Factorizing Multivariate Function Classes

Factorizing Multivariate Polynomials Over Finite Fields

Making problems tractable on big data via preprocessing with polylog-size output

To provide a dichotomy between those queries that can be made feasible on big data after appropriate preprocessing and those for which preprocessing does not help, Fan et al. developed the u-tractability theory. This theory provides a formal foundation for understanding the tractability of query classes in the context of big data. Along this line, we introduce a novel notion of u′-tractability ...

The Variational Gaussian Approximation Revisited

The variational approximation of posterior distributions by multivariate gaussians has been much less popular in the machine learning community compared to the corresponding approximation by factorizing distributions. This is for a good reason: the gaussian approximation is in general plagued by an Omicron(N)(2) number of variational parameters to be optimized, N being the number of random vari...

On some factorization problems

We consider three notions of factorization arising in different frameworks: factorizing languages, factorization of the natural numbers, factorizing codes. A language X ⊆ A∗ is called factorizing if there exists a language Y ⊆ A∗ such that XY = A∗ and the product is unambiguous. This is a decidable property for recognizable languages X . If we consider the particular case of unary alphabets, we...

Bayesian factorization of joint categorical distributions for relational data and classical conditioning models

We explore the problem of infering latent structure in the joint probability of categorical variables by factorizing them into a latent representation for categories and a weight matrix that encodes a PMF, mapping these latent representations to the mass associated with seeing categories appear together. The prior for latent category representations is either the Chinese Restaurant Process (CRP...