An MDL framework for sparse coding and dictionary learning

TL;DR

This paper introduces an MDL-based framework for sparse coding and dictionary learning that automatically determines model parameters, improving applications like image denoising, classification, and low-rank matrix recovery without manual tuning.

Contribution

It presents a parameter-free, MDL-based approach to sparse modeling and dictionary learning, enabling natural incorporation of prior information and broad application scope.

Findings

Parameter-free algorithms for image denoising and classification

Effective low-rank matrix recovery in video applications

Enhanced model selection via MDL principle

Abstract

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as under-fitting or over-fitting given sets of data, are still not well characterized in the literature. As a result, the success of sparse modeling depends on hand-tuning critical parameters for each data and application. This work aims at addressing this by providing a practical and objective characterization of sparse models by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to model selection in statistical inference. The resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which, by virtue of the MDL principle, are completely parameter free. Furthermore, such framework allows to incorporate additional prior information to existing models, such as Markovian dependencies, or to define completely new problem formulations, including in the matrix analysis area, in a natural way. These virtues will be demonstrated with parameter-free algorithms for the classic image denoising and classification problems, and for low-rank matrix recovery in video applications.