New Variational Inference Method Improves Posterior Approximation with Rejection Sampling.

Variational Inference (VI) is a key technique in Bayesian machine learning for approximating complex probability distributions. While recent advancements use neural networks to model implicit distributions, these still face limitations in accuracy due to architectural constraints. This new research proposes Implicit Variational Rejection Sampling (IVRS) to enhance posterior approximation. IVRS integrates implicit distributions with rejection sampling. It employs neural networks to create implicit proposal distributions, then uses a discriminator network for rejection sampling to estimate the density ratio, thereby refining the approximation. The method introduces the Implicit Resampling Evidence Lower Bound (IR-ELBO) to quantify the quality of the resampled distribution and derive a tighter variational lower bound. Experimental results indicate that IVRS surpasses existing variational inference methods in performance.