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Connections between Gaussian Process Regression, Kalman filtering and RTS Smoothing

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If you have a question about this talk, please contact Carl Edward Rasmussen.

As already pointed out in the discussion of O’Hagan’s 1978 article, in a limited sense, Gaussian process regression and Kalman filtering can be considered as different formulations of the one and same estimation problem. Strictly speaking this is only true in the case of one-dimensional input space and we also need a Rauch-Tung-Striebel smoothing step to compute the full posterior. Another point of view is that Gaussian process regression can be interpreted as a single update step of an infinite-dimensional Kalman filter operating in a Hilbert space, and thus a natural approach to inference in spatio-temporal Gaussian processes is to formulate it as an infinite-dimensional state estimation problem. In this talk I will analyze the connections between Gaussian process regression, Kalman filtering and smoothing, and discuss the infinite-dimensional Kalman filtering approach to spatio-temporal Gaussian process regression.

This talk is part of the Machine Learning Reading Group @ CUED series.

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