This package contains a set of functions for evaluating HMMs and GMMs.
The portions written by me are distributed under the terms of the GNU
General Public License. See the file COPYING for details.
* Functions
- The important ones:
- train_gmm - train a GMM from data
- eval_gmm - compute the posterior probability of a GMM given data
- eval_hmm - compute the posterior probabilities of all possible HMM
state sequences given data
- decode_hmm - find the most likely state sequence through the HMM
given data
- Utility functions:
- logsum - takes the sum of a matrix of log likelihoods
- lmvnpdf - compute the log probability of data under a
multivariate Gaussian distribution
* Data Structures
The functions in this toolbox pass around the following structures:
Note: all probabilities are stored as log probabilities
** GMM
- gmm.nmix - number of components in the mixture
- gmm.priors - array of prior log probabilities over each state
- gmm.means - matrix of means (column x is mean of component x)
- gmm.covars - matrix of covariances (column x is the diagonal of the
covariance matrix of component x)
** HMM with GMM observations (does not work with all functions)
- hmm.name -
- hmm.nstates - number of states in the HMM
- hmm.emission_type - 'GMM'
- hmm.start_prob - array of log probs P(first observation is state x)
- hmm.end_prob - array of log probs P(last observation is state x)
- hmm.transmat - matrix of transition log probs (transmat(x,y)
= log(P(transition from state x to state y)))
- hmm.labels - optional cell array of labels for each state in the HMM
(for use in composing HMMs)
- hmm.gmms - array of GMM structures
** HMM with Gaussian observations
- hmm.nstates - number of states in the HMM
- hmm.emission_type - 'gaussian'
- hmm.start_prob - array of log probs P(first observation is state x)
- hmm.end_prob - array of log probs P(last observation is state x)
- hmm.transmat - matrix of transition log probs (transmat(x,y)
= log(P(transition from state x to state y)))
- hmm.labels - optional cell array of labels for each state in the HMM
(for use in composing HMMs)
- hmm.means - matrix of means (column x is mean of state x)
- hmm.covars - matrix of means (column x is the diagonal of the
covariance matrix of component x)
Note that each row of exp(hmm.transmat) does not necessarily sum to 1
because for each state x there is some probability
(exp(hmm.end_prob(x))) that the next transition will be to a
non-emitting exit state (i.e. the current observation is the last
observation in the sequence). The correct invariant is:
sum(exp(hmm.transmat), 2)' + exp(hmm.end_prob) == ones(hmm.nstates, 1)
2007-11-06 Ron Weiss <ronw@ee.columbia.edu>