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Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling
Shanshan Wu · Alexandros Dimakis · Sujay Sanghavi · Felix Xinnan Yu · Daniel Holtmann-Rice · Dmitry Storcheus · Afshin Rostamizadeh · Sanjiv Kumar

Wed Jun 12 12:10 PM -- 12:15 PM (PDT) @ Room 103
in Optimization »
Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a-priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt to data, while still performing well with the widely used $\ell_1$ decoder. The convex $\ell_1$ decoder prevents gradient propagation as needed in standard gradient-based training. Our method is based on the insight that unrolling the convex decoder into $T$ projected subgradient steps can address this issue. Our method can be seen as a data-driven way to learn a compressed sensing measurement matrix. We compare the empirical performance of 10 algorithms over 6 sparse datasets (3 synthetic and 3 real). Our experiments show that there is indeed additional structure beyond sparsity in the real datasets. Our method is able to discover it and exploit it to create excellent reconstructions with fewer measurements (by a factor of 1.1-3x) compared to the previous state-of-the-art methods. We illustrate an application of our method in learning label embeddings for extreme multi-label classification. Our experiments show that our method is able to match or outperform the precision scores of SLEEC, which is one of the state-of-the-art embedding-based approaches for extreme multi-label learning.
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Author Information

Shanshan Wu (University of Texas at Austin)
Alexandros Dimakis (UT Austin)

Alex Dimakis is an Associate Professor at the Electrical and Computer Engineering department, University of Texas at Austin. He received his Ph.D. in electrical engineering and computer sciences from UC Berkeley. He received an ARO young investigator award in 2014, the NSF Career award in 2011, a Google faculty research award in 2012 and the Eli Jury dissertation award in 2008. He is the co-recipient of several best paper awards including the joint Information Theory and Communications Society Best Paper Award in 2012. His research interests include information theory, coding theory and machine learning.

Sujay Sanghavi (UT Austin)
Felix Xinnan Yu (Google AI)
Daniel Holtmann-Rice (Google Inc)
Dmitry Storcheus (Google Research)
Afshin Rostamizadeh (Google)
Sanjiv Kumar (Google Research, NY)

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