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There is a widespread need for statistical methods that can analyzehigh-dimensional datasets with- out imposing restrictive or opaque modelingassumptions. This paper describes a domain-general data analysis method calledCrossCat. CrossCat infers multiple non-overlapping views of the data, eachconsisting of a subset of the variables, and uses a separate nonparametricmixture to model each view. CrossCat is based on approximately Bayesianinference in a hierarchical, nonparamet- ric model for data tables. This modelconsists of a Dirichlet process mixture over the columns of a data table inwhich each mixture component is itself an independent Dirichlet process mixtureover the rows; the inner mixture components are simple parametric models whoseform depends on the types of data in the table. CrossCat combines strengths ofmixture modeling and Bayesian net- work structure learning. Like mixturemodeling, CrossCat can model a broad class of distributions by positing latentvariables, and produces representations that can be efficiently conditioned andsampled from for prediction. Like Bayesian networks, CrossCat represents thedependencies and independencies between variables, and thus remains accuratewhen there are multiple statistical signals. Inference is done via a scalableGibbs sampling scheme; this paper shows that it works well in practice. Thispaper also includes empirical results on heterogeneous tabular data of up to 10million cells, such as hospital cost and quality measures, voting records,unemployment rates, gene expression measurements, and images of handwrittendigits. CrossCat infers structure that is consistent with accepted findings andcommon-sense knowledge in multiple domains and yields predictive accuracycompetitive with generative, discriminative, and model-free alternatives.

CrossCat: A Fully Bayesian Nonparametric Method for Analyzing Heterogeneous, High Dimensional Data