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bninopaul/hidden_markov_model.ipynb

Created July 25, 2017 00:17
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hidden_markov_model.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import string\n",
"import codecs\n",
"pd.set_option('display.max_columns', None)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 1"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class hmm(object):\n",
" def __init__(self):\n",
" pass\n",
"\n",
" def _forward(self, obs):\n",
" \"\"\"\n",
" Compute the scaled forward probability matrix and scaling factors.\n",
" Parameters\n",
" ----------\n",
" obs : ndarray of shape (T,)\n",
" The observation sequence\n",
" Returns\n",
" -------\n",
" alpha : ndarray of shape (T,N)\n",
" The scaled forward probability matrix\n",
" c : ndarray of shape (T,)\n",
" The scaling factors c = [c_1,c_2,...,c_T]\n",
" \"\"\"\n",
" M,N = self.B.shape\n",
" T = len(obs)\n",
" c, alpha = np.zeros(T), np.zeros((T,N))\n",
" c[0] = 1/np.dot(self.pi, self.B[obs[0]])\n",
" alpha[0] = c[0]*(self.pi*self.B[obs[0]])\n",
" for t in range(1, T):\n",
" c[t] = 1/np.dot(np.dot(self.A, alpha[t-1]), self.B[obs[t]])\n",
" alpha[t] = c[t]*(np.dot(self.A, alpha[t-1])*self.B[obs[t]])\n",
" return alpha, c\n",
" \n",
" def _backward(self, obs, c):\n",
" \"\"\"\n",
" Compute the scaled backward probability matrix.\n",
" Parameters\n",
" ----------\n",
" obs : ndarray of shape (T,)\n",
" The observation sequence\n",
" c : ndarray of shape (T,)\n",
" The scaling factors from the forward pass\n",
" Returns\n",
" -------\n",
" beta : ndarray of shape (T,N)\n",
" The scaled backward probability matrix\n",
" \"\"\"\n",
" M,N = self.B.shape\n",
" T = len(obs)\n",
" beta = np.zeros((T,N))\n",
" beta[T-1] = c[T-1]\n",
" for t in range(T-2,-1,-1):\n",
" beta[t] = np.dot(c[t]*self.A.T,(self.B[obs[t+1]]*beta[t+1]))\n",
" return beta\n",
" def _delta(self, obs, alpha, beta):\n",
" \"\"\"\n",
" Compute the delta probabilities.\n",
" Parameters\n",
" ----------\n",
" obs : ndarray of shape (T,)\n",
" The observation sequence\n",
" alpha : ndarray of shape (T,N)\n",
" The scaled forward probability matrix from the forward pass\n",
" beta : ndarray of shape (T,N)\n",
" The scaled backward probability matrix from the backward pass\n",
" Returns\n",
" -------\n",
" delta : ndarray of shape (T-1,N,N)\n",
" The delta probability array\n",
" gamma : ndarray of shape (T,N)\n",
" The gamma probability array\n",
" \"\"\"\n",
" M,N = self.B.shape\n",
" T = len(obs)\n",
" delta = np.zeros((T-1, N, N))\n",
" gamma = np.zeros((T, N))\n",
" \n",
" for t in range(T-1): \n",
" for i in range(N):\n",
" for j in range(N):\n",
" delta[t,i,j] = alpha[t,i]*self.A[j,i]*self.B[obs[t+1],j]*beta[t+1,j]\n",
" gamma[t,i] = np.sum(delta[t,i])\n",
" gamma[T-1] = alpha[T-1]*beta[T-1]/np.dot(alpha[T-1], beta[T-1])\n",
" return delta, gamma\n",
" def _estimate(self, obs, delta, gamma):\n",
" \"\"\"\n",
" Estimate better parameter values.\n",
" Parameters\n",
" ----------\n",
" obs : ndarray of shape (T,)\n",
" The observation sequence\n",
" delta : ndarray of shape (T-1,N,N)\n",
" The delta probability array\n",
" gamma : ndarray of shape (T,N)\n",
" The gamma probability array\n",
" \"\"\"\n",
" # update self.A, self.B, self.pi in place\n",
" M,N = self.B.shape\n",
" T = len(obs)\n",
" for i in range(N):\n",
" for j in range(N):\n",
" self.A[i,j] = np.sum(delta[:,j,i])/np.sum(gamma[:-1,j])\n",
" for i in range(M):\n",
" for j in range(N):\n",
" self.B[i,j] = np.sum(gamma[:,j][obs==i])/np.sum(gamma[:,j])\n",
" self.pi = gamma[0,:]\n",
" \n",
" def fit(self, obs, N, A=None, B=None, pi=None, max_iter=100, tol=1e-3):\n",
" \"\"\"\n",
" Fit the model parameters to a given observation sequence.\n",
" Parameters\n",
" ----------\n",
" obs : ndarray of shape (T,)\n",
" Observation sequence on which to train the model.\n",
" A : stochastic ndarray of shape (N,N)\n",
" Initialization of state transition matrix\n",
