Automatic Bayesian Density Analysis
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Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for density estimation, even when taking into account mixtures of probabilistic models, are not flexible enough to deal with the uncertainty inherent to real-world data: they are generally restricted to a priori fixed homogeneous likelihood model and to latent variable structures where expressiveness comes at the price of tractability. We propose Automatic Bayesian Density Analysis (ABDA) to go beyond classical mixture model density estimation, casting uncertainty estimation on both the underlying structure in the data, as well as the selection of adequate likelihood models for the data---thus statistical data types of the variable in the data---into a joint inference problem. Specifically, ABDA relies on a hierarchical model explicitly incorporating arbitrarily rich collections of likelihood models at a local level, while capturing global variable interactions by an expressive deep structure built on a sum-product network. Extensive empirical evidence shows that ABDA is more accurate than density estimators in the literature at dealing with both kinds of uncertainties, at modeling and predicting real-world (mixed continuous and discrete) data in both transductive and inductive scenarios, and at recovering the statistical data types.
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