Learning Nonparametric Volterra Kernels with Gaussian Processes
This provides a method for researchers and practitioners in machine learning and systems engineering to perform nonlinear, nonparametric Bayesian analysis on complex data, though it is incremental as it builds on existing Volterra series and Gaussian process frameworks.
The paper tackles the problem of learning nonlinear operators nonparametrically by introducing the nonparametric Volterra kernels model (NVKM), which uses Gaussian processes to represent Volterra series kernels, enabling scalable Bayesian inference for regression and system identification tasks.
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.