# Deep State-Space Gaussian Processes

arXiv: https://arxiv.org/abs/2008.04733 · HTML: https://mlsanity.com/paper/2008.04733/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2020.

## Built on by (most cited first, 9 of 9)

- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [Deep Horseshoe Gaussian Processes](https://mlsanity.com/paper/2403.01737/) (2024)
- [Non-stationary Gaussian process discriminant analysis with variable selection for high-dimensional functional data](https://mlsanity.com/paper/2109.14171/) (2021)
- [Temporal Gaussian Process Regression in Logarithmic Time](https://mlsanity.com/paper/2102.09964/) (2021)
- [Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularization](https://mlsanity.com/paper/2105.09695/) (2021)
- [Variational Elliptical Processes](https://mlsanity.com/paper/2311.12566/) (2023)
- [Probabilistic Estimation of Instantaneous Frequencies of Chirp Signals](https://mlsanity.com/paper/2205.06306/) (2022)
- [From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learning](https://mlsanity.com/paper/2503.05799/) (2025)

## Abstract (arXiv)

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.