving from state $i$ to state $j$, s.t.  $ \\sum^{N}_{j=1} a_{ij} = 1$ $ \\forall i$\n",
    "\n",
    "* An emission probability distribution, the probabilities of observations $x_n$ being generated from a state $z_n$\n",
    "\n",
    "* An initial probability distribution over states. $\\pi_n$ is the probability that the Markov chain will start in state $n$. Also, $\\sum^{N}_{n=1} \\pi_n = 1 $\n",
    "\n",
    "\n",
    "### Additional packages (if using your own machine)\n",
    "\n",
    "For this lab we need `hmmlearn`, `nltk`, `ipywidgets`, so **if you are using your own machine** which you can install with conda:\n",
    "\n",
    "```python\n",
    "conda install -c conda-forge hmmlearn\n",
    "conda install -c anaconda nltk\n",
    "conda install -c conda-forge ipywidgets\n",
    "```\n",
    "\n",
    "Let's import the libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from hmmlearn import hmm\n",
    "from IPython import display\n",
    "\n",
    "import nltk\n",
    "from nltk.corpus import brown\n",
    "from nltk.probability import ConditionalFreqDist,ConditionalProbDist,MLEProbDist\n",
    "import itertools\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "# interactive display\n",
    "import ipywidgets as widgets\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1) HMM with 2 states\n",
    "We will start with a warm up exercise where you have to implement an HMM with 2 states and then analyse how the transition probability and emission noise influence the output. Your task is to create a function `hmm_model` that has three arguments:\n",
    "1. `switch_prob`: The probability of switching to the other state.\n",
    "2. `noise_level`: The variance of the emission distribution, i.e. the measurement/observation noise.\n",
    "3. `startprob`: The probabilities of starting in each state (`shape=(2,1)`).\n",
    "\n",
    "Your function should create a [hmm.GaussianHMM](https://hmmlearn.readthedocs.io/en/latest/api.html#hmmlearn.hmm.GaussianHMM) model with two states (hidden states) and `covariance_type=\"full\"`. Modify the following model attributes:\n",
    "* `startprob_`: Using the `startprob` argument.\n",
    "* `transmat_`: Implement a transition matrix with probability of transition for both states being $p_{transition} = $ `switch_prob`.\n",
    "* `means_`: Add mean $\\mu_1 = 1$ and $\\mu_2 = -1$ for each state\n",
    "* `covars_`: Using the the `noise_level` argument. (note: the shape should be `(2, 1, 1)`, i.e. two $1\\times1$ covariance matrices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_hmm(model, states, observations):\n",
    "    \"\"\"Plots HMM states and observations for 1d states and observations.\n",
    "\n",
    "    Args:\n",
    "    model (hmmlearn model):               hmmlearn model used to get state means.\n",
    "    states (numpy array of floats):       Samples of the states.\n",
    "    observations (numpy array of floats): Samples of the states.\n",
    "    \"\"\"\n",
    "\n",
    "    nsteps = states.size\n",
    "    fig, ax1 = plt.subplots(figsize=(8,4))\n",
    "    states_forplot = list(map(lambda s: model.means_[s], states))\n",
    "    ax1.step(np.arange(nstep), states_forplot, \"--\", where=\"mid\", alpha=1.0, c=\"green\")\n",
    "    ax1.set_xlabel(\"Time\")\n",
    "    ax1.set_ylabel(\"Latent State\", c=\"green\")\n",
    "    ax1.set_yticks([-1, 1])\n",
    "    ax1.set_yticklabels([\"State 1\", \"State 0\"])\n",
    "\n",
    "    ax2 = ax1.twinx()\n",
    "    ax2.plot(np.arange(nstep), observations.flatten(), c=\"blue\")\n",
    "    ax2.set_ylabel(\"Observations\", c=\"blue\")\n",
    "    ax1.set_ylim(ax2.get_ylim())\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "##CORRECT ANSWER##\n",
    "def hmm_model(switch_prob, noise_level, startprob):\n",
    "    \"\"\"Create an HMM with binary state variable and 1D Gaussian observations\n",
    "    \"\"\"\n",
    "    \n",
    "    n_components = 2\n",
    "    model = hmm.GaussianHMM(n_components=n_components, covariance_type=\"full\")\n",
    "    model.startprob_ = startprob\n",
    "    # should be shape (2, 2), i.e., a transition matrix for 2 states\n",
    "    model.transmat_ = np.array([[1. - switch_prob, switch_prob],\n",
    "                                [switch_prob, 1. - switch_prob]])\n",
    "    model.means_ = np.array([[1.0], [-1.0]])\n",
    "\n",
    "    # should be shape (2, 1, 1), i.e., 2 1x1 covariance matrices\n",
    "    model.covars_ = np.ones((2, 1, 1)) * noise_level\n",
    "    \n",
    "    return model\n",
    "##CORRECT ANSWER##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, execute the cell below to run your `hmm_model` and visualise the output with the provided `plot_hmm` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 371,
       "width": 791
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(101)\n",
    "nstep = 50\n",
    "model = hmm_model(switch_prob=0.1, noise_level=1e-8, startprob=np.array([1.0, 0.0]))\n",
    "observations, states = model.sample(nstep)\n",
    "plot_hmm(model, states, observations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the cell below and experiment with the interactive widget window. Try changing the value of `switch_prob` and `noise_level`, how does that changes the output?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b4dd9e1c6a1c4735a2843078d4298941",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='switch_prob', max=1.0, step=0.01), FloatSlider(value…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title\n",
    "\n",
    "#@markdown Make sure you execute this cell to enable the widget!\n",
    "np.random.seed(101)\n",
    "nstep = 50\n",
    "\n",
    "@widgets.interact\n",
    "def plot(switch_prob=(0., 1, .01), log10_noise_level=(-8., 1., .01)):\n",
    "    model = hmm_model(switch_prob=switch_prob,\n",
    "                    noise_level=10.**log10_noise_level,\n",
    "                    startprob=[1.0, 0.0])\n",
    "\n",
    "    observations, states = model.sample(nstep)\n",
    "    observations = observations.flatten()\n",
    "    plot_hmm(model, states, observations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) HMM Part-of-Speech Tagging\n",
    "\n",
    "Part-of-speech (POS) tagging enables the extraction of meaningful information about words in a sentence and their relation to neighbouring words. Knowing whether a word is a noun or a verb provides us information about their most likely neighboring words (such as nouns are preceded by determiners and adjectives, verbs by nouns) and syntactic structure (nouns are generally part of noun phrases), making POS tagging a key aspect of parsing. Parts of speech are useful features for labeling named entities like people or organisations in information extraction, or for coreference resolution. A word’s part of speech can even play a role in speech recognition or synthesis, e.g., the word content is pronounced CONtent when it is a noun and conTENT when it is an adjective.\n",
    "\n",
