A generalized risk approach to path inference based on hidden Markov models

Motivated by the continuing interest in discrete time hidden Markov models (HMMs), this paper reexamines these models using a risk-based approach. Simple modifications of the classical optimization criteria for hidden path inference lead to a new class of hidden path estimators. The estimators are efficiently computed in the usual forward-backward manner and a corresponding dynamic programming algorithm is also presented. A particularly interesting subclass of such alignments are sandwiched between the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or pointwise maximum a posteriori (PMAP), estimator. Similar to previous work, the new class is parameterized by a small number of tunable parameters. Unlike their previously proposed relatives, the new parameters and class are more explicit and have clear interpretations, and bypass the issue of numerical scaling, which can be particularly valuable for applications.