We present the Copula Bayesian Network model for representing multivariate continuous distributions, while taking advantage of the relative ease of estimating univariate distributions. Using a novel copula-based reparameterization of a conditional density, joined with a graph that encodes independencies, our model offers great flexibility in modeling high-dimensional densities, while maintaining control over the form of the univariate marginals. We demonstrate the advantage of our framework for

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... generalization over standard Bayesian networks as well as tree structured copula models for varied real-life domains that are of substantially higher dimension than those typically considered in the copula literature.