# Deep state-space Gaussian processes

Zheng Zhao*, Muhammad Emzir, Simo Särkkä

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

17 Lataukset (Pure)

## Abstrakti

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.

Alkuperäiskieli Englanti 75 26 STATISTICS AND COMPUTING 31 6 https://doi.org/10.1007/s11222-021-10050-6 Julkaistu - marraskuuta 2021 A1 Julkaistu artikkeli, soviteltu

## Sormenjälki

Sukella tutkimusaiheisiin 'Deep state-space Gaussian processes'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.