# Gaussian Process Convolutional Dictionary Learning

arXiv: https://arxiv.org/abs/2104.00530 · HTML: https://mlsanity.com/paper/2104.00530/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 28 Mar 2021.

## Builds on (most cited first, 6 of 6)

- [Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization](https://mlsanity.com/paper/1310.7991/) (2013)
- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains](https://mlsanity.com/paper/1604.03053/) (2016)
- [Sparsity Based Poisson Denoising with Dictionary Learning](https://mlsanity.com/paper/1309.4306/) (2013)
- [Group Invariant Dictionary Learning](https://mlsanity.com/paper/2007.07550/) (2020)
- [PSF Estimation in Crowded Astronomical Imagery as a Convolutional Dictionary Learning Problem](https://mlsanity.com/paper/2101.01268/) (2021)

## Built on by (most cited first, 1 of 1)

- [Mixture Model Auto-Encoders: Deep Clustering through Dictionary Learning](https://mlsanity.com/paper/2110.04683/) (2021)

## Abstract (arXiv)

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.