Copula Bayesian Networks
Gal Elidan · 2010
Multivariate real-valued distributions are of paramount importance in a variety of fields ranging from computational biology and neuro-science to economics to climatology. Choosing and estimating a useful form for the marginal distribution of each variable in the domain is often a straightforward task. In contrast, aside from the normal representation, few univariate distributions have a convenient multivariate generalization. Indeed, modeling and estimation of flexible (skewed, multi-modal, heavy tailed) high-dimensional distributions is still a formidable challenge. In this work we present a novel multivariate density model that is a marriage of the copula and Bayesian networks frameworks. Our construction offers great flexibility in modeling high dimensional distributions and results in consistent generalization advantages in varied domains. In addition, our model gives rise to an efficient mean-field like approximate inference procedure, facilitating practical structure learning in non-linear domains. Copulas [11, 15] are functions that link given (or estimated) univariate marginals into a joint distribution. This allows us to robustly estimate marginals (e.g. using a nonparametric approach), and then use only few parameters to capture the dependencies.