Inference-less Density Estimation using Copula Bayesian Networks

by   Gal Elidan, et al.

We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of such models 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.




Combining Smoothing Spline with Conditional Gaussian Graphical Model for Density and Graph Estimation

Multivariate density estimation and graphical models play important role...

High-dimensional Mixed Graphical Models

While graphical models for continuous data (Gaussian graphical models) a...

Lipschitz Parametrization of Probabilistic Graphical Models

We show that the log-likelihood of several probabilistic graphical model...

On the Geometry of Bayesian Graphical Models with Hidden Variables

In this paper we investigate the geometry of the likelihood of the unkno...

Bayesian Learning of Sum-Product Networks

Sum-product networks (SPNs) are flexible density estimators and have rec...

Discovery and density estimation of latent confounders in Bayesian networks with evidence lower bound

Discovering and parameterising latent confounders represent important an...

Bounds all around: training energy-based models with bidirectional bounds

Energy-based models (EBMs) provide an elegant framework for density esti...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.