Deep State-Space Gaussian Processes
This work addresses computational bottlenecks in DGP regression for applications like signal processing and astrophysics, though it appears incremental as it builds on existing state-space and DGP frameworks.
The paper tackles the computational complexity of deep Gaussian process (DGP) regression by proposing a state-space approach that represents DGPs as hierarchical systems of linear stochastic differential equations, enabling efficient sequential estimation with linear scaling in measurements. It demonstrates the method on synthetic signals and gravitational wave detection from LIGO data.
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.