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Simple, efficient, and neural algorithms for sparse coding

Author(s)
Arora, Sanjeev; Ge, Rong; Ma, Tengyu; Moitra, Ankur
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Abstract
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard formulation is as a non-convex optimization problem which is solved in practice by heuristics based on alternating minimization. Re- cent work has resulted in several algorithms for sparse coding with provable guarantees, but somewhat surprisingly these are outperformed by the simple alternating minimization heuristics. Here we give a general framework for understanding alternating minimization which we leverage to analyze existing heuristics and to design new ones also with provable guarantees. Some of these algorithms seem implementable on simple neural architectures, which was the original motivation of Olshausen and Field (1997a) in introducing sparse coding. We also give the first efficient algorithm for sparse coding that works almost up to the information theoretic limit for sparse recovery on incoherent dictionaries. All previous algorithms that approached or surpassed this limit run in time exponential in some natural parameter. Finally, our algorithms improve upon the sample complexity of existing approaches. We believe that our analysis framework will have applications in other settings where simple iterative algorithms are used.
Date issued
2015
URI
http://hdl.handle.net/1721.1/115969
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics
Journal
Proceedings of Machine Learning Research
Publisher
Proceedings of Machine Learning Research
Citation
Arora, Sanjeev et al. "Simple, efficient, and neural algorithms for sparse coding." Proceedings of Machine Learning Research 40 (2015): 113-149 © 2015 The Authors
Version: Final published version
ISSN
1938-7228

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