Learning Nonparametric Volterra Kernels with Gaussian Processes
Learning Nonparametric Volterra Kernels with Gaussian Processes
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发表时间：
2021-06
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通讯作者：
M. Ross;M. Smith;Mauricio A Álvarez
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作者：
M. Ross;M. Smith;Mauricio A Álvarez
本文介绍了一种非线性算子的非参数贝叶斯学习方法，通过使用 Volterra 级数和用高斯过程 (GP) 表示的核，我们将其称为非参数 Volterra 核模型 (NVKM)。当算子的输入函数不可观察并且具有 GP 先验时，NVKM 构成了单输出回归和多输出回归的强大方法，并且可以被视为非线性和非参数潜在力模型。当观察输入函数时，NVKM可用于进行贝叶斯系统识别。我们利用 GP 显式函数有效采样的最新进展，通过 Volterra 级数映射过程实现，而无需求助于数值积分，从而通过双随机变分推理实现可扩展性，并避免了对输出过程的高斯近似的需要。我们使用标准基准演示了模型在多输出回归和系统识别方面的性能。
This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels model (NVKM). When the input function to the operator is unobserved and has a GP prior, the NVKM constitutes a powerful method for both single and multiple output regression, and can be viewed as a nonlinear and nonparametric latent force model. When the input function is observed, the NVKM can be used to perform Bayesian system identification. We use recent advances in efficient sampling of explicit functions from GPs to map process realisations through the Volterra series without resorting to numerical integration, allowing scalability through doubly stochastic variational inference, and avoiding the need for Gaussian approximations of the output processes. We demonstrate the performance of the model for both multiple output regression and system identification using standard benchmarks.