Lifted Variational Inference

Abstract

We present a lifted inference algorithm for relational hybrid graphical models. Hybrid graphical models with continuous and discrete variables naturally represent many real-world applications in robotics, financial market predictions, and weather analysis. Inference with such large models is challenging because relational structures deteriorate rapidly with current inference procedures. The main contribution of this paper is a relational variational-inference lemma that enables factoring density functions into a mixture of independent identically distributed multi-valued Bernoulli trials. This lemma enables a relational factoring step that takes hybrid ground potentials and finds a close to optimal lifted relational model for the joint density. This step is then used for efficient inference without referring to ground random variables. The new method allows us to build various efficient inference algorithms. As an example, we provide a lifted Markov Chain Monte Carlo (MCMC) algorithm that requires fewer samples and generates each sample faster than possible before. We provide an error analysis of the variational method when applying to relational models. Our approach is applicable to general large relational models.