    "Part-of-speech tagging is the process of assigning a POS tag to each word token in a given text. The input to a tagging algorithm is a sequence of tokenised words and the output is a sequence of tags, one per token. Particularly, words are ambiguous as they have more than one possible POS and the goal is to find the correct tag for each situation.\n",
    "For example, \"book\" can be a verb (\"book that flight\") or a noun (\"hand me that book\"). The goal of POS-tagging is to resolve these ambiguities, choosing the proper tag for the context.\n",
    "\n",
    "\n",
    "In this section we introduce the use of the Hidden Markov Model for part-of-speech tagging. The HMM can be used as a sequence tagger to assign a tag or class label to each unit in an observed sequence, thus mapping a sequence of observations to a sequence of labels. A HMM is a probabilistic sequence model: given a sequence of units (words, letters, morphemes, sentences), it computes a probability distribution over possible sequences of labels and chooses the best label sequence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1) Brown corpus dataset\n",
    "The Brown corpus is a common dataset in Natural Language Processing (NLP), it is available from the NLTK library and it supports POS tagged information. Run the cell below to download the dataset and the universal tagset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[nltk_data] Downloading package brown to /home/uw20605/nltk_data...\n",
      "[nltk_data]   Package brown is already up-to-date!\n",
      "[nltk_data] Downloading package universal_tagset to\n",
      "[nltk_data]     /home/uw20605/nltk_data...\n",
      "[nltk_data]   Package universal_tagset is already up-to-date!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Brown dataset\n",
    "nltk.download('brown')\n",
    "nltk.download('universal_tagset')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we need to get the dataset and split it into training and testing.\n",
    "Run the following cells to achieve that and to prepare the dataset in the correct format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "nltk_data = list(brown.tagged_sents(tagset='universal'))\n",
    "train_set,test_set = train_test_split(nltk_data,\n",
    "                                      train_size=0.80,\n",
    "                                      test_size=0.20,\n",
    "                                      random_state=101\n",
    "                                      )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of tagged words in the training set: 927092\n",
      "Number of tagged words in the test set: 234100\n"
     ]
    }
   ],
   "source": [
    "# create list of train and test tagged words\n",
    "train_tagged_words = [ tup for sent in train_set for tup in sent ]\n",
    "test_tagged_words = [ tup for sent in test_set for tup in sent ]\n",
    "print(f'Number of tagged words in the training set: {len(train_tagged_words)}')\n",
    "print(f'Number of tagged words in the test set: {len(test_tagged_words)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's explore the different types of tags by running the next cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of possible tags: 12\n",
      "Possible tags: {'X', 'ADP', 'DET', 'ADV', 'NOUN', 'NUM', 'PRON', 'PRT', 'CONJ', 'ADJ', '.', 'VERB'}\n"
     ]
    }
   ],
   "source": [
    "tags = {tag for word, tag in train_tagged_words}\n",
    "print(f'Number of possible tags: {len(tags)}')\n",
    "print(f'Possible tags: {tags}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell, explores the structure of the dataset in terms of words and sentences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Words example: [('A', 'DET'), ('Newfoundland', 'NOUN'), ('sat', 'VERB'), ('solemnly', 'ADV'), ('beside', 'ADP')]\n",
      "Sentence example: [('A', 'DET'), ('Newfoundland', 'NOUN'), ('sat', 'VERB'), ('solemnly', 'ADV'), ('beside', 'ADP'), ('a', 'DET'), ('doghouse', 'NOUN'), ('half', 'PRT'), ('his', 'DET'), ('size', 'NOUN'), ('.', '.')]\n"
     ]
    }
   ],
   "source": [
    "print('Words example: {}'.format(train_tagged_words[0:5]))\n",
    "print('Sentence example: {}'.format(train_set[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2) POS tagging model\n",
    "\n",
    "Two of the main components of HMMs are the transition model and the emission model. You already got a taste of how the two models operate in the exercise 1. Your task now is two implement both models for POS tagging model.\n",
    "\n",
    "Specifically, the transition model $P(tag_{t+1}|tag_t)$ will estimate the probability of the next tag given the current tag while the emission model $P(word|tag_t)$ will estimate the probability of observing a word given the current tag.\n",
    "\n",
    "Note: the provided hints link to the `ntlk.probability` functions, however you are free to use any other libraries such as `numpy`.\n",
    "\n",
    "#### 2.2.1) Emission Model\n",
    "Given the tagged words, the main steps are:\n",
    "1. Create a list of tuples ($tag, word$) from the input `words` which will be utilised in step 2. (careful: `words` contains tuples of ($word, tag$))\n",
    "2. Calculate the frequency for each word given the corresponding tag. (hint: [ConditionalFreqDist](https://www.nltk.org/api/nltk.html?highlight=conditionalfreqdist#nltk.probability.ConditionalFreqDist)) \n",
    "3. Calculate the conditional probability distribution given the frequency distribution of step 2. (hint: [ConditionalProbDist](https://www.nltk.org/api/nltk.html?highlight=conditionalprobdist#nltk.probability.ConditionalProbDist) with `probdist_factory`=`MLEProbDist`)\n",
    "\n",
    "Implement these steps in the cell below in a function `emission_model` that has one argument, `words`, containing a list of `(word, tag)` pairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write your code here\n",
    "\n",
    "##CORRECT ANSWER##\n",
    "def emission_model(words):\n",
    "    # calculate frequency of each word given tag\n",
    "    # calculate conditional prob given the tag\n",
    "    \n",
    "    data = [(tag, word) for (word, tag) in words]\n",
    "    emission_F = ConditionalFreqDist(data)\n",
    "    emission_P = ConditionalProbDist(emission_F, probdist_factory=MLEProbDist)\n",
    "    \n",
    "    return emission_P\n",
    "##CORRECT ANSWER##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2.2) Transition Model\n",
    "Given the tagged sentences, the main steps are:\n",
    "1. Create chain of tuples ($tag_{t}, tag_{t+1}$) to be passed to `ConditionalFreqDist()`. To achieve this efficiently:\n",
    "    * Create a generator expression (similar to list comprehension but replacing `[]` with `()` which iterates over each sentence and for each sentence creates a pair of ($tag_{t}, tag_{t+1}$) (if you are curious about generator expressions, you can read [this](https://wiki.python.org/moin/Generators) and [this](https://realpython.com/introduction-to-python-generators/))\n",
    "    * Create a chain from the ouput of the generator (hint: [itertools.chain.from_iterable()](https://docs.python.org/3.4/library/itertools.html#itertools.chain.from_iterable))\n",
