Stochastic Variational Inference for Bayesian Time Series Models

Bayesian models provide powerful tools for analyzing complex time series data, but performing inference with large datasets is a challenge. Stochastic variational inference (SVI) provides a new framework for approximating model posteriors with only a small number of passes through the data, enabling such models to be fit at scale. However, its application to time series models has not been studied. In this paper we develop SVI algorithms for several common Bayesian time series models, namely the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and the non-parametric HDP-HMM and HDP-HSMM. In addition, because HSMM inference can be expensive even in the minibatch setting of SVI, we develop fast approximate updates for HSMMs with durations distributions that are negative binomials or mixtures of negative binomials.

[1]  R. Moore,et al.  Explicit modelling of state occupancy in hidden Markov models for automatic speech recognition , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[2]  A. Cook,et al.  Experimental evaluation of duration modelling techniques for automatic speech recognition , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[3]  L. Eon Bottou.  Online Learning and Stochastic Approximations , 1998 .

[4]  Léon Bottou,et al.  On-line learning and stochastic approximations , 1999 .

[5]  Kevin P. Murphy.  Hidden semi-Markov models ( HSMMs ) , 2002 .

[6]  Matthew J. Beal.  Variational algorithms for approximate Bayesian inference , 2003 .

[7]  Thomas L. Griffiths,et al.  Integrating Topics and Syntax , 2004, NIPS.

[8]  Yann Guédon,et al.  Hidden hybrid Markov/semi-Markov chains , 2005, Comput. Stat. Data Anal..

[9]  M. T. Johnson,et al.  Capacity and complexity of HMM duration modeling techniques , 2005, IEEE Signal Processing Letters.

[10]  Paul Fearnhead,et al.  Exact and efficient Bayesian inference for multiple changepoint problems , 2006, Stat. Comput..

[11]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[12]  Jan Bulla,et al.  Stylized facts of financial time series and hidden semi-Markov models , 2006, Comput. Stat. Data Anal..

[13]  H. Robbins.  A Stochastic Approximation Method , 1951 .

[14]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[15]  Dan Klein,et al.  The Infinite PCFG Using Hierarchical Dirichlet Processes , 2007, EMNLP.

[16]  Nicolas Henry Hudson.  Inference in Hybrid Systems with Applications in Neural Prosthetics , 2009 .

[17]  Michael I. Jordan,et al.  Sharing Features among Dynamical Systems with Beta Processes , 2009, NIPS.

[18]  Francis R. Bach,et al.  Online Learning for Latent Dirichlet Allocation , 2010, NIPS.

[19]  Chong Wang,et al.  Online Variational Inference for the Hierarchical Dirichlet Process , 2011, AISTATS.

[20]  Michael I. Jordan,et al.  Bayesian Nonparametric Inference of Switching Dynamic Linear Models , 2010, IEEE Transactions on Signal Processing.

[21]  Chong Wang,et al.  Truncation-free Online Variational Inference for Bayesian Nonparametric Models , 2012, NIPS.

[22]  Shamim Nemati,et al.  Discovering shared dynamics in physiological signals: Application to patient monitoring in ICU , 2012, 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[23]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[24]  Erik B. Sudderth,et al.  Truly Nonparametric Online Variational Inference for Hierarchical Dirichlet Processes , 2012, NIPS.

[25]  D. Blei,et al.  Truncation-free stochastic variational inference for Bayesian nonparametric models , 2012, NIPS 2012.

[26]  Matthew J. Johnson,et al.  Bayesian nonparametric hidden semi-Markov models , 2012, J. Mach. Learn. Res..

[27]  Rob Phillips,et al.  Analysis of DNA Looping Kinetics in Tethered Particle Motion Experiments using Hidden Markov Models , 2013 .

[28]  Chong Wang,et al.  An Adaptive Learning Rate for Stochastic Variational Inference , 2013, ICML.

[29]  Chong Wang,et al.  Stochastic variational inference , 2012, J. Mach. Learn. Res..

[30]  Andre Wibisono,et al.  Streaming Variational Bayes , 2013, NIPS.