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.
翻译:本文涉及对深高斯进程(DGP)回归的州- 空间方法。 我们通过在等级结构中将高斯进程(GP)前端的长度尺度和尺度置于高斯进程下一个层次的长度尺度和尺度上,来构建DGP。 州- 空间方法的构想是将DGP作为线性随机差异方程式(SDEs)的非线性等级系统,其中每个SDE都相当于有条件的GP。 DGP回归问题随后成为一个州估算问题。 我们可以使用州- 空间DGP的Markov属性,以顺序方法对状态进行高效估算。 计算的复杂性尺度与测量数量线性。 在此基础上,我们制定州- 空间 MAP 以及巴伊西亚过滤和顺利解决DGP回归问题的办法。 我们展示了拟议的合成非静止信号模型和方法的性能,并应用州- 空间 DGP 来检测LIGP 测量的重力波。