State Sequence Analysis in Hidden Markov Models

Given a discrete time finite state hidden Markov model (HMM) and a sequence of observations, there are different ways to estimate the hidden behavior of the system. In this paper, the problem of finding the most probable state sequence is considered. The state sequence, as opposed to the state trajectory, specifies the sequence of states that the HMM visits but does not specify the dwelling times in these states. This inference problem is relevant in a variety of domains, like text analysis, speech recognition, or behavior recognition, where the exact timing of hidden state transitions is not nearly as important as the sequence of states visited. No existing algorithm addresses this inference question adequately. Leveraging previous work on continuous time Markov chains, we develop a provably correct algorithm, called state sequence analysis, that addresses this inference question in HMMs. We discuss and illustrate empirically the differences between finding the most probable state sequence directly and doing so through running the Viterbi algorithm and collapsing repetitive state visitations. Experimental results in two synthetic domains demonstrate that the Viterbi-based approach can be significantly suboptimal compared to state sequence analysis. Further, we demonstrate the benefits of the proposed approach on a real activity recognition problem.