CUED Publications database

Learning stationary time series using Gaussian processes with nonparametric kernels

Tobar, F and Bui, TD and Turner, RE (2015) Learning stationary time series using Gaussian processes with nonparametric kernels. In: UNSPECIFIED pp. 3501-3509..

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Abstract

We introduce the Gaussian Process Convolution Model (GPCM), a two-stage nonparametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametricwindow moving average process and, conditionally, is itself a Gaussian process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian process. One of the main contributions of the paper is to develop a novel variational freeenergy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: UNSPECIFIED
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:32
Last Modified: 23 Nov 2017 03:40
DOI: