Expectation Propagation in Gaussian Process Dynamical Systems

By Marc Peter Deisenroth, Shakir Mohamed. 2012

48 citations recorded by the source corpus.

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos, or neural recordings are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian process dynamical systems as a rich model class that is appropriate for such an analysis. We present a new approximate message-passing algorithm for Bayesian state estimation and inference in Gaussian process dynamical systems, a non-parametric probabilistic generalization of commonly used state-space models. We derive our message-passing algorithm using Expectation Propagation and provide a unifying perspective on message passing in general state-space models. We show that existing Gaussian filters and smoothers appear as special cases within our inference framework, and that these existing approaches can be improved upon using iterated message passing. Using both synthetic and real-world data, we demonstrate that iterated message passing can improve inference in a wide range of tasks in Bayesian state estimation, thus leading to improved predictions and more effective decision making.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

Effective Bayesian Modeling of Groups of Related Count Time Series (2014, positive): “More recently, the expectation propagation (EP) algorithm of Minka (2001), a generalization of ADF, has proved successful in a number of non-linear filtering and smoothing problems (Heskes & Zoeter, 2002; Yu et al., 2006; Deisenroth & Mohamed, 2012).”
A Unifying Framework for Sparse Gaussian Process Approximation using Power Expectation Propagation (2016, unknown): “Following (Girard et al., 2003; Deisenroth and Mohamed, 2012; Bui et al., 2016), we approximate the second integral w.”
Robust and Efficient Transfer Learning with Hidden Parameter Markov Decision Processes (2017, methodology): “The HiP-MDP approximates the underlying dynamical system of the task through the training of a Gaussian Process dynamical model (Deisenroth and Mohamed 2012),(Wang, Fleet, and Hertzmann 2005) where only a small portion of the true system dynamics may be observed as is common in partially observable…”
Transfer Learning Across Patient Variations with Hidden Parameter Markov Decision Processes (2016, background): “The HiP-MDP approximates the underlying dynamical system of the task through the training of a Gaussian Process dynamical model [6, 27] where only a small portion of the true system dynamics may be observed as is common in partially observable Markov Decision Processes (POMDP) [12].”
Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC (2013, unknown): “000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053”