TY - GEN

T1 - Probabilistic matrix addition

AU - Agovic, Amrudin

AU - Banerjee, Arindam

AU - Chatterjee, Singdhansu B

PY - 2011/10/7

Y1 - 2011/10/7

N2 - We introduce Probabilistic Matrix Addition (PMA) for modeling real-valued data matrices by simultaneously capturing covariance structure among rows and among columns. PMA additively combines two latent matrices drawn from two Gaussian Processes respectively over rows and columns. The resulting joint distribution over the observed matrix does not factorize over entries, rows, or columns, and can thus capture intricate dependencies in the matrix. Exact inference in PMA is possible, but involves inversion of large matrices, and can be computationally prohibitive. Efficient approximate inference is possible due to the sparse dependency structure among latent variables. We propose two families of approximate inference algorithms for PMA based on Gibbs sampling and MAP inference. We demonstrate the effectiveness of PMA for missing value prediction and multi-label classification problems.

AB - We introduce Probabilistic Matrix Addition (PMA) for modeling real-valued data matrices by simultaneously capturing covariance structure among rows and among columns. PMA additively combines two latent matrices drawn from two Gaussian Processes respectively over rows and columns. The resulting joint distribution over the observed matrix does not factorize over entries, rows, or columns, and can thus capture intricate dependencies in the matrix. Exact inference in PMA is possible, but involves inversion of large matrices, and can be computationally prohibitive. Efficient approximate inference is possible due to the sparse dependency structure among latent variables. We propose two families of approximate inference algorithms for PMA based on Gibbs sampling and MAP inference. We demonstrate the effectiveness of PMA for missing value prediction and multi-label classification problems.

UR - http://www.scopus.com/inward/record.url?scp=80053449894&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:80053449894

SN - 9781450306195

T3 - Proceedings of the 28th International Conference on Machine Learning, ICML 2011

SP - 1025

EP - 1032

BT - Proceedings of the 28th International Conference on Machine Learning, ICML 2011

T2 - 28th International Conference on Machine Learning, ICML 2011

Y2 - 28 June 2011 through 2 July 2011

ER -