A New Hybrid Risk-Based Approach to Hidden Layer Inference in Hidden Markov Models

Motivated by the continuing interest in discrete time hidden Markov models (HMMs), we re-examine these models using a risk based approach. Simple modifications of the classical optimisation criteria for hidden path inference lead to a new class of path estimators. A particularly interesting subclass of those are sandwiched in between the most common maximum a posteriori (MAP), or Viterbi, path and marginal posterior mode (MPM), or pointwise MAP, estimators. Similar to previous work by others, the new class is parameterised by a small number of tunable parameters and the estimators are efficiently computed in the usual forward-backward manner. We also present a suitable dynamic programming algorithm for this purpose. Unlike their previously proposed relatives, the new parameters and class are more explicit, hence have clear interpretations, and also enjoy some other computational benefits.
Joint work with J. Lember of Tartu University, Tartu, Estonia