#5742. Deep state-space Gaussian processes

July 2026publication date
Proposal available till 11-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Statistics and Probability;
Statistics, Probability and Uncertainty;
Computational Theory and Mathematics;
Theoretical Computer Science;
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Abstract:
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.
Keywords:
Deep Gaussian process; Gaussian filtering and smoothing; Gaussian process regression; Gravitational wave detection; Maximum a posteriori estimate; Particle filter; State space; Stochastic differential equation

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