" B : stochastic ndarray of shape (M,N)\n",
" Initialization of state observation matrix\n",
" pi : stochastic ndarray of shape (N,)\n",
" Initialization of initial state distribution\n",
" max_iter : integer\n",
" The maximum number of iterations to take\n",
" tol : float\n",
" The convergence threshold for change in log-probability\n",
" \"\"\"\n",
" # initialize self.A, self.B, self.pi\n",
" # run the iteration\n",
" M = len(set(obs))\n",
" if A is not None:\n",
" self.A = A/np.sum(A, axis=0) #make sure it is column-stochastic\n",
" N,_ = A.shape\n",
" else:\n",
" self.A = np.random.dirichlet(np.ones(N), size=N).T\n",
" \n",
" if B is not None:\n",
" self.B = B/np.sum(B, axis=0)\n",
" else:\n",
" self.B = np.random.dirichlet(np.ones(M), size=N).T\n",
" \n",
" if pi is not None:\n",
" self.pi = pi/np.sum(pi)\n",
" else:\n",
" self.pi = np.random.dirichlet(np.ones(N))\n",
" \n",
" alpha, c = self._forward(obs)\n",
" log_lkhood0 = - np.sum(np.log(c))\n",
" for i in range(max_iter):\n",
" if i%10==0:\n",
" print(\"Iter: %d, log_lkhood: %f\"%(i, log_lkhood0))\n",
" alpha, c = self._forward(obs)\n",
" beta = self._backward(obs, c)\n",
" delta, gamma = self._delta(obs, alpha, beta)\n",
" \n",
" #update params\n",
" self._estimate(obs, delta, gamma)\n",
" \n",
" alpha, c = self._forward(obs)\n",
" log_lkhood1 = - np.sum(np.log(c))\n",
" if abs(log_lkhood0-log_lkhood1)< tol:\n",
" break\n",
" log_lkhood0=log_lkhood1\n"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#toy data\n",
"A = np.array([[.7, .4],[.3, .6]])\n",
"B = np.array([[.1,.7],[.4, .2],[.5, .1]])\n",
"pi = np.array([.6, .4])\n",
"obs = np.array([0, 1, 0, 2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 2"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-4.6429135909\n"
]
}
],
"source": [
"#test for forward pass\n",
"h = hmm()\n",
"h.A = A\n",
"h.B = B\n",
"h.pi = pi\n",
"alpha, c = h._forward(obs)\n",
"print(-np.log(c).sum()) # the log prob of observation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 3"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 3.1361635 , 2.89939354],\n",
" [ 2.86699344, 4.39229044],\n",
" [ 3.898812 , 2.66760821],\n",
" [ 3.56816483, 3.56816483]])"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#test the backward pass\n",
"beta = h._backward(obs, c)\n",
"beta"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 4"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"delta, gamma = h._delta(obs, alpha, beta)"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[[ 0.14166321, 0.0465066 ],\n",
" [ 0.37776855, 0.43406164]],\n",
"\n",
" [[ 0.17015868, 0.34927307],\n",
" [ 0.05871895, 0.4218493 ]],\n",
"\n",
" [[ 0.21080834, 0.01806929],\n",
" [ 0.59317106, 0.17795132]]])"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"delta"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.18816981, 0.81183019],\n",
" [ 0.51943175, 0.48056825],\n",
" [ 0.22887763, 0.77112237],\n",
" [ 0.8039794 , 0.1960206 ]])"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gamma"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### Problem 5"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 0.55807991 0.49898142]\n",
" [ 0.44192009 0.50101858]]\n",
"[[ 0.23961928 0.70056364]\n",
" [ 0.29844534 0.21268397]\n",
" [ 0.46193538 0.08675238]]\n",
"[ 0.18816981 0.81183019]\n"
]
}
],
"source": [
"h._estimate(obs, delta, gamma)\n",
"print(h.A)\n",
"print(h.B)\n",
"print(h.pi)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 6"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def vec_translate(a, my_dict):\n",
" # translate numpy array from symbols to state numbers or vice versa\n",
" return np.vectorize(my_dict.__getitem__)(a)\n",
"def prep_data(filename):\n",
" # Get the data as a single string\n",
" with codecs.open(filename, encoding='utf-8') as f:\n",
" data=f.read().lower() #and convert to all lower case\n",
" #remove punctuation and newlines\n",
