Tight Variational Bounds via Random Projections and I-Projections
This addresses a fundamental limitation in variational inference for probabilistic modeling, offering a theoretically sound solution with practical benefits.
The paper tackles the problem of poor approximation quality in variational inference by introducing random projections to reduce model complexity while preserving key distribution properties, resulting in provable guarantees and dramatic empirical improvements in partition function and marginal probability estimates.
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.