|Stochastic Systems Group|
Semi-Markovianity and the HDP-HMM
Hidden Markov Models (HMMs) have proven to be very useful general models for sequential data. However, classical HMMs have two significant disadvantages: (1) state duration distributions are necessarily restricted to a geometric form that is not appropriate for many real-world data, and (2) the number of possible hidden states must be set a priori so model complexity cannot be inferred from data within a Bayesian framework.
Recent work in Bayesian nonparametrics has addressed the latter issue. In particular, the Hierarchical Dirichlet Process HMM (HDP-HMM) has provided a powerful framework for inferring arbitrarily large state complexity from data. However, the HDP-HMM does not address the former disadvantage of non-Markovianity in real data. The disadvantage is even amplified in the nonparametric setting, since non-Markovian behavior in data can lead to the creation of unnecessary extra states and unrealistically rapid switching dynamics.
In this talk I will present my Masters thesis work on employing semi-Markovian ideas within the nonparametric HDP-HMM framework. I will describe an explicit-duration HDP-HSMM model and efficient inference via a blocked Gibbs sampler. I will also motivate the importance of semi-Markovian modeling for real-world applications and show some synthetic results.
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