" remove_punct_map = {ord(char): None for char in string.punctuation+\"\\n\\r\"}\n",
" data = data.translate(remove_punct_map)\n",
"\n",
" # make a list of the symbols in the data\n",
" symbols = sorted(list(set(data)))\n",
" \n",
" # convert the data to a NumPy array of symbols\n",
" a = np.array(list(data))\n",
" \n",
" #make a conversion dictionary from symbols to state numbers\n",
" symbols_to_obsstates = {x:i for i,x in enumerate(symbols)}\n",
" \n",
" #convert the symbols in a to state numbers\n",
" obs_sequence = vec_translate(a,symbols_to_obsstates)\n",
" return symbols, obs_sequence"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"symbols, obs = prep_data('declaration.txt')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 7"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 0, log_lkhood: -27984.694651\n",
"Iter: 10, log_lkhood: -22096.451772\n",
"Iter: 20, log_lkhood: -21855.613115\n",
"Iter: 30, log_lkhood: -21652.715537\n",
"Iter: 40, log_lkhood: -21579.418872\n",
"Iter: 50, log_lkhood: -21552.504780\n",
"Iter: 60, log_lkhood: -21536.276039\n",
"Iter: 70, log_lkhood: -21522.869274\n",
"Iter: 80, log_lkhood: -21513.910457\n",
"Iter: 90, log_lkhood: -21510.120438\n",
"Iter: 100, log_lkhood: -21508.393164\n",
"Iter: 110, log_lkhood: -21507.256295\n",
"Iter: 120, log_lkhood: -21506.391586\n",
"Iter: 130, log_lkhood: -21505.756749\n",
"Iter: 140, log_lkhood: -21505.322756\n",
"Iter: 150, log_lkhood: -21505.042934\n",
"Iter: 160, log_lkhood: -21504.869024\n",
"Iter: 170, log_lkhood: -21504.762593\n",
"Iter: 180, log_lkhood: -21504.697269\n",
"Iter: 190, log_lkhood: -21504.656458\n"
]
}
],
"source": [
"hmm_ = hmm()\n",
"hmm_.fit(obs, N=2, max_iter=200)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th></th>\n",
" <th>a</th>\n",
" <th>b</th>\n",
" <th>c</th>\n",
" <th>d</th>\n",
" <th>e</th>\n",
" <th>f</th>\n",
" <th>g</th>\n",
" <th>h</th>\n",
" <th>i</th>\n",
" <th>j</th>\n",
" <th>k</th>\n",
" <th>l</th>\n",
" <th>m</th>\n",
" <th>n</th>\n",
" <th>o</th>\n",
" <th>p</th>\n",
" <th>q</th>\n",
" <th>r</th>\n",
" <th>s</th>\n",
" <th>t</th>\n",
" <th>u</th>\n",
" <th>v</th>\n",
" <th>w</th>\n",
" <th>x</th>\n",
" <th>y</th>\n",
" <th>z</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.301</td>\n",
" <td>0.131</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.235</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td>0.123</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.14</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.057</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.011</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.046</td>\n",
" <td></td>\n",
" <td>0.023</td>\n",
" <td>0.044</td>\n",
" <td>0.06</td>\n",
" <td></td>\n",
" <td>0.043</td>\n",
" <td>0.031</td>\n",
" <td>0.083</td>\n",
" <td></td>\n",
" <td>0.004</td>\n",
" <td>0.003</td>\n",
" <td>0.055</td>\n",
" <td>0.035</td>\n",
" <td>0.116</td>\n",
" <td></td>\n",
" <td>0.033</td>\n",
" <td>0.001</td>\n",
" <td>0.102</td>\n",
" <td>0.115</td>\n",
" <td>0.153</td>\n",
" <td></td>\n",
" <td>0.018</td>\n",
" <td>0.023</td>\n",
" <td>0.002</td>\n",
" <td>0.009</td>\n",
" <td>0.001</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" a b c d e f g h i j \\\n",
"0 0.301 0.131 0.235 0.001 0.123 \n",
"1 0.046 0.023 0.044 0.06 0.043 0.031 0.083 0.004 \n",
"\n",
" k l m n o p q r s t u \\\n",
"0 0.14 0.057 \n",
"1 0.003 0.055 0.035 0.116 0.033 0.001 0.102 0.115 0.153 \n",
"\n",
" v w x y z \n",
"0 0.011 \n",
"1 0.018 0.023 0.002 0.009 0.001 "
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#probability emission matrix for the letters and the space\n",
"B = pd.DataFrame(np.around(hmm_.B, 3), index=symbols).T\n",
"B.replace(B[B==0], \" \")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 8"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 0, log_lkhood: -25103.772576\n",
"Iter: 10, log_lkhood: -21481.699828\n",
"Iter: 20, log_lkhood: -20978.434993\n",
"Iter: 30, log_lkhood: -20951.726801\n",
