Optimal Decoding of Hidden Markov Models With Consistency Constraints

Hidden Markov Models (HMM) are interpretable statistical models that specify distributions over sequences of symbols by assuming these symbols are generated from hidden states. Once learned, these models can be used to determine the most likely sequence of hidden states for unseen observable sequences. This is done in practice by solving the shortest path problem in a layered directed acyclic graph using dynamic programming. In some applications, although the hidden states are unknown, we argue that it is known that some observable elements must be generated from the same hidden state. Finding the most likely hidden state in this contrained setting is however a hard problem. We propose a number of alternative approaches for this problem: an Integer Programming (IP), Dynamic Programming (DP), a Branch and Bound (B\&B) and a Cost Function Network (CFN) approach. Our experiments show that the DP approach does not scale well; B\&B scales better for a small number of constraints imposed on many elements and CFNs are the most robust approach when many smaller constraints are imposed. Finally, we show that the addition of consistency constraints indeed allows to better recover the correct hidden states