662 research outputs found
Probabilistic Latent Variable Models as Nonnegative Factorizations
This paper presents a family of probabilistic latent variable models that can be used for analysis of nonnegative data. We show that there are strong ties between nonnegative matrix
factorization and this family, and provide some straightforward extensions which can help in dealing with shift invariances, higher-order decompositions and sparsity constraints. We argue through these extensions that the use of this approach allows for rapid development of complex statistical models for analyzing nonnegative data
Bayesian Conditional Tensor Factorizations for High-Dimensional Classification
In many application areas, data are collected on a categorical response and
high-dimensional categorical predictors, with the goals being to build a
parsimonious model for classification while doing inferences on the important
predictors. In settings such as genomics, there can be complex interactions
among the predictors. By using a carefully-structured Tucker factorization, we
define a model that can characterize any conditional probability, while
facilitating variable selection and modeling of higher-order interactions.
Following a Bayesian approach, we propose a Markov chain Monte Carlo algorithm
for posterior computation accommodating uncertainty in the predictors to be
included. Under near sparsity assumptions, the posterior distribution for the
conditional probability is shown to achieve close to the parametric rate of
contraction even in ultra high-dimensional settings. The methods are
illustrated using simulation examples and biomedical applications
- …