"Iter: 40, log_lkhood: -20949.497910\n",
"Iter: 50, log_lkhood: -20949.070237\n",
"Iter: 60, log_lkhood: -20948.771320\n",
"Iter: 70, log_lkhood: -20948.301344\n",
"Iter: 80, log_lkhood: -20947.924887\n",
"Iter: 90, log_lkhood: -20947.816960\n",
"Iter: 100, log_lkhood: -20947.796648\n",
"Iter: 110, log_lkhood: -20947.791887\n",
"Iter: 120, log_lkhood: -20947.790252\n",
"Iter: 130, log_lkhood: -20947.789541\n",
"Iter: 140, log_lkhood: -20947.789191\n",
"Iter: 150, log_lkhood: -20947.789006\n",
"Iter: 160, log_lkhood: -20947.788900\n",
"Iter: 170, log_lkhood: -20947.788836\n",
"Iter: 180, log_lkhood: -20947.788795\n",
"Iter: 190, log_lkhood: -20947.788765\n"
]
}
],
"source": [
"# hmm with 3 states\n",
"hmm_3 = hmm()\n",
"hmm_3.fit(obs, N=3, max_iter=200)"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
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" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.359</td>\n",
" <td>0.068</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.213</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.096</td>\n",
" <td>0.113</td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td>0.001</td>\n",
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" <td>0.003</td>\n",
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" <td>0.001</td>\n",
" <td>0.038</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.006</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.008</td>\n",
" <td>0.043</td>\n",
" <td>0.086</td>\n",
" <td>0.043</td>\n",
" <td>0.056</td>\n",
" <td>0.043</td>\n",
" <td>0.012</td>\n",
" <td></td>\n",
" <td>0.005</td>\n",
" <td>0.004</td>\n",
" <td>0.055</td>\n",
" <td>0.039</td>\n",
" <td>0.049</td>\n",
" <td></td>\n",
" <td>0.024</td>\n",
" <td>0.002</td>\n",
" <td>0.106</td>\n",
" <td>0.129</td>\n",
" <td>0.218</td>\n",
" <td></td>\n",
" <td>0.025</td>\n",
" <td>0.028</td>\n",
" <td>0.002</td>\n",
" <td>0.021</td>\n",
" <td>0.001</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.072</td>\n",
" <td>0.156</td>\n",
" <td>0.044</td>\n",
" <td>0.035</td>\n",
" <td></td>\n",
" <td>0.023</td>\n",
" <td>0.01</td>\n",
" <td>0.004</td>\n",
" <td></td>\n",
" <td>0.049</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.038</td>\n",
" <td>0.018</td>\n",
" <td>0.209</td>\n",
" <td>0.111</td>\n",
" <td>0.041</td>\n",
" <td></td>\n",
" <td>0.064</td>\n",
" <td>0.060</td>\n",
" <td></td>\n",
" <td>0.052</td>\n",
" <td></td>\n",
" <td>0.01</td>\n",
" <td>0.003</td>\n",
" <td></td>\n",
" <td></td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" a b c d e f g h i \\\n",
"0 0.359 0.068 0.213 0.096 0.113 \n",
"1 0.008 0.043 0.086 0.043 0.056 0.043 0.012 \n",
"2 0.072 0.156 0.044 0.035 0.023 0.01 0.004 0.049 \n",
"\n",
" j k l m n o p q r s \\\n",
"0 0.001 0.001 0.101 0.003 0.001 \n",
"1 0.005 0.004 0.055 0.039 0.049 0.024 0.002 0.106 0.129 \n",
"2 0.038 0.018 0.209 0.111 0.041 0.064 0.060 \n",
"\n",
" t u v w x y z \n",
"0 0.001 0.038 0.006 \n",
"1 0.218 0.025 0.028 0.002 0.021 0.001 \n",
"2 0.052 0.01 0.003 "
]
},
"execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#probability emission matrix for the letters and the space\n",
"B = pd.DataFrame(np.around(hmm_3.B, 3), index=symbols).T\n",
"B.replace(B[B==0], \" \")"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 0, log_lkhood: -26491.366237\n",
"Iter: 10, log_lkhood: -21084.722971\n",
"Iter: 20, log_lkhood: -20639.194883\n",
"Iter: 30, log_lkhood: -20594.095902\n",
"Iter: 40, log_lkhood: -20584.392092\n",
"Iter: 50, log_lkhood: -20580.165584\n",
"Iter: 60, log_lkhood: -20577.197153\n",
"Iter: 70, log_lkhood: -20573.903547\n",
"Iter: 80, log_lkhood: -20567.329903\n",
"Iter: 90, log_lkhood: -20549.905328\n",
"Iter: 100, log_lkhood: -20539.691760\n",
"Iter: 110, log_lkhood: -20537.063214\n",
"Iter: 120, log_lkhood: -20533.772442\n",
"Iter: 130, log_lkhood: -20526.231557\n",
"Iter: 140, log_lkhood: -20520.965193\n",
"Iter: 150, log_lkhood: -20516.225241\n",
"Iter: 160, log_lkhood: -20510.880567\n",
