Complexity Reduction in Fixed-Lag Smoothing for Hidden Markov Models

In this paper, we investigate approximate smoothing schemes for a class of hidden Markov models (HMMs), namely, HMMs with underlying Markov chains that are nearly completely decomposable. The objective is to obtain substantial computational savings. Our algorithm can not only be used to obtain aggregate smoothed estimates but can be used also to obtain systematically approximate full-order smoothed estimates with computational savings and rigorous performance guarantees, unlike many of the aggregation methods proposed earlier