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Electrical and Computer Engineering
Computer Science
Dean of Engineering

ECE Seminar Series: Identifying Good Regularizers(698/699)

Thursday, March 23, 2017
4:00 PM  to 5:00 PM

1064  Duncan Hall
Rice University
6100 Main St
Houston, Texas, USA

Regularization techniques are widely employed in the solution of inverse problems in data analysis and scientific computing due to their effectiveness in addressing difficulties due to ill-posedness. In their most common manifestation, these methods take the form of penalty functions added to the objective in optimization-based approaches for solving inverse problems. The purpose of the penalty function is to induce a desired structure in the solution, and these functions are specified based on prior domain-specific expertise. For example, regularization is useful for promoting smoothness, sparsity, low energy, and large entropy in solutions to inverse problems in image analysis, statistical model selection, and the geosciences. We consider the problem of identifying good regularizers in two different contexts. First, we describe a general framework to transform notions of structure (based on domain expertise) to convex regularizers. Our method generalizes convex relaxations based on the L1 norm and the nuclear norm that are widely used for identifying sparse vectors and low-rank matrices in problems such as compressed sensing, the lasso, and matrix completion. Next, we consider the problem of learning suitable regularizers from data in settings in which precise domain knowledge is not directly available; the objective is to identify a regularizer to promote the type of structure contained in the data. To address this challenge, we present an approach to learn convex regularizers from data that can be computed efficiently via semidefinite programming. The regularizers obtained using both these frameworks lead to tractable convex relaxations for a broad range of inverse problems. We discuss the theoretical attributes of these techniques and we provide experimental demonstrations of their utility in practice.

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