"Iter: 170, log_lkhood: -20506.710549\n",
"Iter: 180, log_lkhood: -20504.449060\n",
"Iter: 190, log_lkhood: -20503.471245\n"
]
}
],
"source": [
"# hmm with 4 states\n",
"hmm_4 = hmm()\n",
"hmm_4.fit(obs, N=4, max_iter=200)"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th></th>\n",
" <th>a</th>\n",
" <th>b</th>\n",
" <th>c</th>\n",
" <th>d</th>\n",
" <th>e</th>\n",
" <th>f</th>\n",
" <th>g</th>\n",
" <th>h</th>\n",
" <th>i</th>\n",
" <th>j</th>\n",
" <th>k</th>\n",
" <th>l</th>\n",
" <th>m</th>\n",
" <th>n</th>\n",
" <th>o</th>\n",
" <th>p</th>\n",
" <th>q</th>\n",
" <th>r</th>\n",
" <th>s</th>\n",
" <th>t</th>\n",
" <th>u</th>\n",
" <th>v</th>\n",
" <th>w</th>\n",
" <th>x</th>\n",
" <th>y</th>\n",
" <th>z</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td></td>\n",
" <td>0.007</td>\n",
" <td>0.004</td>\n",
" <td></td>\n",
" <td>0.002</td>\n",
" <td>0.663</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td>0.002</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.192</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.029</td>\n",
" <td>0.044</td>\n",
" <td>0.02</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.037</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td></td>\n",
" <td>0.124</td>\n",
" <td>0.044</td>\n",
" <td>0.05</td>\n",
" <td></td>\n",
" <td>0.046</td>\n",
" <td>0.015</td>\n",
" <td>0.017</td>\n",
" <td></td>\n",
" <td>0.056</td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td>0.028</td>\n",
" <td></td>\n",
" <td>0.165</td>\n",
" <td>0.138</td>\n",
" <td>0.037</td>\n",
" <td></td>\n",
" <td>0.021</td>\n",
" <td>0.053</td>\n",
" <td>0.14</td>\n",
" <td>0.043</td>\n",
" <td></td>\n",
" <td>0.023</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.635</td>\n",
" <td>0.107</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.165</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.01</td>\n",
" <td></td>\n",
" <td>0.005</td>\n",
" <td>0.01</td>\n",
" <td></td>\n",
" <td>0.018</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.049</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.031</td>\n",
" <td>0.096</td>\n",
" <td></td>\n",
" <td>0.058</td>\n",
" <td>0.037</td>\n",
" <td>0.134</td>\n",
" <td></td>\n",
" <td>0.006</td>\n",
" <td>0.004</td>\n",
" <td>0.064</td>\n",
" <td>0.047</td>\n",
" <td>0.056</td>\n",
" <td></td>\n",
" <td>0.016</td>\n",
" <td>0.002</td>\n",
" <td>0.133</td>\n",
" <td>0.129</td>\n",
" <td>0.117</td>\n",
" <td></td>\n",
" <td>0.028</td>\n",
" <td>0.019</td>\n",
" <td>0.003</td>\n",
" <td>0.015</td>\n",
" <td>0.002</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" a b c d e f g h i \\\n",
"0 0.007 0.004 0.002 0.663 \n",
"1 0.124 0.044 0.05 0.046 0.015 0.017 0.056 \n",
"2 0.635 0.107 0.001 0.165 \n",
"3 0.031 0.096 0.058 0.037 0.134 \n",
"\n",
" j k l m n o p q r s \\\n",
"0 0.001 0.002 0.192 0.029 \n",
"1 0.001 0.028 0.165 0.138 0.037 0.021 0.053 \n",
"2 0.01 0.005 0.01 0.018 \n",
"3 0.006 0.004 0.064 0.047 0.056 0.016 0.002 0.133 0.129 \n",
"\n",
" t u v w x y z \n",
"0 0.044 0.02 0.037 \n",
"1 0.14 0.043 0.023 \n",
"2 0.049 \n",
"3 0.117 0.028 0.019 0.003 0.015 0.002 "
]
},
"execution_count": 104,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#probability emission matrix for the letters and the space\n",
"B = pd.DataFrame(np.around(hmm_4.B, 3), index=symbols).T\n",
"B.replace(B[B==0], \" \")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Problem 9\n"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"symbols, obs = prep_data('WarAndPeace.txt')"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 0, log_lkhood: -207306.469625\n",
"Iter: 10, log_lkhood: -167057.782077\n",
"Iter: 20, log_lkhood: -159928.818875\n",
"Iter: 30, log_lkhood: -158425.865835\n",
"Iter: 40, log_lkhood: -158388.675449\n",
"Iter: 50, log_lkhood: -158386.868491\n",
"Iter: 60, log_lkhood: -158385.870035\n",
"Iter: 70, log_lkhood: -158385.682049\n",
"Iter: 80, log_lkhood: -158385.635383\n",
