NoodL: Provable online dictionary learning and sparse coding

Sirisha Rambhatla, Xingguo Li, Jarvis Haupt

Research output: Contribution to conferencePaper

Abstract

We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are unknown, the corresponding optimization is inherently non-convex. This was a major challenge until recently, when provable algorithms for dictionary learning were proposed. Yet, these provide guarantees only on the recovery of the dictionary, without explicit recovery guarantees on the coefficients. Moreover, any estimation error in the dictionary adversely impacts the ability to successfully localize and estimate the coefficients. This potentially limits the utility of existing provable dictionary learning methods in applications where coefficient recovery is of interest. To this end, we develop NOODL: a simple Neurally plausible alternating Optimization-based Online Dictionary Learning algorithm, which recovers both the dictionary and coefficients exactly at a geometric rate, when initialized appropriately. Our algorithm, NOODL, is also scalable and amenable for large scale distributed implementations in neural architectures, by which we mean that it only involves simple linear and non-linear operations. Finally, we corroborate these theoretical results via experimental evaluation of the proposed algorithm with the current state-of-the-art techniques.

Original languageEnglish (US)
StatePublished - Jan 1 2019
Event7th International Conference on Learning Representations, ICLR 2019 - New Orleans, United States
Duration: May 6 2019May 9 2019

Conference

Conference7th International Conference on Learning Representations, ICLR 2019
CountryUnited States
CityNew Orleans
Period5/6/195/9/19

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Rambhatla, S., Li, X., & Haupt, J. (2019). NoodL: Provable online dictionary learning and sparse coding. Paper presented at 7th International Conference on Learning Representations, ICLR 2019, New Orleans, United States.