Modelling Non-Smooth Signals with Complex Spectral Structure

• URL: http://arxiv.org/abs/2203.06997v1
• Date: Mon, 14 Mar 2022 11:02:38 GMT
• Title: Modelling Non-Smooth Signals with Complex Spectral Structure
• Authors: Wessel P. Bruinsma and Martin Tegn\'er and Richard E. Turner
• Abstract summary: We redesign the GPCM model to induce a richer distribution over the spectrum with relaxed assumptions about smoothness. We also propose a more effective variational inference scheme, going beyond the mean-field assumption. The proposed variations of the GPCM are validated in experiments on synthetic and real-world data, showing promising results.
• Score: 26.749261270690432
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth signals. Moreover, inference in the GPCM currently requires (1) a mean-field assumption, resulting in poorly calibrated uncertainties, and (2) a tedious variational optimisation of large covariance matrices. We redesign the GPCM model to induce a richer distribution over the spectrum with relaxed assumptions about smoothness: the Causal Gaussian Process Convolution Model (CGPCM) introduces a causality assumption into the GPCM, and the Rough Gaussian Process Convolution Model (RGPCM) can be interpreted as a Bayesian nonparametric generalisation of the fractional Ornstein-Uhlenbeck process. We also propose a more effective variational inference scheme, going beyond the mean-field assumption: we design a Gibbs sampler which directly samples from the optimal variational solution, circumventing any variational optimisation entirely. The proposed variations of the GPCM are validated in experiments on synthetic and real-world data, showing promising results.

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