Bayesian Nonparametric Inference of Switching Dynamic Linear Models

By Emily B. Fox, Erik B. Sudderth, Michael I. Jordan, Alan S. Willsky. 2010

264 citations recorded by the source corpus.

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR processes with varying autoregressive order. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA stock index and a maneuvering target tracking application.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Composing graphical models with neural networks for structured representations and fast inference (2016, methodology): “This SLDS model combines both continuous and discrete latent variables with rich nonlinear observations.”
Learning human activities and object affordances from RGB-D videos (2012, methodology): “pply dynamic programming techniques to ﬁnd the optimal segmentation. Second, the complex human-object interactions are poorly approximated with a linear dynamical system, therefore techniques such as Fox et al. (2011) cannot be directly applied. Third, the boundary between two sub-activities is ofte”
A Tempt to Unify Heterogeneous Driving Databases using Traffic Primitives (2018, unknown): “Here the sticky hierarchical Dirichlet Process with HMM (HDP-HMM)( γ, α, H ) is employed[23] by adding an extra parameter κ > 0 , thus we have the sticky HDP-HMM as where T is the data length.”
Forecasting realized volatility of agricultural commodity futures with infinite Hidden Markov HAR models (2019, unknown): “The DP process is first proposed by Ferguson (1973) while we use the version of Fox et al. (2011). The DP process is determined by the positive concentration parameter c and the base distribution G0 which has the form G0 = (1− ρ) π + ρδi, where 0 < ρ < 1 denotes the sticky parameter that enhances th”
Granger Causality: A Review and Recent Advances (2021, methodology): “5b, is somewhat similar to the eﬀect of the automatic relevance determination (ARD) priors proposed in the Bayesian nonparametric approach of Fox et al. (2011) for switching dynamic linear models.”
Dynamical Variational Autoencoders: A Comprehensive Review (2020, methodology): “This model can be seen as an extension of the Switching Kalman Filter (Murphy, 1998; Fox et al., 2011) to a DNN-based observation model; see also (Linderman et al.”
Identification of jump Markov linear models using particle filters (2014, methodology): “[16] and [17], making use of Bayesian nonparametric models and mixed integer programming, respectively.”
Spectrally resolved fast transient brain states in electrophysiological data (2016, unknown): “MAR models have also previously been used as observation models for HMMs in the context of speech processing (Juang and Rabiner, 1985), for neural signal analysis (Cassidy and Brown, 2002), and in the signal processing literature (Fox et al., 2011).”
Structured VAEs: Composing Probabilistic Graphical Models and Variational Autoencoders (2016, methodology): “In this paper we illustrate the SVAE using graphical models based on switching linear dynamical systems (SLDS) (Murphy, 2012; Fox et al., 2011).”
Stochastic variational inference (2012, background): “…many variants) (Rabiner, 1989; Fine et al., 1998; Fox et al., 2011b; Paisley and Carin, 2009), Kalman ﬁl-ters (and many variants) (Kalman, 1960; Fox et al., 2011a), factorial models (Ghahramani and Jordan, 1997), hierarchical linear regression models (Gelman and Hill, 2007), hierarchical…”