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Designed Measurements for Vector Count Data
Liming Wang · David Carlson · Miguel Rodrigues · David Wilcox · Robert Calderbank · Lawrence Carin

Sat Dec 07 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor
We consider design of linear projection measurements for a vector Poisson signal model. The projections are performed on the vector Poisson rate, $X\in\mathbb{R}_+^n$, and the observed data are a vector of counts, $Y\in\mathbb{Z}_+^m$. The projection matrix is designed by maximizing mutual information between $Y$ and $X$, $I(Y;X)$. When there is a latent class label $C\in\{1,\dots,L\}$ associated with $X$, we consider 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).

Author Information

Liming Wang (Duke University)
David Carlson (Duke University)
Miguel Rodrigues (UCL)
David Wilcox (Purdue University)
Robert Calderbank (Duke University)
Lawrence Carin (KAUST)

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