"Iter: 90, log_lkhood: -158385.618570\n",
"Iter: 100, log_lkhood: -158385.612079\n",
"Iter: 110, log_lkhood: -158385.609413\n",
"Iter: 120, log_lkhood: -158385.608213\n",
"Iter: 130, log_lkhood: -158385.607596\n",
"Iter: 140, log_lkhood: -158385.607222\n",
"Iter: 150, log_lkhood: -158385.606958\n",
"Iter: 160, log_lkhood: -158385.606750\n",
"Iter: 170, log_lkhood: -158385.606576\n",
"Iter: 180, log_lkhood: -158385.606425\n",
"Iter: 190, log_lkhood: -158385.606292\n"
]
}
],
"source": [
"hmm_2 = hmm()\n",
"hmm_2.fit(obs, N=2, max_iter=200)"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th></th>\n",
" <th>́</th>\n",
" <th>а</th>\n",
" <th>б</th>\n",
" <th>в</th>\n",
" <th>г</th>\n",
" <th>д</th>\n",
" <th>е</th>\n",
" <th>ж</th>\n",
" <th>з</th>\n",
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" <th>ы</th>\n",
" <th>ь</th>\n",
" <th>э</th>\n",
" <th>ю</th>\n",
" <th>я</th>\n",
" <th>ё</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.215</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.025</td>\n",
" <td>0.066</td>\n",
" <td>0.03</td>\n",
" <td>0.039</td>\n",
" <td>0.018</td>\n",
" <td>0.014</td>\n",
" <td>0.025</td>\n",
" <td>0.002</td>\n",
" <td>0.015</td>\n",
" <td>0.050</td>\n",
" <td>0.072</td>\n",
" <td>0.038</td>\n",
" <td>0.097</td>\n",
" <td></td>\n",
" <td>0.035</td>\n",
" <td>0.06</td>\n",
" <td>0.051</td>\n",
" <td>0.078</td>\n",
" <td></td>\n",
" <td>0.002</td>\n",
" <td>0.011</td>\n",
" <td>0.005</td>\n",
" <td>0.017</td>\n",
" <td>0.011</td>\n",
" <td>0.005</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" <td>0.008</td>\n",
" <td>0.013</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.088</td>\n",
" <td></td>\n",
" <td>0.176</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.143</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.131</td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.241</td>\n",
" <td>0.006</td>\n",
" <td></td>\n",
" <td>0.028</td>\n",
" <td></td>\n",
" <td>0.059</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.004</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.038</td>\n",
" <td>0.043</td>\n",
" <td>0.007</td>\n",
" <td>0.002</td>\n",
" <td>0.033</td>\n",
" <td></td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" ́ а б в г д е ж з и \\\n",
"0 0.215 0.025 0.066 0.03 0.039 0.018 0.014 0.025 0.002 \n",
"1 0.088 0.176 0.143 0.131 \n",
"\n",
" й к л м н о п р с т у \\\n",
"0 0.015 0.050 0.072 0.038 0.097 0.035 0.06 0.051 0.078 \n",
"1 0.001 0.241 0.006 0.028 0.059 \n",
"\n",
" ф х ц ч ш щ ъ ы ь э ю \\\n",
"0 0.002 0.011 0.005 0.017 0.011 0.005 0.001 0.008 \n",
"1 0.004 0.038 0.043 0.007 0.002 \n",
"\n",
" я ё \n",
"0 0.013 \n",
"1 0.033 "
]
},
"execution_count": 109,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#probability emission matrix for the letters and the space\n",
"B = pd.DataFrame(np.around(hmm_2.B, 3), index=symbols).T\n",
"B.replace(B[B==0], \" \")"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 0, log_lkhood: -206722.641505\n",
"Iter: 10, log_lkhood: -167016.909821\n",
"Iter: 20, log_lkhood: -166640.153796\n",
"Iter: 30, log_lkhood: -166376.748867\n",
"Iter: 40, log_lkhood: -166239.097332\n",
"Iter: 50, log_lkhood: -166188.786042\n",
"Iter: 60, log_lkhood: -166161.622674\n",
"Iter: 70, log_lkhood: -166141.460107\n",
"Iter: 80, log_lkhood: -166122.366250\n",
"Iter: 90, log_lkhood: -166105.709010\n",
"Iter: 100, log_lkhood: -166087.292232\n",
"Iter: 110, log_lkhood: -166060.262078\n",
"Iter: 120, log_lkhood: -166027.852430\n",
"Iter: 130, log_lkhood: -165995.554904\n",
"Iter: 140, log_lkhood: -165920.602652\n",
"Iter: 150, log_lkhood: -165879.112254\n",
"Iter: 160, log_lkhood: -165862.662407\n",
"Iter: 170, log_lkhood: -165834.125206\n",
"Iter: 180, log_lkhood: -165786.659524\n",
"Iter: 190, log_lkhood: -165752.703862\n"
]
}
],
"source": [
"hmm_3 = hmm()\n",
"hmm_3.fit(obs, N=3, max_iter=200)"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {
"collapsed": false
},
"outputs": [
