Abstract

Variational inference has significantly advanced probabilistic modeling. However, it maximizes a lower bound of the log-likelihood rather than the log-likelihood itself, potentially compromising estimation accuracy. To address this limitation, we propose a novel estimation method based on importance sampling. Our approach efficiently trains an Amortized Adaptive Proposal Distribution (AAPD), which serves as the proposal distribution for importance sampling.

Empirical evaluations demonstrate that our method outperforms existing approaches in latent variable modeling across both synthetic and real-world datasets, showcasing its versatility in diverse applications. Moreover, when applied to mixed-effects modeling, our method addresses key limitations of classical statistical approaches, particularly their difficulty in handling non-Gaussian random effects.