DMCA
Cemgil, “Probabilistic latent tensor factorization
| Venue: | in LVA/ICA, 2010 |
| Citations: | 13 - 0 self |
BibTeX
@INPROCEEDINGS{Yılmaz_cemgil,“probabilistic,
author = {Y. Kenan Yılmaz and A. Taylan Cemgil},
title = {Cemgil, “Probabilistic latent tensor factorization},
booktitle = {in LVA/ICA, 2010},
year = {},
pages = {346--353}
}
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Abstract
Abstract. We develop a probabilistic framework for multiway analysis of high dimensional datasets. By exploiting a link between graphical models and tensor factorization models we can realize any arbitrary tensor factorization structure, and many popular models such as CP or TUCKER models with Euclidean error and their non-negative variants with KL error appear as special cases. Due to the duality between exponential families and Bregman divergences, we can cast the problem as inference in a model with Gaussian or Poisson components, where tensor factorisation reduces to a parameter estimation problem. We derive the generic form of update equations for multiplicative and alternating least squares. We also propose a straightforward matricisation procedure to convert element-wise equations into the matrix forms to ease implementation and parallelisation.
Keyphrases
probabilistic latent tensor factorization tensor factorisation reduces update equation tucker model exponential family straightforward matricisation procedure special case element-wise equation probabilistic framework kl error euclidean error poisson component matrix form multiway analysis non-negative variant bregman divergence parameter estimation problem arbitrary tensor factorization structure tensor factorization model many popular model generic form high dimensional datasets graphical model