    "2. Calculate the frequency of the next tag given the previous tag. (hint: [ConditionalFreqDist](https://www.nltk.org/api/nltk.html))\n",
    "3. Calculate the conditional probability distribution of the next tag given the previous tag. (hint: [ConditionalProbDist](https://www.nltk.org/api/nltk.html))\n",
    "\n",
    "Implement these steps in the cell below in a function `transition_model` that has one argument, `sentences`, containing the dataset of sentences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write your code here\n",
    "\n",
    "##CORRECT ANSWER##\n",
    "def transition_model(sentences):\n",
    "    # iterate over each sentence\n",
    "    # calculate the frequency of the next tag given the previous tag \n",
    "    # calculate the conditional probability distribution of the next tag given the previous tag\n",
    "    \n",
    "    tagGenerators=(((s[i][1],s[i+1][1]) for i in range(len(s)-1)) for s in sentences)\n",
    "    data = itertools.chain.from_iterable(tagGenerators)\n",
    "    \n",
    "    transition_F = ConditionalFreqDist(data)\n",
    "    transition_P = ConditionalProbDist(transition_F, MLEProbDist)\n",
    "    \n",
    "    return transition_P\n",
    "##CORRECT ANSWER##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilising the previously created models, the cell below trains the emission and transition models, the former using tagged words and the later on tagged sentences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "emission_p = emission_model(train_tagged_words)\n",
    "transition_p = transition_model(train_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the Brown corpus, the trained HMM gives the following probabilities:\n",
    "* The probability of observing the world `city` given the tag `NOUN`.\n",
    "* The probability of the tag `VERB` given the tag `NOUN`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p(city|NOUN) =  0.0009174311926605505\n",
      "p(VERB|NOUN) =  0.15875670429120206\n"
     ]
    }
   ],
   "source": [
    "p_city_NOUN = emission_p['NOUN'].prob('city')\n",
    "p_VERB_NOUN = transition_p['NOUN'].prob('VERB')\n",
    "print('p(city|NOUN) = ', p_city_NOUN)\n",
    "print('p(VERB|NOUN) = ', p_VERB_NOUN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3) Viterbi algorithm\n",
    "\n",
    "The goal of the Viterbi algorithm is to find the most likely sequence of hidden states for a given sequence of observations. Specifically, we will utilise the Viterbi algorithm to find the tags of a sequence of untagged sentences, known as $decoding$. \n",
    "The benefit of this algorithm comes from its ability to efficiently determine the most probable path amongst the exponentially many possibilities. Doing so, it can reduce the complexity from $O(N^T)$ to $O(NT)$ where $N$ is the total number of words and $T$ is the total number of tags.\n",
    "\n",
    "Your task is to implement Viterbi algorithm and perform HMM decoding.\n",
    "Complete the missing `to-do` lines.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def viterbi(observed_seq, states, start_p, transition_p, emit_p):\n",
    "    eps = 0.00000001\n",
    "    \n",
    "    # Initialise the list, V, that will contain a dictionary for each element in the sequence. Each dictionary \n",
    "    # has the possible states (tags) as keys and its values are a dictionary with the keys:\n",
    "    # 'prob': the probability of the sequence until this point\n",
    "    # 'prev': the previous state used for backtracking.\n",
    "    V = [dict()] \n",
    "    for state in states:\n",
    "        # Compute the probability of each possible state for the first token in the sequence.\n",
    "        V[0][state] = {\"prob\": start_p[state] * emit_p[state].prob(observed_seq[0]), \"prev\": None}\n",
    "\n",
    "    # Run Viterbi for t > 0\n",
    "    for t in range(1, len(observed_seq)):\n",
    "        V.append({})\n",
    "        for state in states:\n",
    "            # In the forward pass, for each element of the observed_seq we want to store the maximum \n",
    "            # probability for the each state as well as the previous state. This probability is the product of\n",
    "            # the maximum transition probability and the emission probability.\n",
    "            \n",
    "            # First we calculate the max_transition_prob by going through all the combinations between states.\n",
    "            # The next line just initialises the max_transition_prob:\n",
    "            max_transition_prob = -1\n",
    "\n",
    "            for prev_state in states:\n",
    "                # Next, we calculate each possible transition probability that results in tag_t = state.\n",
    "                # The transition probability is given by the product between\n",
    "                # the prob of the sequence until t-1 where tag_{t-1} = prev_state,\n",
    "                # and the transition probability from prev_state to state.\n",
    "                transition_prob = V[t - 1][prev_state][\"prob\"] * transition_p[prev_state].prob(state) #to-do\n",
    "                \n",
    "                #update the maximum transition_prob accordingly\n",
    "                if transition_prob > max_transition_prob:\n",
    "                    max_transition_prob = transition_prob\n",
    "                    prev_state_selected = prev_state\n",
    "                    \n",
    "            # Calculate the max_prob given by the product of the maximum transition probability and the \n",
    "            # emission probability . Remember to add eps to each probability before multiplying them together\n",
    "            max_prob = (max_transition_prob + eps) * (emit_p[state].prob(observed_seq[t]) + eps) #to-do\n",
    "            \n",
    "            V[t][state] = {\"prob\": max_prob, \"prev\": prev_state_selected}\n",
    "\n",
    "    most_likely_seq = []\n",
    "    max_prob = 0.0\n",
    "    previous = None\n",
    "    # Get most probable final state before backtracking\n",
    "    for state, data in V[-1].items():\n",
    "        if data[\"prob\"] > max_prob:\n",
    "            max_prob = data[\"prob\"]\n",
    "            best_state = state\n",
    "    most_likely_seq.append(best_state)\n",
    "    previous = best_state\n",
    "\n",
    "    # Backtrack until the first observation\n",
    "    for t in range(len(V) - 2, -1, -1):\n",
    "        # add the most likely tag to the most_likely_seq. Remember: we are backtracking hence we need to \n",
    "        # add before the last tag (hint: most_likely_seq.insert() )\n",
    "        most_likely_seq.insert(0, V[t + 1][previous][\"prev\"]) # to-do\n",
    "        \n",
    "        previous = V[t + 1][previous][\"prev\"]\n",
    "\n",
    "    # print ('The steps of states are ' + ' '.join(most_likely_seq) + ' with highest probability of %s' % max_prob)\n",
    "\n",
    "    return list(zip(observed_seq, most_likely_seq))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the cell below to get `n=10` random sentences as test data (untagged words)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random, time\n",
