Exact Sampling and Decoding in High-Order Hidden Markov Models

We present a method for exact optimization and sampling from high order Hidden Markov Models (HMMs), which are generally handled by approximation techniques. Motivated by adaptive rejection sampling and heuristic search, we propose a strategy based on sequentially refining a lower-order language model that is an upper bound on the true model we wish to decode and sample from. This allows us to build tractable variable-order HMMs. The ARPA format for language models is extended to enable an efficient use of the max-backoff quantities required to compute the upper bound. We evaluate our approach on two problems: a SMS-retrieval task and a POS tagging experiment using 5-gram models. Results show that the same approach can be used for exact optimization and sampling, while explicitly constructing only a fraction of the total implicit state-space.