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#!/usr/bin/env python
# -*- coding:utf-8 -*-
# Viterbi algorithm
# http://en.wikipedia.org/wiki/Viterbi_algorithm
#
# > python viterbi.py
# 0 1 2
# Rainy: 0.06000 0.03840 0.01344
# Sunny: 0.24000 0.04320 0.00259
# (0.01344, ['Sunny', 'Rainy', 'Rainy'])
# HMM
states = ('Rainy', 'Sunny')
observations = ['walk', 'shop', 'clean']
start_probability = {'Rainy': 0.6, 'Sunny': 0.4}
transition_probability = {
'Rainy' : {'Rainy': 0.7, 'Sunny': 0.3},
'Sunny' : {'Rainy': 0.4, 'Sunny': 0.6},
}
emission_probability = {
'Rainy' : {'walk': 0.1, 'shop': 0.4, 'clean': 0.5},
'Sunny' : {'walk': 0.6, 'shop': 0.3, 'clean': 0.1},
}
# Helps visualize the steps of Viterbi.
def print_dptable(V):
print " ",
for i in range(len(V)): print "%7d" % i,
print
for y in V[0].keys():
print "%.5s: " % y,
for t in range(len(V)):
print "%.7s" % ("%f" % V[t][y]),
print
def viterbi(obs, states, start_p, trans_p, emit_p):
V = [{}]
path = {}
# Initialize base cases (t == 0)
for y in states:
V[0][y] = start_p[y] * emit_p[y][obs[0]]
path[y] = [y]
# Run Viterbi for t > 0
for t in range(1,len(obs)):
V.append({})
newpath = {}
for y in states:
(prob, state) = max([(V[t-1][y0] * trans_p[y0][y] * emit_p[y][obs[t]], y0) for y0 in states])
V[t][y] = prob
newpath[y] = path[state] + [y]
# Don't need to remember the old paths
path = newpath
print_dptable(V)
(prob, state) = max([(V[len(obs) - 1][y], y) for y in states])
return (prob, path[state])
print viterbi(observations,
states,
start_probability,
transition_probability,
emission_probability)
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