Tight Variational Bounds via Random Projections and I-Projections

TL;DR

This paper introduces a novel approach combining random projections with information projections to improve variational inference, providing theoretical guarantees and empirical improvements in approximation quality for complex models.

Contribution

It proposes a new class of random projections integrated with information projections, offering provable guarantees on approximation quality regardless of model complexity.

Findings

Enhanced partition function estimates on synthetic data

Improved marginal probability estimates on real data

Theoretical guarantees on approximation quality

Abstract

Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on the quality of the approximation obtained. To overcome this issue, we introduce a new class of random projections to reduce the dimensionality and hence the complexity of the original model. In the spirit of random projections, the projection preserves (with high probability) key properties of the target distribution. We show that information projections can be combined with random projections to obtain provable guarantees on the quality of the approximation obtained, regardless of the complexity of the original model. We demonstrate empirically that augmenting mean field with a random projection step dramatically improves partition function and marginal probability estimates, both on synthetic and real world data.