Question

I am starting to learn hidden markov models and on the wiki page, as well as on github there are alot of examples but most of the probabilities are already there(70% change of rain, 30% chance of changing state, etc..). The spell checking or sentences examples, seem to study books and then rank the probabilities of words.

So does the markov model include a way of figuring out the probabilities or are we suppose to some other other model to pre-calculate it?

Sorry if this question is off. I think its straightforward how the hidden markov model selects probable sequences but the probability part is a bit grey to me(because its often provided). Examples or any info would be great.

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For those not familiar with markov models, here’s an example(from wikipedia) http://en.wikipedia.org/wiki/Viterbi_algorithm and http://en.wikipedia.org/wiki/Hidden_Markov_model

#!/usr/bin/env python

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},
   }

#application code
# Helps visualize the steps of Viterbi.
def print_dptable(V):
    print "    ",
    for i in range(len(V)): print "%7s" % ("%d" % 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])



#start trigger
def example():
    return viterbi(observations,
                   states,
                   start_probability,
                   transition_probability,
                   emission_probability)
print example()

Answer 1

You’re looking for an EM (expectation maximization) algorithm to compute the unknown parameters from sets of observed sequences. Probably the most commonly used is the Baum-Welch algorithm, which uses the forward-backward algorithm.

For reference, here is a set of slides I’ve used previously to review HMMs. It has a nice overview of Forward-Backward, Viterbi, and Baum-Welch