{
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" <td>0.045</td>\n",
" <td>0.052</td>\n",
" <td>0.092</td>\n",
" <td>0.013</td>\n",
" <td></td>\n",
" <td>0.012</td>\n",
" <td>0.001</td>\n",
" <td>0.021</td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.02</td>\n",
" <td>0.006</td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.124</td>\n",
" <td></td>\n",
" <td>0.048</td>\n",
" <td>0.048</td>\n",
" <td>0.033</td>\n",
" <td></td>\n",
" <td>0.048</td>\n",
" <td>0.142</td>\n",
" <td>0.028</td>\n",
" <td>0.001</td>\n",
" <td>0.069</td>\n",
" <td>0.019</td>\n",
" <td></td>\n",
" <td>0.046</td>\n",
" <td>0.047</td>\n",
" <td>0.098</td>\n",
" <td>0.036</td>\n",
" <td></td>\n",
" <td>0.052</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.051</td>\n",
" <td>0.002</td>\n",
" <td>0.005</td>\n",
" <td>0.007</td>\n",
" <td>0.001</td>\n",
" <td>0.021</td>\n",
" <td>0.01</td>\n",
" <td>0.001</td>\n",
" <td>0.05</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.014</td>\n",
" <td></td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.195</td>\n",
" <td></td>\n",
" <td>0.180</td>\n",
" <td></td>\n",
" <td>0.024</td>\n",
" <td>0.005</td>\n",
" <td>0.003</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.05</td>\n",
" <td>0.070</td>\n",
" <td></td>\n",
" <td>0.081</td>\n",
" <td>0.068</td>\n",
" <td>0.006</td>\n",
" <td>0.072</td>\n",
" <td></td>\n",
" <td>0.006</td>\n",
" <td>0.008</td>\n",
" <td>0.071</td>\n",
" <td>0.031</td>\n",
" <td>0.010</td>\n",
" <td>0.002</td>\n",
" <td></td>\n",
" <td>0.002</td>\n",
" <td>0.009</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.033</td>\n",
" <td></td>\n",
" <td>0.005</td>\n",
" <td>0.068</td>\n",
" <td></td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" ́ а б в г д е ж з и \\\n",
"0 0.171 0.006 0.002 0.055 0.04 0.020 0.064 0.030 \n",
"1 0.124 0.048 0.048 0.033 0.048 0.142 0.028 0.001 0.069 \n",
"2 0.195 0.180 0.024 0.005 0.003 0.05 0.070 \n",
"\n",
" й к л м н о п р с т \\\n",
"0 0.008 0.015 0.023 0.017 0.020 0.212 0.053 0.045 0.052 0.092 \n",
"1 0.019 0.046 0.047 0.098 0.036 0.052 \n",
"2 0.081 0.068 0.006 0.072 0.006 0.008 0.071 0.031 \n",
"\n",
" у ф х ц ч ш щ ъ ы ь э \\\n",
"0 0.013 0.012 0.001 0.021 0.001 0.02 0.006 \n",
"1 0.051 0.002 0.005 0.007 0.001 0.021 0.01 0.001 0.05 \n",
"2 0.010 0.002 0.002 0.009 0.033 \n",
"\n",
" ю я ё \n",
"0 0.001 \n",
"1 0.014 \n",
"2 0.005 0.068 "
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#probability emission matrix for the letters and the space\n",
"B = pd.DataFrame(np.around(hmm_3.B, 3), index=symbols).T\n",
"B.replace(B[B==0], \" \")"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 0, log_lkhood: -204826.378984\n",
"Iter: 10, log_lkhood: -158387.129848\n",
"Iter: 20, log_lkhood: -153366.552658\n",
"Iter: 30, log_lkhood: -152717.446563\n",
"Iter: 40, log_lkhood: -152568.968634\n",
"Iter: 50, log_lkhood: -152506.637600\n",
"Iter: 60, log_lkhood: -152475.317134\n",
"Iter: 70, log_lkhood: -152454.696123\n",
"Iter: 80, log_lkhood: -152438.634036\n",
"Iter: 90, log_lkhood: -152426.087514\n",
"Iter: 100, log_lkhood: -152417.145420\n",
"Iter: 110, log_lkhood: -152411.385141\n",
"Iter: 120, log_lkhood: -152407.907331\n",
"Iter: 130, log_lkhood: -152405.862370\n",
"Iter: 140, log_lkhood: -152404.664465\n",
"Iter: 150, log_lkhood: -152403.957874\n",
"Iter: 160, log_lkhood: -152403.536247\n",
"Iter: 170, log_lkhood: -152403.281592\n",
"Iter: 180, log_lkhood: -152403.126194\n",
"Iter: 190, log_lkhood: -152403.030619\n"
]
}
],
"source": [
"hmm_4 = hmm()\n",
"hmm_4.fit(obs, N=4, max_iter=200)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th></th>\n",
" <th>́</th>\n",
" <th>а</th>\n",
" <th>б</th>\n",
" <th>в</th>\n",
" <th>г</th>\n",
" <th>д</th>\n",
" <th>е</th>\n",
" <th>ж</th>\n",
" <th>з</th>\n",
" <th>и</th>\n",
" <th>й</th>\n",
" <th>к</th>\n",
" <th>л</th>\n",
" <th>м</th>\n",
" <th>н</th>\n",
" <th>о</th>\n",
" <th>п</th>\n",
" <th>р</th>\n",
" <th>с</th>\n",
