Inference-less Density Estimation using Copula Bayesian Networks
Uncertainty in Artificial Intelligence (UAI)
We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of suchmodels depends on our ability to perform efﬁcient inference, and can be prohibitive even for relatively modest domains. Recently, we introduced the Copula Bayesian Network (CBN) density model - a ﬂexible framework that captures complex high-dimensional dependency structures while offering direct control over the univariate marginals, leading to improved generalization. In this work we show that the CBN model also offers signiﬁcant computational advantages when training data is partially
observed. Concretely, we leverage on the specialized form of the model to derive a computationally amenable learning objective that is a lower bound on the log-likelihood function. Importantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribution, thus facilitating practical learning of highdimensional densities. We demonstrate the effectiveness of our approach for learning the structure and parameters of a CBN model for two reallife continuous domains.