Notice
Optimal Convex and Nonconvex Regularizers for a Data Source
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Descriptif
Regularization is a widespread technique used in statistical estimation problems that helps to capture low dimensional structure in the data and improve signal recovery. For computational and geometric reasons, many regularizers are induced by certain classes of convex bodies, such as polyhedral regularizers in dictionary learning. We propose a generalization of this approach by formulating an optimization problem over the space of star bodies to learn the best regularizer for a given dataset. Through a connection with a dual mixed volume inequality for star bodies, we provide a characterization of the population risk minimizers of this problem and establish strong consistency of the empirical risk minimizers. Based on joint work with Oscar Leong, Yong Sheng Soh, and Venkat Chandrasekaran.
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