" <th>т</th>\n",
" <th>у</th>\n",
" <th>ф</th>\n",
" <th>х</th>\n",
" <th>ц</th>\n",
" <th>ч</th>\n",
" <th>ш</th>\n",
" <th>щ</th>\n",
" <th>ъ</th>\n",
" <th>ы</th>\n",
" <th>ь</th>\n",
" <th>э</th>\n",
" <th>ю</th>\n",
" <th>я</th>\n",
" <th>ё</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.504</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.004</td>\n",
" <td>0.052</td>\n",
" <td>0.009</td>\n",
" <td>0.019</td>\n",
" <td>0.056</td>\n",
" <td></td>\n",
" <td>0.01</td>\n",
" <td>0.008</td>\n",
" <td>0.04</td>\n",
" <td>0.034</td>\n",
" <td></td>\n",
" <td>0.008</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.025</td>\n",
" <td>0.002</td>\n",
" <td>0.112</td>\n",
" <td>0.022</td>\n",
" <td>0.001</td>\n",
" <td>0.002</td>\n",
" <td>0.003</td>\n",
" <td></td>\n",
" <td>0.016</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.012</td>\n",
" <td>0.021</td>\n",
" <td>0.039</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.009</td>\n",
" <td></td>\n",
" <td>0.203</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" <td>0.159</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.15</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.278</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.067</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.043</td>\n",
" <td>0.052</td>\n",
" <td></td>\n",
" <td>0.003</td>\n",
" <td>0.034</td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.155</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.031</td>\n",
" <td>0.054</td>\n",
" <td>0.046</td>\n",
" <td>0.046</td>\n",
" <td></td>\n",
" <td>0.024</td>\n",
" <td>0.047</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.03</td>\n",
" <td>0.156</td>\n",
" <td>0.07</td>\n",
" <td>0.113</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.056</td>\n",
" <td>0.03</td>\n",
" <td>0.068</td>\n",
" <td></td>\n",
" <td>0.002</td>\n",
" <td>0.019</td>\n",
" <td>0.008</td>\n",
" <td>0.019</td>\n",
" <td>0.02</td>\n",
" <td>0.005</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.076</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.035</td>\n",
" <td>0.073</td>\n",
" <td>0.028</td>\n",
" <td>0.042</td>\n",
" <td></td>\n",
" <td>0.016</td>\n",
" <td>0.016</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td>0.071</td>\n",
" <td>0.056</td>\n",
" <td>0.032</td>\n",
" <td>0.154</td>\n",
" <td></td>\n",
" <td>0.074</td>\n",
" <td>0.104</td>\n",
" <td>0.047</td>\n",
" <td>0.121</td>\n",
" <td></td>\n",
" <td>0.002</td>\n",
" <td>0.01</td>\n",
" <td>0.006</td>\n",
" <td>0.018</td>\n",
" <td>0.011</td>\n",
" <td>0.008</td>\n",
" <td>0.001</td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" <td></td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" ́ а б в г д е ж з и \\\n",
"0 0.504 0.004 0.052 0.009 0.019 0.056 0.01 0.008 \n",
"1 0.009 0.203 0.001 0.159 0.15 \n",
"2 0.155 0.031 0.054 0.046 0.046 0.024 0.047 \n",
"3 0.076 0.035 0.073 0.028 0.042 0.016 0.016 \n",
"\n",
" й к л м н о п р с т у \\\n",
"0 0.04 0.034 0.008 0.025 0.002 0.112 0.022 0.001 \n",
"1 0.278 0.067 \n",
"2 0.03 0.156 0.07 0.113 0.056 0.03 0.068 \n",
"3 0.071 0.056 0.032 0.154 0.074 0.104 0.047 0.121 \n",
"\n",
" ф х ц ч ш щ ъ ы ь э \\\n",
"0 0.002 0.003 0.016 0.012 \n",
"1 0.043 0.052 \n",
"2 0.002 0.019 0.008 0.019 0.02 0.005 \n",
"3 0.002 0.01 0.006 0.018 0.011 0.008 0.001 \n",
"\n",
" ю я ё \n",
"0 0.021 0.039 \n",
"1 0.003 0.034 \n",
"2 \n",
"3 "
]
},
"execution_count": 113,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#probability emission matrix for the letters and the space\n",
"B = pd.DataFrame(np.around(hmm_4.B, 3), index=symbols).T\n",
"B.replace(B[B==0], \" \")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [conda env:impact]",
"language": "python",
"name": "conda-env-impact-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
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"nbformat": 4,
"nbformat_minor": 1
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