Python Viterbi algorithm

Question

The code below is a Python implementation I found here of the Viterbi algorithm used in the HMM model. The link also gives a test case.

In __init__, I understand that:

initialProb is the probability to start at the given state,
transProb is the probability to move from one state to another at any given time, but

the parameter I don't understand is obsProb. Can someone please explain it?

import numpy as np

'''
N: number of hidden states
'''
class Decoder(object):
def __init__(self, initialProb, transProb, obsProb):
    self.N = initialProb.shape[0]
    self.initialProb = initialProb
    self.transProb = transProb
    self.obsProb = obsProb
    assert self.initialProb.shape == (self.N, 1)
    assert self.transProb.shape == (self.N, self.N)
    assert self.obsProb.shape[0] == self.N

def Obs(self, obs):
    return self.obsProb[:, obs, None]

def Decode(self, obs):
    trellis = np.zeros((self.N, len(obs)))
    backpt = np.ones((self.N, len(obs)), 'int32') * -1

    # initialization
    trellis[:, 0] = np.squeeze(self.initialProb * self.Obs(obs[0]))

    for t in xrange(1, len(obs)):
        trellis[:, t] = (trellis[:, t-1, None].dot(self.Obs(obs[t]).T) * self.transProb).max(0)
        backpt[:, t] = (np.tile(trellis[:, t-1, None], [1, self.N]) * self.transProb).argmax(0)
    # termination
    tokens = [trellis[:, -1].argmax()]
    for i in xrange(len(obs)-1, 0, -1):
        tokens.append(backpt[tokens[-1], i])
    return tokens[::-1]

I wonder if it's not named well. I expect that it is referring to the observation sequence. (I don't have any experience with the vetirbi algorithm, but there is this wikipedia page ) — jcfollower
– jcfollower, Commented Aug 19, 2015 at 19:18
obsProb in github.com/phvu/misc/blob/master/viterbi/viterbi.py corresponds to emission_probability (emit_p) in en.wikipedia.org/wiki/Viterbi_algorithm#Example and represents the hidden state probabilities. obsProb is indexed with the input data in viterbi.py at lines 16-17 (github.com/phvu/misc/blob/master/viterbi/viterbi.py#L16) to initialize the trellis array at line 24 (github.com/phvu/misc/blob/master/viterbi/viterbi.py#L24) — user4322779
– user4322779, Commented Aug 19, 2015 at 20:28
@Tris Nefzger , thanks for the emit part that was confusing me . — Epsilon
– Epsilon, Commented Aug 21, 2015 at 8:41

m7thon · Accepted Answer · 2015-08-19 23:04:04Z

5

A HMM with N hidden states and M possible discrete observation values is defined by the following parameters:

initialProb (vector of size N): The initial state distribution. The entry initialProb[i] is the probability P(x_0 = i) of being in state i initially (at time 0).
transProb (matrix of size NxN): The transition probability matrix. The entry transProb[i][j] is the probability P(x_{t+1} = j | x_t = i) of transitioning from state i to j.
obsProb (matrix of size NxM): The emission probability matrix. The entry obsProb[i][j] is the probability P(y_t = j | x_t = i) of emitting symbol j from state i.

Often, these parameters are named \pi, T and E, respectively, or \pi, A and B.

The standard reference on HMMs is the tutorial by Rabiner, by the way.

edited Aug 19, 2015 at 23:04

answered Aug 19, 2015 at 22:49

m7thon

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