Compute likelihood of sequence and states under Gaussian HMM

[alimanfoo]

Apologies for the newbie question, but I have a Gaussian HMM for which the transition matrix and emission probabilities are known, and I would like to compute the likelihood for a particular sequence of data given a particular sequence of hidden states. The log_probability() method on the HiddenMarkovModel class says it can do this if a path is provided, but how do I specify the path?

Thanks in advance.

[jmschrei]

Howdy

Looks like I actually removed that feature without updating the documentation. Sorry about that!

Until I re-add it, you can use the following code to do it:

model = HiddenMarkovModel...
path = [list of state objects]
path_idxs = map(path, model.states.index)

logp = 0
# First add in emissions
j = 0
for state in path:
    if state.distribution is not None:
        logp += state.distribution.log_probability(sequence[j])
        j += 1

# Now add in the transitions
trans = numpy.log(model.dense_transition_matrix())
for start, end in zip(path_idxs[:-1], path_idxs[1:]):
    logp += trans[start, end]

print logp

Note: This is untested pseudocode I just hand-wrote, there may be some minor issues with it. Let me know if there are major issues! It may be memory-inefficient for large models since it uses the dense transition matrix instead of the internal sparse representation.

[alimanfoo]

Thank you, much appreciated.

On Wed, 22 Mar 2017 at 21:58, Jacob Schreiber notifications@github.com wrote:

Howdy

Looks like I actually removed that feature without updating the documentation. Sorry about that!

Until I re-add it, you can use the following pseudocode to do it:

model = HiddenMarkovModel... path = [list of state objects] path_idxs = map(path, model.states.index)

logp = 0

First add in emissions

j = 0 for state in path: if state.distribution is not None: logp += state.distribution.log_probability(sequence[j]) j += 1

Now add in the transitions

trans = numpy.log(model.dense_transition_matrix()) for start, end in zip(path_idxs[:-1], path_idxs[1:]): logp += trans[start, end]

print logp

Note: This is untested pseudocode I just hand-wrote, there may be some minor issues with it. Let me know if there are major issues! It may be memory-inefficient for large models since it uses the dense transition matrix instead of the internal sparse representation.

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