Designed measurements for vector count data

Liming Wang, David Carlson, Miguel Dias Rodrigues, David Wilcox, Robert Calderbank, Lawrence Carin

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

16 Scopus citations

Abstract

We consider design of linear projection measurements for a vector Poisson signal model. The projections are performed on the vector Poisson rate,X ∈ ℝ+ n, and the observed data are a vector of counts, Y ∈ ℤ + m. The projection matrix is designed by maximizing mutual information between Y and X, I(Y;X). When there is a latent class label C ∈ {1; : : : ;L} associated with X, we onsider the mutual information with respect to Y and C, I(Y ;C). New analytic expressions for the gradient of I(Y ;X) and I(Y ;C) are presented, with gradient performed with respect to the measurement matrix. Connections are made to the more widely studied Gaussian measurement model. Example results are presented for compressive topic modeling of a document corpora (word counting), and hyperspectral compressive sensing for chemical classification (photon counting).
Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
StatePublished - Jan 1 2013
Externally publishedYes

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