    "# Let's test our Viterbi algorithm on a few sample sentences of test dataset\n",
    "random.seed(1234)      #define a random seed to get same sentences when run multiple times\n",
    "\n",
    "n = 10\n",
    "# n = 11468 # whole test set\n",
    "# choose random n numbers\n",
    "rndom = [random.randint(1,len(test_set)) for x in range(n)]\n",
    "\n",
    "# list of 10 sentences on which we test the model\n",
    "test_run = [test_set[i] for i in rndom]\n",
    " \n",
    "# list of tagged words\n",
    "test_run_base = [tup for sent in test_run for tup in sent]\n",
    " \n",
    "# list of untagged words\n",
    "test_tagged_words = [tup[0] for sent in test_run for tup in sent]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the cell below to check your implementation of the Viterbi algorithm on the test set and its POS tagging accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken in seconds:  0.027213335037231445\n",
      "Viterbi Algorithm Accuracy:  97.05882352941177\n"
     ]
    }
   ],
   "source": [
    "possible_tags = list(set([pair[1] for pair in train_tagged_words]))\n",
    "start_pr = {}\n",
    "for tag in possible_tags:\n",
    "    start_pr[tag] = 1.0/len(possible_tags)\n",
    "    \n",
    "start = time.time()\n",
    "predicted_tags = viterbi(test_tagged_words, possible_tags, start_pr, transition_p, emission_p)\n",
    "end = time.time()\n",
    "difference = end-start\n",
    "\n",
    "print(\"Time taken in seconds: \", difference)\n",
    "\n",
    "# accuracy \n",
    "predicted_correct = [i for i, j in zip(predicted_tags, test_run_base) if i == j]  \n",
    "\n",
    "accuracy = len(predicted_correct)/len(predicted_tags)\n",
    "print('Viterbi Algorithm Accuracy: ', accuracy*100)\n",
    "\n",
    "# accuracy ~= 97 for only 10 sentences (136 words)\n",
    "# accuracy ~= 94.239 in 45 secs for all test data (234100 words)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's print the print the first 10 words and their predicted tags."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('I', 'PRON'),\n",
       " ('forced', 'VERB'),\n",
       " ('confidence', 'NOUN'),\n",
       " ('into', 'ADP'),\n",
       " ('myself', 'PRON'),\n",
       " ('.', '.'),\n",
       " ('Falling', 'VERB'),\n",
       " ('somewhere', 'ADV'),\n",
       " ('in', 'ADP'),\n",
       " ('a', 'DET')]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predicted_tags[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as well as the mispredicted tags:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('undeniably', 'VERB') ('undeniably', 'ADV')\n",
      "('there', 'PRT') ('there', 'ADV')\n",
      "('that', 'PRON') ('that', 'DET')\n",
      "('wetly', 'NOUN') ('wetly', 'ADV')\n"
     ]
    }
   ],
   "source": [
    "for i, j in zip(predicted_tags, test_run_base):\n",
    "    if i != j:\n",
    "        print(i,j)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How well does the model predict? Can you make any observations regarding the wrongly-predicted tags?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3) Robot localisation -- Optional\n",
    "\n",
    "Another application of HMM application is robot localisation, which is the focus of this exercise. \n",
    "\n",
    "We have a robot which is deployed to Mars to collect some samples. However, during the landing phase, the connection got temporarily lost and we are not sure where exactly the robot is. Luckily, the map of the area is available and the robot is provided with a sensor that can detect rocky surface.\n",
    "\n",
    "The aim is to use an HMM to localise the robot where the hidden variable $z$ is the position of the robot and the observation $x$ is given by the sensor measurement. \n",
    "The figure at the top of the lab sheet, taken from Bishop, shows the relation between hidden variables $z$ with the observable variables $x$.  \n",
    "\n",
    "We will achieve this through the discrete case of the Bayes Filter which consists of mainly two steps:\n",
    "prediction step and measurement step. Your task will be to implement these two steps which is given by the following pseudocode.\n",
    "\n",
    "First step:\n",
    "$$ \\overline{p}_{k,t} = \\sum_i p(z_k | u_t, z_i) p_{i, t-1} $$\n",
    "where:\n",
    "* $\\overline{p}_{k,t}$: the predicted belief of the new state $z_k$ at the current time $t$ based on the action (control $u_t$). \n",
    "* $p_{i, t-1}$: the belief of state $z_i$ at the previous time step $t_1$\n",
    "* $p(z_k | u_t, z_i)$ : the transition probability of moving from state $z_i$ to state $z_k$ when taking action $u_t$.\n",
    "\n",
    "In the second step, the knowledge from the measurement model $p(x_t | z_k)$ is combined with the predicted belief $\\overline{p}_{k,t}$ to obtain the posterior belief $p_{i, t-1}$ of each state. This posterior belief becomes the current belief for the next time step.\n",
    "\n",
    "$$ p_{i, t} = \\eta p(x_t | z_k) \\overline{p}_{k,t}  $$\n",
    "$p(x_t | z_k)$ is also known as the likelihood, i.e. how likely it is to see an observation given the robot is in location $z_k$. We need to get the likelihood before implementing the belief. Moreover $\\eta$ is the normalising term such that the probability adds to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We provide the implementation of both World and Robot class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class World():\n",
    "    def __init__(self,start=(0,0),N=15):\n",
    "        self.world = np.zeros((N,N))\n",
    "        self.world[0,:] = 1\n",
    "        self.world[-1,:] = 1\n",
    "        self.world[:,0] = 1\n",
    "        self.world[:,-1] = 1\n",
    "        self.world[5, 6:12] = 1\n",
    "        self.world[6:11, 9] = 1\n",
    "        self.world[7:10, 6] = 1\n",
    "        self.world[11, 4:10] = 1\n",
    "        self.N = N\n",
    "    \n",
    "    def get_world(self):\n",
    "        return self.world\n",
    "    def set_world(self,N):\n",
    "        self.world = np.zeros((N,N))\n",
    "    def show_world(self):\n",
    "        fig, ax = plt.subplots(figsize=(5,5))\n",
    "        ax.grid(which='major', axis='both', linestyle='-', color='k', linewidth=1)\n",
    "        ax.set_xticks(np.arange(-.5, self.N, 1));\n",
    "        ax.set_yticks(np.arange(-.5, self.N, 1));\n",
    "#         ax.axis('off')\n",
    "        im = ax.imshow(self.world)\n",
    "        plt.colorbar(im)\n",
    "        plt.show()\n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The robot has 4 possible actions: up, down, left and right. Each action will transition the robot in the new state with probability `p_move`. At each state the robot can measure whether the surface is rocky or normal by calling `measurement()` with the sensor's noise value of `p_sense`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Robot:\n",
    "    def __init__(self, p_move, p_sense, world):\n",
    "        self.location = np.random.randint(0,world.shape[0],2)\n",
    "        self.p_move = p_move\n",
    "        self.p_sense = p_sense\n",
    "        self.world =  world\n",
    "        self.N = self.world.shape[0]\n",
