Documentation

A Hidden Markov model consists of a number of (hidden) states and a set of emissions. There is a vector for the initial probability of each state and a matrix containing the probability for switching from one state to another one. The distribution field points to probability distributions that associate every state with emissions of different probability. Famous distribution instances are discrete and Gaussian distributions. See Math.HiddenMarkovModel.Distribution for details.

The transition matrix is transposed with respect to popular HMM descriptions. But I think this is the natural orientation, because this way you can write "transition matrix times probability column vector".

Create a model with uniform probabilities for initial vector and transition matrix given a distribution for the emissions. You can use this as a starting point for trainUnsupervised.

Logarithm of the likelihood to observe the given sequence. We return the logarithm because the likelihood can be so small that it may be rounded to zero in the choosen number type.

Reveal the state sequence that led most likely to the observed sequence of emissions. It is found using the Viterbi algorithm.

A trained model is a temporary form of a Hidden Markov model that we need during the training on multiple training sequences. It allows to collect knowledge over many sequences with mergeTrained, even with mixed supervised and unsupervised training. You finish the training by converting the trained model back to a plain modul using finishTraining.

You can create a trained model in three ways:

• supervised training using an emission sequence with associated states,
• unsupervised training using an emission sequence and an existing Hidden Markov Model,
• derive it from state sequence patterns, cf. Math.HiddenMarkovModel.Pattern.

Contribute a manually labeled emission sequence to a HMM training.

Consider a superposition of all possible state sequences weighted by the likelihood to produce the observed emission sequence. Now train the model with respect to all of these sequences with respect to the weights. This is done by the Baum-Welch algorithm.

Compute maximum deviation between initial and transition probabilities. You can use this as abort criterion for unsupervised training. We omit computation of differences between the emission probabilities. This simplifies matters a lot and should suffice for defining an abort criterion.