All work through Chapter 6 done.

.gitignore

@@ -11,4 +11,5 @@ doc-sensitivity*
 *.zip
 *.pdf
 *.tar.gz
-User Identification From Walking Activity
+User Identification From Walking Activity
+mobypos.txt

Listing 6.1-6.6.ipynb

@@ -0,0 +1,227 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 84,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import tensorflow as tf "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class HMM(object):\n",
+    "    def __init__(self, initial_prob, trans_prob, obs_prob):\n",
+    "        self.N = np.size(initial_prob)\n",
+    "        self.initial_prob = initial_prob\n",
+    "        self.trans_prob = trans_prob\n",
+    "        self.emission = tf.constant(obs_prob)\n",
+    "        assert self.initial_prob.shape == (self.N, 1)\n",
+    "        assert self.trans_prob.shape == (self.N, self.N)\n",
+    "        assert obs_prob.shape[0] == self.N\n",
+    "        self.obs_idx = tf.placeholder(tf.int32)\n",
+    "        self.fwd = tf.placeholder(tf.float64)\n",
+    "        \n",
+    "    def get_emission(self, obs_idx):\n",
+    "        slice_location = [0, obs_idx]\n",
+    "        num_rows = tf.shape(self.emission)[0]\n",
+    "        slice_shape = [num_rows, 1]\n",
+    "        return tf.slice(self.emission, slice_location, slice_shape)\n",
+    "    \n",
+    "    def forward_init_op(self):\n",
+    "        obs_prob = self.get_emission(self.obs_idx)\n",
+    "        fwd = tf.multiply(self.initial_prob, obs_prob)\n",
+    "        return fwd\n",
+    "    \n",
+    "    def forward_op(self):\n",
+    "        transitions = tf.matmul(self.fwd,\n",
+    "        tf.transpose(self.get_emission(self.obs_idx)))\n",
+    "        weighted_transitions = transitions * self.trans_prob\n",
+    "        fwd = tf.reduce_sum(weighted_transitions, 0)\n",
+    "        return tf.reshape(fwd, tf.shape(self.fwd))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def forward_algorithm(sess, hmm, observations):\n",
+    "    fwd = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs_idx:observations[0]})\n",
+    "    for t in range(1, len(observations)):\n",
+    "        fwd = sess.run(hmm.forward_op(), feed_dict={hmm.obs_idx:observations[t], hmm.fwd: fwd})\n",
+    "    prob = sess.run(tf.reduce_sum(fwd))\n",
+    "    return prob"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Probability of observing [0, 1, 1, 2, 1] is 0.004540300799999999\n"
+     ]
+    }
+   ],
+   "source": [
+    "initial_prob = np.array([[0.6],[0.4]])\n",
+    "trans_prob = np.array([[0.7, 0.3],\n",
+    "                       [0.4, 0.6]])\n",
+    "obs_prob = np.array([[0.1, 0.4, 0.5],\n",
+    "                     [0.6, 0.3, 0.1]])\n",
+    "hmm = HMM(initial_prob=initial_prob, trans_prob=trans_prob, obs_prob=obs_prob)\n",
+    "observations = [0, 1, 1, 2, 1]\n",
+    "with tf.Session() as sess:\n",
+    "    prob = forward_algorithm(sess, hmm, observations)\n",
+    "    print('Probability of observing {} is {}'.format(observations, prob))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# this walks through the loop unfolding to learn more about how the HMM is actually doing the comuptation in this \n",
+    "# simple weather example\n",
+    "\n",
+    "# basically in the first iteration to initialize, the HMM takes the first observation index, 0, aka 'walk'\n",
+    "# and multiplies the probabilities of walking when it is raining / sunny times by the initial probabilities of it being rainy\n",
+    "# or sunny to get a composite probability for it being rainy or sunny and having walked\n",
+    "\n",
+    "# then the next step steps through the rest of the observations, 'shopping', 'shopping', 'cleaning', 'shopping', and does\n",
+    "# the following\n",
+    "\n",
+    "# for 'shopping', it takes the emission probability of seeing shopping in each state at that point, and multiplies it by the existing\n",
+    "# forward model, then applies the weighted transition probabilities in each actual state (Rainy or Sunny), \n",
+    "# through multiplication, and then accumulates them (through reduce_sum) to get the cumulitative probability of being \n",
+    "# in either state given the observations thus far ('walk', 'shopping')\n",
+    "\n",
+    "# it does the same thing for the next observations, 'shopping', 'cleaning' and 'shopping' to get the cumultative probability\n",
+    "# of being in either state\n",
+    "\n",
+    "# the final answer is the cumultation of either probability, so the likelihood of that sequence of events happening, \n",
+    "# but not necessarily the highest probability state you are in\n",
+    "\n",
+    "with tf.Session() as sess:\n",
+    "    slice_location = [0, 0]\n",
+    "    num_rows = tf.shape(tf.constant(obs_prob))[0]\n",
+    "    slice_shape = [num_rows, 1]\n",
+    "    fwd0 = tf.slice(tf.constant(obs_prob), slice_location, slice_shape)\n",
+    "    fwd0_eval = fwd0.eval()\n",
+    "    fwd0 = tf.multiply(initial_prob, fwd0)\n",
+    "    fwd0_eval = fwd0.eval()\n",
+    "    transitions1 = tf.matmul(fwd0, tf.transpose(np.array([[0.4], [0.3]])))\n",
+    "    weighted_transitions1 = transitions1 * trans_prob\n",
+    "    fwd1 = tf.reduce_sum(weighted_transitions1, 0)\n",
+    "    fwd1_prs_e = fwd1.eval()\n",
+    "    fwd1 = tf.reshape(fwd1, tf.shape(fwd0))\n",
+    "    fwd1_eval = fwd1.eval()\n",
+    "    \n",
+    "    transitions2 = tf.matmul(fwd1, tf.transpose(np.array([[0.4], [0.3]])))\n",
+    "    weighted_transitions2 = transitions2 * trans_prob\n",
+    "    fwd2 = tf.reduce_sum(weighted_transitions2, 0)\n",
+    "    fwd2_prs_e = fwd2.eval()\n",
+    "    fwd2 = tf.reshape(fwd2, tf.shape(fwd1))\n",
+    "    fwd2_eval = fwd2.eval()\n",
+    "    \n",
+    "\n",
+    "    transitions3 = tf.matmul(fwd2, tf.transpose(np.array([[0.5], [0.1]])))\n",
+    "    weighted_transitions3 = transitions3 * trans_prob\n",
+    "    fwd3 = tf.reduce_sum(weighted_transitions3, 0)\n",
+    "    fwd3_prs_e = fwd3.eval()\n",
+    "    fwd3 = tf.reshape(fwd3, tf.shape(fwd2))\n",
+    "    fwd3_eval = fwd3.eval()\n",
+    "    \n",
+    "    transitions4 = tf.matmul(fwd3, tf.transpose(np.array([[0.4], [0.3]])))\n",
+    "    weighted_transitions4 = transitions4 * trans_prob\n",
+    "    fwd4 = tf.reduce_sum(weighted_transitions4, 0)\n",
+    "    fwd4_prs_e = fwd4.eval()\n",
+    "    fwd4 = tf.reshape(fwd4, tf.shape(fwd3))\n",
+    "    fwd4_eval = fwd4.eval()\n",
+    "    \n",
+    "    final_prob = tf.reduce_sum(fwd4)\n",
+    "    final_prob_e = final_prob.eval()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0.06]\n",
+      " [0.24]]\n",
+      "[0.0552 0.0486]\n",
+      "[[0.0552]\n",
+      " [0.0486]]\n",
+      "[0.023232 0.013716]\n",
+      "[[0.023232]\n",
+      " [0.013716]]\n",
+      "[0.0108744  0.00151992]\n",
+      "[[0.0108744 ]\n",
+      " [0.00151992]]\n",
+      "[0.00328802 0.00125228]\n",
+      "[[0.00328802]\n",
+      " [0.00125228]]\n",
+      "0.004540300799999999\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(fwd0_eval)\n",
+    "print(fwd1_prs_e)\n",
+    "print(fwd1_eval)\n",
+    "print(fwd2_prs_e)\n",
+    "print(fwd2_eval)\n",
+    "print(fwd3_prs_e)\n",
+    "print(fwd3_eval)\n",
+    "print(fwd4_prs_e)\n",
+    "print(fwd4_eval)\n",
+    "print(final_prob_e)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.0b1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}