Deep state-space Gaussian processes

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-s...

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Bibliographic Details
Published in:Statistics and computing 2021-11, Vol.31 (6), Article 75
Main Authors: Zhao, Zheng, Emzir, Muhammad, Särkkä, Simo
Format: Article
Language:English
Subjects:
Artificial Intelligence
Differential equations
Gaussian process
Gravitational waves
Mathematics and Statistics
Probability and Statistics in Computer Science
Regression
State estimation
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-021-10050-6