论文标题
深度州空间高斯流程
Deep State-Space Gaussian Processes
论文作者
论文摘要
本文涉及一种状态空间的深高斯过程（DGP）回归。我们通过层次将转换的高斯过程（GP）先验构建在层次结构中下一个高斯过程的长度尺度和幅度上。状态空间方法的想法是将DGP表示为线性随机微分方程（SDE）的非线性分层系统，其中每个SDE都对应于条件GP。然后，DGP回归问题成为状态估计问题，我们可以通过使用状态空间DGP的Markov属性有效地估算状态。计算复杂性相对于测量数量线性缩放。基于此，我们制定了状态空间图以及贝叶斯过滤和平滑解决方案，以解决DGP回归问题。我们证明了提出的模型和方法在合成非平稳信号上的性能，并将状态空间DGP应用于Ligo测量中的重力波。
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.
