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Rich and complex time-series data, such as those generated from engineering sys- tems, 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 appropriate for such analysis. In particular, we present a message passing algorithm for approximate inference in GPDSs based on expectation propagation. By phrasing inference as a general mes- sage passing problem, we iterate forward-backward smoothing. We obtain more accurate posterior distributions over latent structures, resulting in improved pre- dictive performance compared to state-of-the-art GPDS smoothers, which are spe- cial cases of our general iterative message passing algorithm. Hence, we provide a unifying approach within which to contextualize message passing in GPDSs.
Author Information
Marc Deisenroth (University College London)

Professor Marc Deisenroth is the DeepMind Chair in Artificial Intelligence at University College London and the Deputy Director of UCL's Centre for Artificial Intelligence. He also holds a visiting faculty position at the University of Johannesburg and Imperial College London. Marc's research interests center around data-efficient machine learning, probabilistic modeling and autonomous decision making. Marc was Program Chair of EWRL 2012, Workshops Chair of RSS 2013, EXPO-Co-Chair of ICML 2020, and Tutorials Co-Chair of NeurIPS 2021. In 2019, Marc co-organized the Machine Learning Summer School in London. He received Paper Awards at ICRA 2014, ICCAS 2016, and ICML 2020. He is co-author of the book [Mathematics for Machine Learning](https://mml-book.github.io) published by Cambridge University Press (2020).
Shakir Mohamed (DeepMind)

Shakir Mohamed is a senior staff scientist at DeepMind in London. Shakir's main interests lie at the intersection of approximate Bayesian inference, deep learning and reinforcement learning, and the role that machine learning systems at this intersection have in the development of more intelligent and general-purpose learning systems. Before moving to London, Shakir held a Junior Research Fellowship from the Canadian Institute for Advanced Research (CIFAR), based in Vancouver at the University of British Columbia with Nando de Freitas. Shakir completed his PhD with Zoubin Ghahramani at the University of Cambridge, where he was a Commonwealth Scholar to the United Kingdom. Shakir is from South Africa and completed his previous degrees in Electrical and Information Engineering at the University of the Witwatersrand, Johannesburg.
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