Hierarchical Dirichlet Process Hidden Semi-Markov Models

Given a set of sequential data in an unsupervised setting, we often aim to infer meaningful states present in the data along with characteristics that describe and distinguish those states. For example, in a speaker diarization (or who-spoke-when) problem, we are given a single audio recording of a meeting and wish to infer the number of speakers present, when they speak, and some characteristics governing their individual speech patterns [108, 31]. Or in separating a home power signal into the power signals of individual devices, we could perform the task much better if we were able to exploit our prior knowledge about the levels and durations of each device’s power modes [66]. Such learning problems for sequential data are pervasive, and so we would like to build general models that are both flexible enough to be applicable to many domains and expressive enough to encode the appropriate information. Hidden Markov Models (HMMs) have proven to be excellent general models for approaching learning problems in sequential data, but they have two significant disadvantages: first, state duration distributions are necessarily restricted to a geometric form that is not appropriate for many real-world data; second, the number of hidden states must be set a priori so that model complexity is not inferred from data in a way that scales with the size and complexity of the data. 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 representing a posterior over state complexity while maintaining e cient inference algorithms [106, 5]. However, the HDP-HMM does not address the issue of non-Markovianity in real data. The Markovian disadvantage is in fact compounded in the nonparametric setting, since non-Markovian behavior in data can lead to the creation of unnecessary extra states and unrealistically rapid switching dynamics [31]. One approach to avoiding the rapid-switching problem is the Sticky HDP-HMM [31],