Nonlinear information-theoretic compressive measurement design

Liming Wang, Abolfazl Razi, Miguel Dias Rodrigues, Robert Calderbank, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We investigate design of general nonlinear functions for mapping high-dimensional data into a lower-dimensional (compressive) space. The nonlinear measurements are assumed contaminated by additive Gaussian noise. Depending on the application, we are either interested in recovering the high-dimensional data from the nonlinear compressive measurements, or performing classification directly based on these measurements. The latter case corresponds to classification based on nonlinearly constituted and noisy features. The nonlinear measurement functions are designed based on constrained mutual- information optimization. New analytic results are developed for the gradient of mutual information in this setting, for arbitrary input-signal statistics. We make connections to kernel-based methods, such as the support vector machine. Encouraging results are presented on multiple datasets, for both signal recovery and classification. The nonlinear approach is shown to be particularly valuable in high-noise scenarios.
Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)rasmussen@ptd.net
Pages2896-2907
Number of pages12
ISBN (Print)9781634393973
StatePublished - Jan 1 2014
Externally publishedYes

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