Inference-less Density Estimation using Copula Bayesian Networks

TL;DR

This paper introduces a novel inference-less density estimation method using Copula Bayesian Networks, enabling efficient learning of high-dimensional continuous models with missing data by avoiding costly inference procedures.

Contribution

It presents a new learning objective for CBNs that simplifies training with incomplete data, improving computational efficiency and scalability.

Findings

Effective structure and parameter learning demonstrated on real-world datasets.

The approach outperforms traditional inference-based methods in computational speed.

Successfully models complex high-dimensional dependencies with partial observations.

Abstract

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.