This is a toy library that implements first- through Nth-order hidden Markov models.

At present, miniHMM offers some benefits hard to find in other HMM libraries:

• Its algorithms are numerically stable

• It is able to compute high order hidden Markov models, which allow states to depend on the Nth previous states, rather than only on the immediate previous state.

  Concretely, high-order models are implemented via a translation layer that converts high-order models of arbitrary degree into mathematically equivalent first-order models over a virtual state space. This implementation allows all algorithms developed for first-order models to be applied in higher dimensions. See minihmm.represent for further detail.

• Emissions may be univariate or multivariate (for multidimensional emissions), continuous or discrete. See minihmm.factors for examples of distributions that can be built out-of-the-box, and for hints on designing new ones,
• Multiple distinct estimators are available for probability distributions, enabling e.g. addition of model noise, pseudocounts, et c during model training. See minihmm.estimators for details.
• HMMs of all sorts can be trained via a Baum-Welch implementation with some bells & whistles (e.g. noise scheduling, parallelization, parameter-tying (via estimator classes), et c)
• In addition to the Viterbi algorithm (the maximum likelihood solution for a total sequence of states), states may be inferred by:
  • Probabilistically sampling valid sequences from their posterior distribution, given a sequence of emissions. This enables estimates of robustness and non-deterministic samples to be drawn
  • Labeling individual states by highest posterior probabilities (even though this doesn't guarantee a valid path)

This library is in beta, and breaking changes are not uncommon. We try to be polite by announcing these in the changelog.