PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Inference-less Density Estimation using Copula Bayesian Networks
Gal Elidan
Uncertainty in Artificial Intelligence (UAI) Volume 26, 2010.

Abstract

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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7059
Deposited By:Gal Elidan
Deposited On:25 February 2011