Gaussian Process Convolutional Dictionary Learning

TL;DR

GPCDL introduces a Gaussian Process prior into convolutional dictionary learning to enforce smoothness in learned templates, improving accuracy and interpretability especially in low SNR scenarios.

Contribution

It presents a flexible, theoretically grounded framework that incorporates Gaussian Process priors into CDL, enhancing template smoothness and predictive performance.

Findings

GPCDL learns smoother, more accurate dictionaries than unregularized methods.

The approach improves predictive performance in neural spiking data analysis.

The method is adaptable to different smoothness assumptions via kernel choice.

Abstract

Convolutional dictionary learning (CDL), the problem of estimating shift-invariant templates from data, is typically conducted in the absence of a prior/structure on the templates. In data-scarce or low signal-to-noise ratio (SNR) regimes, learned templates overfit the data and lack smoothness, which can affect the predictive performance of downstream tasks. To address this limitation, we propose GPCDL, a convolutional dictionary learning framework that enforces priors on templates using Gaussian Processes (GPs). With the focus on smoothness, we show theoretically that imposing a GP prior is equivalent to Wiener filtering the learned templates, thereby suppressing high-frequency components and promoting smoothness. We show that the algorithm is a simple extension of the classical iteratively reweighted least squares algorithm, independent of the choice of GP kernels. This property allows one to experiment flexibly with different smoothness assumptions. Through simulation, we show that GPCDL learns smooth dictionaries with better accuracy than the unregularized alternative across a range of SNRs. Through an application to neural spiking data, we show that GPCDL learns a more accurate and visually-interpretable smooth dictionary, leading to superior predictive performance compared to non-regularized CDL, as well as parametric alternatives.