    "        self.possibleActions = ['U', 'D', 'L', 'R']\n",
    "        self.tracking_error = []\n",
    "        self.homing_error = []\n",
    "\n",
    "    # The robot transition are noisy with prob_move to follow the action and (1-p_move) of staying\n",
    "    # in the same location\n",
    "    def transition(self,action):\n",
    "        if (np.random.rand() < self.p_move):\n",
    "            if(action == 'U' ):\n",
    "                self.location =  (max(0,self.location[0]-1), self.location[1])\n",
    "            elif(action == 'R'):\n",
    "                self.location = (self.location[0], min(self.N-1,self.location[1]+1))\n",
    "            elif(action == 'D'):\n",
    "                self.location = (min(self.N-1,self.location[0]+1), self.location[1])\n",
    "            elif(action == 'L'):\n",
    "                self.location = (self.location[0], max(0,self.location[1]-1))\n",
    "            \n",
    "        return self.location\n",
    "\n",
    "    # Measurement model which returns 1 when the surface is rocky and 0 otherwise.\n",
    "    # As in transition model, the sensor can be noisy with p_sense of returning the correct value.\n",
    "    def measurement(self):\n",
    "        if (np.random.rand() < self.p_sense):\n",
    "            return self.world[int(self.location[0]),int(self.location[1])]\n",
    "        else:\n",
    "            if self.world[int(self.location[0]),int(self.location[1])] == 0:\n",
    "                return 1\n",
    "            else:\n",
    "                return 0\n",
    "\n",
    "    # transition model of the robot assuming no noise\n",
    "    def transition_no_noise(self,location,action):\n",
    "        if(action == 'U' ):\n",
    "            location =  (max(0,location[0]-1), location[1])\n",
    "        elif(action == 'R'):\n",
    "            location = (location[0], min(self.N-1,location[1]+1))\n",
    "        elif(action == 'D'):\n",
    "            location = (min(self.N-1,location[0]+1), location[1])\n",
    "        elif(action == 'L'):\n",
    "            location = (location[0], max(0,location[1]-1))\n",
    "            \n",
    "        return location\n",
    "\n",
    "    def visualise_true_position(self):\n",
    "        x = self.world.copy()\n",
    "        x[int(self.location[0]),int(self.location[1])] = 0.5\n",
    "#         x[int(self.home[0]),int(self.home[1])] = 0.7\n",
    "\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The map is discrete and represented through grids where each grid indicates a position. \n",
    "As displayed below, the yellow corresponds to the rocky surface while the purple corresponds to the normal surface. The sensor measurement will output a value of 1 for the rocky surface and a value of 0 for the normal surface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 418,
       "width": 443
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "world = World(15)\n",
    "world.show_world()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following two cells to initialise the robot class and show the starting position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_move = .9  # original value 0.9\n",
    "p_sense = .8 # original value 0.8\n",
    "N = 15\n",
    "# Initialise belief in position - uniform distribution over world\n",
    "state_belief = np.ones((N,N))/(N*N)\n",
    "\n",
    "robot = Robot(p_move,p_sense,world.get_world())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 416
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(robot.visualise_true_position());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell provides helper functions to visualise the true robot position, the predicted belief, the likelihood and the posterior belief."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# helper function to visualise \n",
    "def show(robot, predicted_state_belief, likelihood, state_belief):\n",
    "    plt.clf()\n",
    "    plt.subplot(2,4,1)\n",
    "    plt.cla()\n",
    "    plt.imshow(robot.visualise_true_position())\n",
    "    plt.title('True position in world')\n",
    "    \n",
    "    plt.subplot(2,4,2)\n",
    "    plt.cla()\n",
    "    plt.imshow(predicted_state_belief)\n",
    "    plt.title('Predicted belief given action')\n",
    "    \n",
    "    plt.subplot(2,4,3)\n",
    "    plt.cla()\n",
    "    plt.imshow(likelihood)\n",
    "    plt.title('Likelihood')\n",
    "    \n",
    "    plt.subplot(2,4,4)\n",
    "    plt.cla()\n",
    "    plt.imshow(state_belief)\n",
    "    plt.title('Posterior belief given measurement')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell contains the main algorithm and your task is to fill the missing lines `to-do` (hint: check the provided pseudocode above)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x900 with 4 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 317,
       "width": 1232
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5ywr73H777VM//vhjRt+nMt98802qffv2Gf3t11lnndQLL7yQUb8rV65MXXbZZalmzZpV2m+9evVSn3zySfLe9HW/sp/S+6CqbFNymb/eeuutqcaNG5fbZ/v27TNeJwHypao5flkqGoMqVnrfV56pU6emNt9886TtDjvsUOY42sqVK1N/+MMfUk2aNKlwe96gQYPUxRdfnFq1alW5n1n62CTb+Evne6tWrUpdcsklFealG2+8ceqLL74oN7Zi1TnGVqw694mplHEXqGuqcwwolare7dh3332X6tevX8bHDy+++GLy3vTteSY/ZW2jqnMflO25u6qMPd15552p1q1bVxhr/fr1U8OGDUutWLGi3H5K7+eWLl2a+tWvflVmf2effXaFMZWn9Pd64oknShzjl/5p3LhxRmNWqVT1jidmsh+rynHq2sZWlfU623wvlUqlVq1alTr77LNTRUVF5fbfs2fP1IQJEzLKryrLIffZZ5/k9WuuuSajGEePHp28p3379qlly5aV2a4614f09qlUfscGSueoCxYsSB122GHlfnZRUVHqH//4R/L+yZMnp3r06FFu+xYtWqRef/31jGJ5+OGHM8otDzjggNTcuXPL7WfZsmUVnrtP/2nevHnqX//6V6Wx3XbbbammTZtm1Ocuu+xSZh9V2e6mUpkdY9SUcySl1+ErrriiwnMGQ4cOTfZtCxYsSB144IEVrnPXX399pcsrlUqlPvjgg9S2225b6Xfq0aNHiTHF0qrzuCy9r0x+1mYMvSwNAmqBzz//PIYNGxbz5s2Lli1bxm677RadOnWKOXPmxGuvvZaXGB555JE49thjk6v4mzRpEn379o2NNtoo6tevH5MnT46xY8fGihUrYty4cdGvX78YP358dOjQodpi+Prrr+Pcc8+NOXPmRPPmzWPQoEHRoUOH+O6772LkyJGxcOHCWLVqVfz5z3+OFStWxNVXX11uX6+99lrsu+++sWjRouR3vXv3jl69esWyZcti3Lhx8cUXX0TE6llBdt1113jjjTdi3XXXXaOvt99+Ow4//PCkerdp06bJsmncuHH89NNP8cUXX8RHH31U4vOqYvPNN48zzjgj5s+fH/fee29ERLRs2TKGDh2aVX9lWbRoUQwaNCjeeuut5HedOnWK/v37R4sWLeLzzz+PN954I1auXBkzZsyIgw46KB544IE4/PDDK+17wYIFsc8++8THH38czZo1i/79+0eXLl1i/vz5MXLkyPjhhx8iIuKuu+6KHj16xG9/+9tq+16ZymeMDRo0iF122SWef/75WL58eYwePTr22muvNdqVrrrOtG15V/Y+9NBDceyxx8bKlSsjIqJ+/fqx6667xmabbRYLFiyI119/PZk15/77748pU6bEK6+8Ek2aNKn0O11zzTVx2WWXRcTqq1V69+4dzZo1i6+++ioaNmxY6ftLmz17duyxxx4xadKk5HfdunWL3r17R8OGDeP999+P999/P+64445o0aJFlfsHyjZnzpzkcevWrcttN2vWrNhnn33im2++iSZNmkT//v2ja9euMX/+/Bg3blyJthMmTIg99tgjZsyYERGrr87Zdttto1evXtGsWbOYPn16vPbaazF//vz49ttvY6+99opnn302Bg4cWOZnF3L7MGrUqDjooINi/vz5ye823HDD6N27d7Rr1y4WLlwYkyZNig8++CCWL18eS5YsSdqt7b584cKFMXjw4Bg9enTyu4033jh23HHHaNu2bcyZMyfGjBkT06dPj8WLF8dZZ50VP/30U1x88cXl9nnsscfGI488kjxv3759DBw4MNq0aRNffvllvPbaazFu3Lg49NBDY7PNNst4OVXV3/72txg+fHhErN6H9OnTJxo3bhyffPJJkpfMmDEj9ttvv3jllVeid+/e5fZVE3LWXMbWu3fvOOOMMyJi9VVqEydOjIiIPfbYY43ZwzbYYIOs4lyyZEkMHjw4xo8fn/yuS5cuseuuu0azZs1i0qRJMWbMmHjiiSdKXKWbrcaNG8fhhx8ed9xxR0RE3HfffbHjjjtW+r777rsveXzccceV2SaX68Npp50Wd999d9SrVy/69OkTPXv2jFWrVsW4ceOS7dO7774bQ4cOjWeeeabS/iqzcOHCZJa3tm3bRq9evaJr167RokWLWLZsWUyZMiXGjRsXS5YsiZkzZ8Z+++0Xr776auy8887l9rly5co44ogj4rHHHkt+16hRo+jXr19stNFG0aBBg/juu+/i3XffjRkzZsSqVati2bJlSdsTTjghZs2aVem6GBEV/t9WJJf569133x2nn356RET06NEjdtxxx2jatGlMnDgxRo8eHalUKmbNmhUHHnhgTJgwIdq0aZPVdwCoyyZOnBh77713TJ06NSIiBg4cGI8//ni0bNmyRLuVK1fGkCFD4r///W/yu44dO0afPn1ivfXWiwULFsSbb74ZX3zxRaxYsSKuvPLK+PHHH+P222/P6/e57LLL4vLLL4+IiG233Ta22mqr5Bjj3XffjYiIKVOmxCGHHBLvvPNOueMduRhjq+59onEXoKIxoOrcjq1cuTL233//Enev2XLLLWPLLbeMNm3axJIlS+K7776LDz74IBk7SrfBBhskx8G33HJL8vvi35XWqlWrNT4/V/ugXJy7u/baa+OCCy5Injdu3Dh233332HDDDWPOnDkxcuTImD17dqxcuTJuvPHG+Prrr5OZxStzzjnnxG233RYREVtttVVss8020bBhw5g8eXK13Prx7bffjt///vexbNmyaNeuXQwYMCDatWsX33zzTYwaNSqWLVsWS5cujbPOOivq1asXv/71r8vtq7rHE6tTdcSWvl5PnDgxXn755YiI6NmzZ+yxxx4lPi/b4+mIiLPPPjtuuumm5HmrVq1i0KBBse6668a3334bI0eOjIkTJ8Z+++0XBx98cNafU+y4446L5557LiJWj9ucf/75lb4nfXxnyJAhZeZXuVwfCj02cMopp8R///vfaNSoUfTv3z823njjmDdvXrz88ssxe/bsSKVScdppp0WPHj2ie/fuMXDgwJg+fXq0adMmdt9991hvvfVi+vTp8fLLL8fSpUtjwYIF8T//8z8xadKkaNu2bbmfe8MNN8R5552XzIzVsmXL6NevX3Tp0iVWrlwZn376aYwfPz5SqVQ89dRTsfvuu8eYMWOiWbNma/S1cuXKZMa7Fi1aRK9evWKTTTaJVq1axfLly2PatGkxbty4+Omnn2LhwoVx/PHHR8OGDWPIkCFlxjZixIj41a9+lTxv1apV9OvXLzp37hwNGjSIefPmxeTJk+Pjjz8uMU6Vb4U8R5Lu1ltvjd///vcREbHDDjvEVlttFalUKl5//fVkhtN77703evToEb/73e/isMMOi+effz4aNWoUu+66a2yyySbx008/xcsvvxyzZs2KVCoV5557buy0006x6667lvu5r732Whx44IHx008/RcTqc9877rhj9OjRIxo2bBhfffVVvPHGG7FkyZKYNGlS7LzzzjF27NjYfPPNK/1Oa3Nc1qpVq2T7eu+99ybncoYOHbrGcWpE9mPo5arWcjbIUFVnQGvQoEEqIlJnnHFGav78+SXaLVu2rMRsTJFWsZmJTKp/P/744xJXxA8bNiw1a9asNdp98cUXqV133TVpt++++2YUQ0XSl0OjRo1SEauv4itdaT137tzUUUcdVeL7v/LKK2X2OXv27BKV2JtuummZlev//ve/S1RXH3jggWX2d/DBBydtDjvssNTs2bPLbLdkyZLU008/nTrttNPKfD2Tq0+rMntUVd9z+umnJ+3q16+fuv7669eY6Wvy5Mklroxs1apV6ssvvyyzv/T1vPjKgRNOOGGNdWfhwoWpo48+OmnbokWL1IIFCzL6bhWp6gxo+Y7xz3/+c9JfebP2Fc/Gtu6661batn///kmbN954Y43XP//882TWtYhI7bjjjqnJkyeXaLNy5crUddddV6Ki/Kyzzir3O6T/vzVo0CDVunXr1GOPPbZGuyVLliSPM10f0/9+TZo0Sf373/9eo82LL76YWmeddVIRq6/SK27vSlz4P1W9+nXrrbdO2u+0004lXkvfZhbnJocffvgas/usXLkyuVJt4cKFJWZD2HPPPVOTJk1a43PnzZtX4grMjh07lntVVS62D5nkQ998803SZ/z/V9g899xzZbadPXt26rbbbkudf/75a7yWzb48lUqlhg4dWiJ3Sb8auNiKFStSf//735N9Wv369VNjxowps7/SM7Kde+65JbbXqdTqfUfxfr84D6tov1oV6Z/dqFGjVJMmTcq8+m3cuHElrlLt0aNHavHixWX2Wd05a3XOgJaLfLq6Z6UrdtFFF5XICW+66aY1rv7++OOPk//t9CtEs5kBLZVKpUaNGpW8vv7661d4BXcqlUq9++67JfLRstaJ6l7m6VeoFn/nnXbaKTVhwoQS7VatWpW68cYbS6zjmc7eV5GvvvoqddZZZ6XefPPNcmfjnTdvXur8889PPrdbt24Vztz729/+tkScZ555ZpnLKJVKpd58883U0KFDUx9//PEar2WzLmbynlznr40bN06tu+66qWeffXaNdq+++mqqVatWSdvLLrsso+8FkA81ZQa0N998s8TsnIceeuga+WSxP/zhD0m79dZbL/XQQw+VuY965JFHSsz48tBDD5XZXy5mQGvUqFGqqKgotemmm6befPPNNdo+/PDDJY4t7rnnnjL7TKWqf4wtF/tE4y5Q91TnGFB1bscee+yxEuM948aNKzemjz/+OPXb3/62zO1wKlX181+pVPXvg7I9d5fJ2NOYMWNKzGCzzz77pGbMmFGizZIlS1IXXHBBiWVx3XXXldlf+n6uuN8uXbqUObNOefvwyqR/r+Kxo7LGmKZPn54aNGhQieOx0sfTxXIxnlhdM6DlIrZM8rJsPP/88yXWk5NPPnmN9XTWrFmpQw45ZI3xnWxnQFu4cGGJnKWsMYR0y5YtKzHeWtY4Zi6WeSHHBtJz1OL/md122y319ddfl2g3d+7c1MCBA5O2AwcOTM5Hn3XWWWuco5wwYUKqU6dOSftLL7203BheeumlJGds2LBh6k9/+lOZ5zzfe++91BZbbJH0efrpp5fZ39KlS1MnnXRSauTIkeXOYLdkyZLU1VdfnWw327Rps8b6WGybbbZJPvPMM88sd2bf+fPnpx5++OHUb3/72zJfz/UMaIU8R5K+Djdq1Ci1wQYbpEaPHl2izYoVK0qME7Zp0yZ16aWXpiIiNWDAgErXuQEDBpS7rGbMmJHq0KFD0vboo48u884S3333XerQQw9N2m211VZljvvm6risELM4K0CjIKpagBaxerrzTFQ1Ac9k45ueFP7pT3+qsL8FCxaU2IhWdDCRidLLYb/99iv3JMrKlStTgwcPLvegqdgll1xSYmNbegOb7tFHHy3x+WWdPCoebGvcuHG5O8tMFLIA7fPPPy8xQPW3v/2t3P5mz56d2mijjZK2J510UpntSt8i6uijjy63z8WLF5eYpvrBBx/M6LtVpKoFaPmOcdy4cUlf/fr1W+P1hQsXJjvQk08+OdWzZ89y2y5atCg5OGjWrFmZCV564cImm2xSYvrv0q6//vqkbb169codAE1fdkVFRRmdXM1kfZw4cWKJvssaBC02evToNaZgNRAK/6cqg49PPfVUif+l3/3udyVeL73N3HvvvSu9JfHll1+etN9nn31Sy5cvr7B9+rbqqquuWuP1XG0fMsmHjj322BLbr++++67C71KebPblr732WvKezp07rzH4WNo///nPEsu9tBUrVqQ6d+6cUZ45c+bMNaZQr+4CtMr2q5MmTSpRSHTLLbeU2a66c9bqLEDLRT6diwK0WbNmlRhwLG8QO5Vafcum0rfVyLYAbdWqVakNN9wwafP8889XGOd5552XtD355JPLbFPdy7z07TG6detWYe5/+OGHJ21/9atfVfj51S19sKq8W+FMmjSpxDbyz3/+c9afl6sCtFznr40bN0598MEH5fZ58803J2179uyZ0fcCyIeaUID2wgsvlDi5eOqpp5ZbQD5lypTkpHfLli3LPdlc7OWXX0763Xzzzcu8DVouCtAiVt9eafr06eXGln4Cp6w8O5XKzRhbde8TjbtA3VRdY0DVvR1LP35Lv41cNtJjzkQu9kHZnrvLZOxpt912S9r07ds3tXTp0nL7+81vfpO0bdWqVeqnn35ao03p/VyzZs3KLHpYG+nfq7Lj30WLFpUofDziiCPKbFfd44mpVPUVoOUitlwVoO24445JvwcddFC5t5ZdtmxZMhlCZduQTGI97rjjkjblTahQ7Mknn0zabrrppmW2ycUyL+TYQOnxpc033zy1aNGiMtt+8803SZFT8c8pp5xSbt/3339/pbGuXLky1a1bt4zywFRqdaHReuutl4pYXaw2derUzL9sGa666qrks//+97+v8fr8+fOT17t06VLhLZErk+sCtIjCnCNJpUquw02bNk19+umnZbZbuXJliTHPiEj16tWr3Au809e5oqKi1Lfffltmu5NPPjnj/eCKFStKFLaVdR4gF8dlqZQCNH5GqlqA1qRJk3Jn1Sqtqgl4ZRvf999/P3m9e/fulc5GkEqlUg888EDynoqutMtE+nIoKipKff755xW2nzRpUol7mb///vslXl+1alWJ+1lXdFKt2L777pu0P+qoo9Z4vbhIqG3btlX7cqUUsgAtffaDrbfeutId+kMPPVQiOSurAjt9PW/UqFGlJ8svvPDCpP15552X0XerSFUL0PId4/Lly1MtW7ZMRayuki99AjP96pR77703ueqsrLYvvfRS0navvfZa47PmzJlT4mTyf//73wpjW7lyZYl7lpcuQimWvr058sgjM/remayP6Vdw9e3bt9I+jz/++BKxGAiF/5Pp4OOIESNKFJI0atQo9c0335RoU/rgqryDmmLLli1LDk7r1auX+uqrryqNd/r06cl+fKuttlrj9VxtHyrLh6ZNm1biYL+sK+Iylc2+vPhKxIgoc5aw0latWpUULhcVFa1xBdbTTz+d9NesWbNK88w777yzxHKs7gK03XbbrdL2v//975P222677Rqv5yJnra4CtFzl07koQLvpppuSPjfZZJNKY73iiitK/C2zLUBLpVKp3/3ud0mboUOHlvuZK1euLHFFZ1mzHudimZceIKwsn3rmmWeStjvssEOln1+d3nzzzeSzzz333DLbpBep9e3bd60G9HJRgJaP/LWyY9WffvqpxKDbvHnzMvpuALlW6AK0Bx98sMTsuOXNOFBs2LBhSds//vGPGcWXfoHpO++8s8bruSpAq2yc8NNPP03atm/fvsw21T3Glot9onEXqJuqawyourdjv/jFL5LXR4wYsVbfMX1blIlc7IOyPXdX2dhT+j6mvM9Ot2DBghIzR912221rtCm9n7vwwgszirUq0r9Xy5YtKz1uevHFF5P2DRs2XGPMKhfjialU9RSg5Sq2XBSgffTRR0mfmZxbHT16dIl1ZW0K0J577rmkTdeuXSvchgwZMiRpe8kll6zxeq6WeSHHBkqPLz3++OMVtk8vTG3cuHHqhx9+KLft4sWLk7yxqKiozMLUESNGJP3tscceGcWcfkenTM6rV+T7779P+vqf//mfNV6fPn168npZY8BVkY8CtEKcI0mlSq7D55xzToX9pU/MExGpJ554osL26evck08+ucbrP/zwQ7KetW7dOqPJecaOHZv0WdYd53JxXJZKFaYAbe1vaA15sPfee1d4n+ZceuaZZ5LHRxxxRNSvX7/S9wwaNCh5/MYbb1RbLLvssktsuummFbbp3r179OvXL3k+cuTIEq9PmDAhvvvuu4iIqFevXpxwwgmVfu6pp56aPB41atQar2+44YYRETFnzpy4//77K+2vJnrllVeSxyeddFIUFRVV2P7QQw+Ndu3aRUTE0qVLY+zYsRW233XXXWP99devsM12222XPP7qq68qibj65TvGBg0axC677BIREStWrFjjfyV9XRs4cGAMGDAgo7bF7dKNGTMmli5dGhER7du3j4MOOqjC2OrVqxcnn3xy8rz0/1FZjjrqqErbZCr9844//vhK2w8dOrTaPhvqsmeeeSbOPPPMEj/HHXdc9OjRIw455JCYO3du0vaGG26ILl26lNvX1ltvHZtvvnmFn/f222/HDz/8EBER/fr1i65du1YaY6dOnaJnz54REfHxxx+XiCmicNuHl156KVasWBEREd26dYt99tmnWvrNxIoVK+LFF1+MiNX7jsMOO6zS9xQVFcXAgQMjIiKVSsWYMWNKvJ6+HPfff/9K88wjjzwyGjduXNXQM5bJ3yk9Z/vggw9izpw5JV6vSTlraTU5ttLSc4ojjzyy0liPPfbYavvs9P/pxx57LBYvXlxmu5EjR8a3334bERGdO3eO3XfffY02uV7mTZo0iQMOOKDCNrnMbZcvXx5vvPFG3HLLLfGHP/whhg0bVmLbfssttyRt33///TL7eO6555LHZ555ZqX5f77lI3894ogjKny9ZcuWyfFnKpWKb775ptI+Aeq6v//973HMMcfEsmXLoqioKK699tq46qqrKnxP+n4507GDQuVCle0bevbsGU2bNo2IiFmzZsWCBQvWaFPdY2y52Ccad4G6b23GgKp7O1Z8/iQi4n//93+T8ZV8yPU+qDrP3aVvm7fZZpvYfvvtK2zfvHnzOProo8t8f3mqcwy/LAcffHC0atWqwjZ77LFHdO7cOSL+79g2XS7GE6tLTY6ttPTxnT59+lR6bnXnnXeOjTbaqFo+e88990zOtX399dcxevToMtvNnz8/nnjiieT5cccdt0abfCzzQo4NNG3aNPbdd98K22y55ZbJ49122y3WXXfdcts2adKkRKxljUfleru4atWqGD9+fPzjH/+I4cOHxznnnFNiX3T55Zcnbcsas1p33XWTfPujjz6K1157LaMYC6FQ50hKq+x8Qfo6VNV1bsqUKWu8/tJLLyXHJwcccEC0aNGiwv4iVm+HmjVrFhGZHd9Vx3FZoTQodACQiR122KFgn51+sDB27Ng488wzK31PKpVKHk+dOrXaYunbt29G7fr165ecaH3vvfdKvJb+vGfPntG+fftK+ysuEoqI+O677+Lbb7+NTp06Jb8bMmRIXHnllRGxOkF68MEHY8iQITFo0KDo2LFjRjEXUiqVKrGTT/++5WnYsGH07t07OXH17rvvVngyfquttqq0z/S/xbx58yptX90KEeOAAQOSZThy5MgSy7D4AGGzzTaLzp07lygsK902/eCyrAK09PW+T58+0aBB5bu/9PXgvffei1QqVeFgQ3Vtp1KpVHz44YfJ8z59+lT6nt69e0dRUVGJbQ+wpvHjx8f48eMrbNOyZcv461//GieddFKF7TL5n0/PIWbOnJlRDhERyQFVKpWK6dOnR5s2bZLnhdo+jBs3Lnlc1nY2lz788MNYuHBhRKweRLjgggsyel/637p0Ppa+389kObZo0SK23HLLeOeddzL67KrKJMfr1q1btG/fPmbNmpXkLsVFdhE1K2ctrSbHVlr6utG7d+9K23ft2jXWXXfd+PHHH9f6s7fYYovYdttt4/3334/58+fH448/XuZA2L///e/k8THHHBP16q15XVmul3mPHj2iUaNGFbbJRW67ePHiuPLKK+O2226LmTNnZvSestp9//33JQYh0/+Xaop85K+14RgFoCa57LLL4tJLL42I1RdG3HHHHZVe2Dlr1qyYPHly8vyGG27IqOj5008/TR7nKxdq3bp1hRfhRKy+0KNt27ZJofy8efNKnHDJxRhbde8TjbvAz0O2Y0C52I4dfvjhMXz48Fi1alU8++yzscUWW8RJJ50U++67b2y99dZlHtNVh3zsg6rz3F369j6T5V7c7qabboqI1cu9Ig0bNszoGGhtZDK+U1RUFH369Ilp06ZFxOrvfcghhySvV/d4YnWqybGVVtXxnYiInXbaqVouoKtfv34cddRRceONN0bE6nGcXXfddY12jz76aJJT9e7dO7p167ZGm3ws80KODXTv3j0aNmxYYZv0Itctttii0j7T2//0009rvJ6+TJ9++ulyL1xMl/6dy9surlixIm666aa4/vrrk//vypQ1ZtWwYcM49NBD4/7774+VK1fGnnvuGYcffngcfvjhsfvuu2d0Xj9fCnGOpCy9evWqsK/0daJ79+6VHk9UZR2aPHlyxt+peB88Z86cWLhwYTRv3rzMdtVxXFZICtCoFSqqZs614tkFIlZf+ZJ+9UsmSs9OsTbSr5SpSPpGqfTJsPTnmVQZR0R06NAhmjRpEkuWLImI1TuI9AK03//+9/Hqq6/G6NGjI5VKxZNPPhlPPvlkRERsvPHG0b9//9hzzz0zuvqjEObNmxfLly9Pnme6XNKvhqjsBFjr1q0r7S89yUqPJ18KEWN6EUP6FSkLFy6Mt99+u0Sb9dZbL7bYYov49NNPS7RdtGhRMpjQvHnz2Gmnndb4nGzW+/S/77Jly2L+/PkVrr/VtZ2aN29eLFu2LHmeyf99q1atonXr1nm7egjqkhYtWkT79u1j6623jj333DOGDh2a0SBIJv/z6TnEpEmTYtKkSVWOLz2PKOT24fvvv08eb7LJJmvVV1WlL8cFCxaUmNkoU6XzsfT9QlXyq1wVoFUlhlmzZkXEmjleTcpZS6vJsZWWntMVX5FcmQ022KBaCtAiVl/MUTzwdd99961RgLZkyZJ49NFHS7QvS66XeVXzxuq4wn/OnDkxaNCgjAYG082fP3+N36Vv0xo3blzi2KamyEf+WhuOUQBqitGjR8err74aEau3jf/5z38qnYkrImLGjBklnv/973+v8mfnKxfKZL8QUfG+IRdjbNW9TzTuAj9fmYwB5WI71rNnz7juuuvi3HPPjVQqFZ999llcfPHFcfHFF0erVq2iX79+MWDAgDj00EOjR48eWX+/0vKxD6rOc3dru72v7BxN27ZtMypiXhvVcQ6vuscTq1NNjq20bMd3qstxxx2XFKA98sgjcdNNN61RaHXfffeVaF+WfCzzQo4NZPLZ6f+3VW1fVqzpy3TEiBGV9ldaWctz6dKlcdBBB8ULL7xQpb7KGrOKWF0w/O6778bEiRNj+fLl8cADD8QDDzwQRUVF0bNnz+jfv3/svffesf/++0eTJk2q/B2qSyHOkZSlsvUil+tQJgXvZZkzZ06FBWiZqKljdm7BSa1QPIVgIaxtJffKlSurKZJIpmasTPoGq/TOK30KxvI2bFXts1mzZjFy5Mi44YYb1pjGdsqUKXHvvffG0KFDo2PHjnHBBReUezuhQik9LWWmy6WiZVJaTbulT1kKEeOOO+4YLVu2jIiId955J6kkHz16dLKzTJ+RorgYrXTb4oHDXXbZpcyrJbJZ70u3q+xvXF3bqdLrYzb/90DZhg8fHqlUqsTP/Pnz46uvvoonnngifvOb32R8BV4m//PVcTVYetFGIbcP6dvAfF9JU93LMaLksqwJ29nqyPFqUs5aWk2OrbRCrxvpM5o9//zzScFhsSeeeCLJgbbeeutyr1LN9TIvRN54xhlnJMVnjRs3jtNOOy2eeOKJ+Oyzz2L+/PmxYsWKZNuePj3+qlWr1uirkNu0TOUjf60NxygANUXpwf3PPvsso/flIpfNlerYL+RijK2694nGXeDnIdsxoFydKxg2bFi89tprMXjw4BIznv3000/x/PPPx0UXXRQ9e/aMPfbYIz766KMMv2XF8rEPqs5zd2u7vc/X+H1FasL4TkTucoeaHFtphR7f2WGHHZJbE86ePTueffbZEq9/9913ycWCDRo0iCFDhpTZTz6WeSHHBqr62dUR69ou07KW52WXXZYUn9WrVy+OOeaYeOSRR2LChAnJxQ/p+6Ni5c2uu95668X48ePj0ksvLXHRZCqVigkTJsTtt98ehx9+eHTq1CmuuuqqvI6dpivEOZKyVGW9qAnrUETF36m2j9cpQONnr6wTEunSE44RI0ascdCSyU91WbRoUUbtim9TFRFJcU+x9BMs6e3Wps+I1QNxw4YNi88//zw++uijuOWWW+Koo44qccXAokWL4tprr42BAwfWqCK00iedMl0ulS0TKle/fv1k6uGVK1fG66+/HhHl31KzuBgtvW36bGjl3RYum/W+dLt8/Y1Lr4/Z/N8DNUN6DjFs2LCscoj07Vohtw/p28DSg7G5lr4ct91226yWY/GtkoqlL8uasJ2tjhyvJuWspdXk2CqKtRDrRseOHWPQoEERsfrk9sMPP1zi9Uyujo2oXcs8E9OnT48HH3wwIlbnjy+88ELcdtttceCBB8Zmm20WLVq0iPr16yftKzvxUMhtWqZqU/4K8HPQu3fvuPLKK5Pn559/flx//fWVvi99n9ymTZus9sl33313Lr5STuRijK2694nGXYCK5PJcwa677hrPPfdcfP/99/Gf//wnzj777Nh+++1LFKS98sor0adPnxg9enQW0ZdU2/ZBa7u9rwnHP9U9vlMd44nVqSbHVlGshdrXH3vsscnj9PGciIgHHnggKRrae++9Y7311iuzj9q0zGuL9GX6/vvvV3l5lr5N69KlS5NbAUdE3HvvvXHffffF4YcfHj179oxWrVqVuJilsjGrYi1atIjhw4fH1KlTY/z48XHdddfFIYccEuuss07SZs6cOXHRRRfFYYcdVi1jeZXVTGSjLq7D6d/pxhtvzOo7pc/gWdcoQKPOSZ8WMZNK+sqqVDt06JA8zvTqxlz55ptvqtwufUcUUXI6zEz7++GHH5Lbb5bVZ2lbbrll/PrXv44HHnggpk2bFu+9916ccsopyetvvvlmVrfPypXWrVuX2Plnuly+/vrr5HFly4TypScOxYVnxUVlPXr0KFHdP2DAgKTyu7htecVq6bJZ79P/vo0aNcrbAWzr1q2jUaNGyfNM4v3pp5+qpeIeqF7VnUMUcvuQ/l3SZxbKh/TP/vLLL6vlQDib/cLUqVPX+nPLk00MpXOPmpSzllaTYystfblOmzYto/dMnz69WmNILyz797//nTyePXt2PPfccxHxf1dTlqc2LfNMvPLKK8lA2n777Re77bZbhe3T87iypC+fpUuXrnFrmpqgNuWvAD8XF110UYkitPPOOy9uuOGGCt+Tvs+ZO3dutd22u6bKxRhbde8TjbsAFcnHuYJ11lknDjvssLjxxhvjnXfeie+//z7+9re/Je9bvHhxnHbaaVlEX1Jt2wet7fa+JpyjqY5zeDX5eL4mx1ZaTRnfKT6f9eSTTyYz2keUHO+p6ALD2rTMa4vqXqZvvfVWcnHjVlttVaLwsCyVjVmVVq9evdhxxx3j3HPPjcceeyy+//77eOONN+KQQw5J2jz++OPx3//+d433pu/PqqNmIht1cR2ui9+pOilAo85JH1Aofcua0pYtWxaTJ0+usE2fPn2Sx88///zaBbeWxo4dm1G7cePGJY+33377Eq9tt912yeOJEyfG7NmzK+0v/Wqb9ddfv0RBUCa23XbbuOOOO+KXv/xl8rsnnniiSn0Uy8W0k0VFRbHtttsmz8eMGVPpe1asWBFvvfVW8rz0ciZz6UVjo0aNioULF8bbb7+9xmsRqw8aevXqVWbb5s2bx0477VTmZ6Sv92+99VZG09Gmr/fbbbdd3qY8LSoqiq233jp5nv7/XJ633nqrxs1UApTMIV599dVYunTpWvVXyO1D3759k8fphb/ZqOr2dNttt43GjRtHxOoTP5nmQ5X1WSyT5bhgwYL4+OOP1/pzy5PJd/rss8+S3LaoqKjEvi2iZuWspdXk2EpLXzfSc73yfP3119U+iH/YYYclt4cYM2ZMUvT58MMPJ7cdHzBgQImZhkurTcs8E99++23yuDgXrMhrr71W4esdOnQocaVh8W0vspWLPLE25a8APyeli9DOPffcuPHGG8tt37Fjx9hwww2T58W35qmrcjHGVt37ROMuQEUKca5gnXXWibPOOqvEOZNPPvkkvvzyyyr1U1pt2welb+8zWe4RJbf3NeEcTSbjO6lUKt58883keem4q3s8sTrV5NhKq+r4TkTE+PHjqzWGrl27xi677BIRqwtLH3300YhYfW723XffjYjVs1wdfPDB5fZRm5Z5bVHdY2bVPWZVmXr16sUuu+wSjz76aAwePDj5fVnn3atSMxER1XYL6HR1cR2uTeOuhRgbVIBGnbPxxhsnj99///0K2z7xxBMlZvYqywEHHJA8fvnll3Oy8c3UmDFj4osvvqiwzeTJk0skucW3LCy2+eabx/rrrx8Rq29jmF5lX5677rqr3P6qIn1Zfv/991n10aRJk+Tx8uXLs46ltOJbHUVE3HPPPZUOKj3xxBPJzrpJkybRr1+/aovl52aHHXaIVq1aRUTEe++9F0899VRSiV/W+lZclFbctng92GWXXUrMgJhu5513TooXfvzxx3j66acrjCmVSsU999yTPE9fP/Ih/Xtn8j+aHitQc+yyyy7Rpk2biFhdwPSPf/xjrfss1PZhr732Sraxn3322VodWFV1X960adMS2+HKZpnIRPpyfOaZZyotyH/ooYdyenD8r3/9q9I26be92GabbaJt27YlXq9JOWtpNTm20tKL3x9++OFKT3CWvoVCdWjRokUcdNBByfP7778/IjK/Ojaidi3zTKTfkqayW2csWrQo7r333kr73HfffZPHt9xyy1qdVM7FMUpty18Bfk4uuuiiuOKKK5Ln55xzToVFaPvvv3/yuPgWLXVZdY+x5WKfaNwFqEihzhX069cv2rVrlzwv6xxKVY89atM+KH25v/fee/HBBx9U2H7x4sXx4IMPlvn+QnniiScqnUHopZdeSmbaatiwYVKgVCwX44nVpSbHVlr6+M6bb75ZaUHnmDFj1ri1YnVIH78pHkNKzz3+53/+J7kIsSy1aZnXFuljZvfff3/88MMPa9VfVcasVq1aFbfffvtafV6xoqKiEtv4svYZVamZ+Pbbb+ONN96oltjS1cV1ePDgwcm5ks8//zyeeuqpAkdUvlzVVVREARp1Tu/evZPHFd2f/qefforf/e53GfVXnKikUqk47rjjSkyTWpFly5bFnDlzMmqbiVQqFb/5zW/KvfXUqlWr4je/+U1yELHjjjvGNttsU6JNUVFRiZnILr/88gqnlX366afjySefTJ7/6le/KvH60qVLk6lFK5M+rXD6dMpV0aZNm2Rn/sMPP1TbxvIXv/hF0u+7775bYQIwb968uPDCC5PnRx99dLRu3bpa4vg5ql+/fuy6664RsXod/tOf/pS8VtYtNYsHCUu3rag4sk2bNjFkyJDk+QUXXFDhfdZvueWW5AC3Xr168Ytf/CKzL1NNTj755OTxuHHjKjy5PWbMmOTENFCzNG7cOIYNG5Y8v/jii6tUBFLWQWOhtg+dOnUqsR097bTTsi4mz2Zf/tvf/jZ5/N///rfCHK+07777bo3fDR48OJk9atGiRSX6L23WrFkxfPjwjD8vG6+99lo89NBD5b7+2WeflTipeeqpp67RpiblrLUpttKOOeaY5ATnl19+GX/729/KbTt9+vS45pprchJH6QHKr776KrkCvEmTJnHYYYdV+P7atMwzsckmmySPn3766QpvG3DeeedltH0aNmxYsi0aO3Zs/OUvf8k6vvbt2yePq+uWHbUtfwX4ubn44ovXKEL761//Wmbb8847L+rXrx8REW+//XZcdtllGX9OWblsTVfdY2y52CcadwEqUt3bsZkzZ2b0uXPmzClxrqWscyhVPfaoTfugnj17xm677ZY8P+ussyocM/rDH/6QFI60atUqjjnmmJzHWJn58+dXeN5x8eLFcf755yfPDz744DX+zrkYT6wuNTm20rbaaqvYYYcdImL1uMi5555bbgHmihUr4oILLshJHEceeWRy6+9XXnklvv322xJ5RWUXGNamZV5bHHbYYbHZZptFxOpx4eOOOy7jc80LFiyIhQsXlvhd+pjVq6++WmER6jXXXFNpce38+fOTOyBUprLz7uk1Ew888ECFF1ifc845OSlQqovr8AYbbFDif/dXv/pVxuOBq1atyustsXMxZlkZBWjUOelJ5oMPPhg333zzGm0mTpwYgwYNii+++CI5wVSRm266KVq0aBERER9++GH07t07XnrppXLbf/7553HFFVfExhtvXGIK4LXVqFGjeOaZZ2Lo0KFr7MDmzZsXxx13XIkZSf785z+X2c+wYcOSk66zZs2KPfbYo8zK54ceeqjEAM+BBx5Y4gAgImLGjBnRpUuXOO+888qdxjaVSsVzzz0Xl1xySfK7/fbbr+IvW47GjRtH9+7dI2J1UvjYY49l1U9pm266aZx22mnJ8zPPPDNuueWWNYr9vvjii9h7772TmehatWoVf/jDH6olhp+z9EKz4lucbb755iXuo11s9913T6YMTb8dWlnFaumGDx+e/B9Pnjw5Bg8evMZVL6tWrYqbbrqpRDJ0xhlnlLhKIB969uwZxx9/fPL81FNPLXMw9OWXX46DDz44Vq1aVeJe7kDNcd555yVTb8+fPz923XXX+Mc//lHuQeSsWbPijjvuiB122KHMwpZCbh/+/Oc/JwcsX3/9dfTr16/cmdDmzp0bt99+e4lB2GLZ7Mt33333OOGEE5LnJ598clxwwQXlTh2+dOnSePzxx+PQQw8tMZNUsfr168fll1+ePL/jjjviggsuWOPv8uWXX8bgwYNj+vTpyWBRLjRq1ChOPPHEMmdfeOutt2KvvfZKrqDr1q1bnHLKKWX2U1Ny1toWW7r27dvH2WefnTy/4IILypwd65NPPom99tor5s6dm9HxRFUNHjw4GTiaMGFCnHfeeUkMBx10UDJ7bEVqyzLPxKBBg5Irgr/44os48cQTY+7cuSXa/PTTT/HLX/4ybrvttmjevHmlfXbv3j3OO++85PlFF10UZ511VrkzIo4fPz5OPPHE+OSTT9Z4bauttkoejxgxIuOBwsrUpvwV4Ofo4osvLnFh3LBhw8osQtt0003j//2//5c8v+yyy+LEE0+MadOmldnvypUr46WXXoqhQ4fWiNuJVVUuxtiqe59o3AWoSHVvx4488sjYf//945FHHlmjcKHYN998E0cddVRyLNGtW7ekQCJd+rHHww8/nNF3qU37oKuuuiopmHv99dfjsMMOW2N2omXLlsXvf//7uO6665Lfpe8nCqlRo0Zx2223xfnnn79GoceMGTPiwAMPjA8//DBpW15BYHWPJ1anmhxbaX/84x+Tx48//niceuqpa0yoMXv27DjiiCNizJgxORnfadu2bXI+dNWqVXHWWWfFlClTImL1bXIzmbmvNi3z2qB+/fpx6623JtuaF198MXbbbbcKb8H64YcfxkUXXRQbbrhh8vcrtt122yXn3OfNmxdHHHFEidtyRqweq77kkkvid7/7XaVjVu+880507do1hg8fXuYYVMTqbfV9990XN910U/K7ss67H3jggcltOL/++us49dRTY/HixSXazJ49O4YOHRoPP/xwTv4HIurmOnzllVdGx44dI2J1YddOO+0U//nPf8qdRGj69Onx17/+NXr27FnhhejVrap5Q3Uo+15lUIv1798/9t9//2Q69rPOOituueWW6Nu3bxQVFcWkSZNi3LhxsWrVqjjxxBNjypQp8eqrr1bY55ZbbhkPPPBADBkyJBYtWhSTJk2KvfbaK7p06RI77bRTrLPOOrFs2bL48ccf44MPPig3eV9bF198cfz1r3+N++67Lx5//PEYNGhQdOjQIb7//vt45ZVXSiRO5557buy5555l9tO2bdu4//77Y999902+z/bbbx99+vSJLbbYIpYtWxZvvvlmfPbZZ8l7unXrFnfeeWeZ/c2dOzeuv/76uP7666Ndu3bJzrZx48bxww8/xIcfflhih9y9e/cSJ/aq6rDDDkuuMj3uuOPinnvuic0226zEQNC1115b5X6vvfbaePvtt2P8+PGxYsWKOPPMM+Oqq66KXXfdNVq0aBFffPFFvPbaa8mtmBo0aBB33nmnkzvVoKKZzkpr3759bLXVVsmBWsTqW1XtuOOOFX7GJptsEnfccUcce+yxsXLlyhg7dmz06NEj+vfvH5tuumksXLgwXn/99RL/v3379o2rr746uy+1lm644YYYO3ZsfP7557FkyZI47rjj4rLLLou+fftG/fr144MPPoj33nsvIlYPcj/22GPx9ddfFyRWoHwtWrSIJ554Ivbcc8+YMmVKUiBxwQUXRL9+/WKDDTaIoqKimD17dkyYMCEmTZqUHKSUtx0s1PahS5cu8dBDD8UhhxwSCxYsiClTpsQ+++wTXbt2jd69e0e7du1iwYIFMXny5Hj//fdj+fLlcfDBB5fZVzb78v/93/+NGTNmxAsvvBCpVCquvfba+Nvf/hY77bRTbLrpptG0adOYN29efPHFF/HRRx8lt1kvvtqxtJNPPjmefvrpePTRR5PPu/vuu2PgwIHRunXrJEdcsWJF7LTTTtGtW7eczXxwzTXXxNlnnx3HH398XHrppdGvX79o1KhRfPLJJ/Hmm28m7Zo1axb33ntviamz09WUnLW2xVbapZdeGi+//HK88847sXLlyjjzzDPj6quvjl122SWaNWsWkydPjtGjR8eqVavif/7nf2LWrFnJ8UT6tPtro0GDBjFkyJDkYpri9TSi8qtji9WmZV6Ztm3bxvnnn58Ujt53333x7LPPRp8+fWKDDTaIGTNmxKhRo2LhwoVRv379+Pvf/16iaLU8V155ZUycODGZ8fnmm2+O22+/PXbeeefYaKONokGDBvHdd9/FO++8EzNmzIiIKHFSu9i+++4bzZo1i0WLFsUHH3wQm2++eQwYMCDatGmTXDix9957x957712l713b8leAQrjttttixIgRGbe//PLLy7xAIVu///3vIyKSk/vDhg2LoqKi+M1vflOi3fDhw+Orr75KbuV4zz33xL///e/YbrvtomfPntGiRYv46aef4uuvv44PPvggGeNLv2K9NqnuMbZc7BONuwAVqc7t2KpVq+KZZ56JZ555Jho2bBhbbrlldO/ePVq3bh3z58+Pr7/+OjlnFbG6OKK82bgPO+yweO655yIi4ne/+10899xz0atXrxJFA7///e+jbdu2yfPatA/q169fXHXVVclsVE8++WRsuOGGMXDgwOjSpUvMmTMnRo0aVWJWuUMPPTTOOeecvMdaliuuuCIpjrvrrrti0KBB0bZt2/jmm29i1KhRJYrSrrnmmthiiy3K7CcX44nVpSbHVtq+++4bv/71r+Pvf/97RET885//jP/85z8xaNCgWHfddePbb7+NkSNHxqJFi2LjjTeOgw8+OLkDQXWN70SsHscpzlfTx3eOPvropAiqIrVpmdcWe+65Z9x6661x+umnx8qVK2PcuHHRu3fv6NatW2y33XbRtm3bWLx4cXz33Xfx/vvvV3ibznr16sUf//jHZIbdF198Mbp37x4777xzdO3aNWbNmhWjRo1K7jZw++23x7HHHlthfN99911cfvnlcfnll0eHDh1iu+22i/XXX7/McaqI1bURRx111Br9NGvWLP7whz8kF4n/+9//jhdeeCEGDhwYrVq1iqlTp8Zrr70WixYtii233DIGDx5cori3utTFdbhjx47x+OOPx3777RczZ86MGTNmxBFHHBHrrbde9OnTJzp06BCrVq2KWbNmxccffxxffvllQW6Dfdhhh8Vtt90WERG33nprvPvuu7H99tuXuPXv6aefHptuumn1fWgKCmD48OGpiEhFRGr33Xcvs80JJ5yQtLnrrruq1P+sWbNSO+64Y/L+sn5OPvnk1JIlS1K777578ruRI0dW2O/777+f2mGHHSrsN/1no402Sr333ntVir200sthzJgxqU6dOpX7mfXq1UtdcMEFqVWrVlXa99ixY1ObbLJJpd9jzz33TP3www9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",
      "text/plain": [
       "<Figure size 1500x900 with 4 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 317,
       "width": 1232
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the discrete Bayes filter\n",
    "plt.figure(figsize=(15,9))\n",
    "\n",
    "N = 15\n",
    "steps = 100\n",
    "# Create list of possible states in world (x,y coordinates)\n",
    "possible_states = np.array(np.meshgrid(np.linspace(0,N-1,N),np.linspace(0,N-1,N))).reshape(2,-1).T\n",
    "\n",
    "for step in range(steps):\n",
    "    \n",
    "    # Sample a random action\n",
    "    a = np.random.choice(['U','D','L','R'])\n",
    "    \n",
    "    # Move the robot according to the action and sense the measurement\n",
    "    state = robot.transition(a)\n",
    "    measurement = robot.measurement()\n",
    "    \n",
    "    # Make prediction about state belief given action\n",
    "    predicted_state_belief = np.zeros((N,N))\n",
    "    \n",
    "    for state in possible_states.astype(int):\n",
    "        \n",
    "        new_state = robot.transition_no_noise(state,a)\n",
    "        \n",
    "        predicted_state_belief[state[0],state[1]] += (1-p_move)*state_belief[state[0],state[1]] # to-do\n",
    "        predicted_state_belief[new_state[0],new_state[1]] += p_move*state_belief[state[0],state[1]] # to-do\n",
    "   \n",
    "    # Evaluate sensor belief for each possible state\n",
    "    likelihood = np.zeros((N,N))\n",
    "    for state in possible_states.astype(int):\n",
    "        \n",
    "        match = measurement == world.get_world()[state[0],state[1]]\n",
    "        likelihood[state[0],state[1]] = match*p_sense + (1-match)*(1-p_sense) # to-do\n",
    "    \n",
    "    # Compute posterior belief over possible states\n",
    "    state_belief = likelihood*predicted_state_belief # to-do\n",
    "    \n",
    "    # normalising\n",
    "    state_belief = (state_belief+1e-15)\n",
    "    state_belief = state_belief/np.sum(state_belief) \n",
    "    \n",
    "    # Make a function to display\n",
    "    show(robot, predicted_state_belief, likelihood, state_belief)\n",
    "\n",
    "    display.clear_output(wait=True)\n",
    "    display.display(plt.gcf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Change the `p_move` and `p_sense` values and re-run the experiment with different values. How these probabilities affect the performance?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wrap-up"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations, you have reached the end of this lab. Let's summarise what we have learnt:\n",
    "* Understand the role of the HMM components \n",
    "* Key applications of HMM such as POS tagger\n",
    "* Perform POS tagging through the transition model and the emission model.\n",
    "* Implemented the Viterbi algorithm and the discrete Bayes filter algorithm.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "* COMS30035 Machine Learning\n",
    "* Bishop - Pattern Recognition and Machine Learning: Chapter 13 - Sequential Data\n",
    "* [Probabilistic Robotics](http://www.probabilistic-robotics.org) \n",
    "* University of Edinburgh's Foundations of Natural Language Processing (FNLP) and Decision Making in Robots and Autonomous Agents (DMR) courses\n",
    "* [Hussain Mujtaba](https://www.mygreatlearning.com/blog/pos-tagging/)\n",
    "* [Neuromatch Academy 2020](https://www.neuromatchacademy.org)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The End :)\n",
    "\n",
    "<video controls src=\"gif.mp4\" width=\"200\">"
   ]
  }
 ],
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