Stochastic Variational Inference for HMMs, HSMMs, and Nonparametric Extensions
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چکیده
Hierarchical Bayesian time series models can be applied to complex data in many domains, including data arising from behavior and motion [32, 33], home energy consumption [60], physiological signals [69], single-molecule biophysics [71], brain-machine interfaces [54], and natural language and text [44, 70]. However, for many of these applications there are very large and growing datasets, and scaling Bayesian inference in rich hierarchical models to these large datasets is a fundamental challenge. Many Bayesian inference algorithms, including standard Gibbs sampling and mean field algorithms, require a complete pass over the data in each iteration and thus do not scale well. In contrast, some recent Bayesian inference methods require only a small number of passes [52] and can even operate in the single-pass or streaming settings [15]. In particular, stochastic variational inference (SVI) [52] provides a general framework for scalable inference based on mean field and stochastic gradient descent. However, while SVI has been studied extensively for topic models [53, 115, 17, 114, 92, 52], it has not been applied to time series. In this chapter, we develop SVI algorithms for the core Bayesian time series models of this thesis, namely the hidden Markov model (HMM) and hidden semi-Markov model (HSMM), as well as their nonparametric extensions based on the hierarchical Dirichlet process (HDP), the HDP-HMM and HDP-HSMM. Both the HMM and HDP-HMM are ubiquitous in time series modeling, and so the SVI algorithms developed here are widely applicable. However, as discussed in the previous chapter, general HSMM inference subroutines have time complexity that scales quadratically with observation sequence length, and such quadratic scaling can be impractical even in the setting of SVI. To address this shortcoming, we use the methods developed in Chapter 4 for Bayesian inference in (HDP-)HSMMs with negative binomial durations to provide approximate
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Bayesian time series models and scalable inference
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