Gaussian Process Convolutional Dictionary Learning
This work addresses the issue of template smoothness in CDL for researchers in signal processing and neuroscience, offering an incremental improvement over existing methods.
The authors tackled the problem of overfitting and lack of smoothness in convolutional dictionary learning (CDL) under low data or SNR conditions by proposing GPCDL, which enforces Gaussian Process priors on templates. They demonstrated through simulation and neural data that GPCDL learns smoother dictionaries with better accuracy and predictive performance compared to unregularized CDL and parametric alternatives, achieving superior results in specific applications.
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.