TY - GEN

T1 - Designed measurements for vector count data

AU - Wang, Liming

AU - Carlson, David

AU - Rodrigues, Miguel Dias

AU - Wilcox, David

AU - Calderbank, Robert

AU - Carin, Lawrence

N1 - Generated from Scopus record by KAUST IRTS on 2021-02-09

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84899007047&partnerID=8YFLogxK

M3 - Conference contribution

BT - Advances in Neural Information Processing Systems

PB - Neural information processing systems foundation

ER -