Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

通过最小化前向χ^2散度来优化建议分布以增强对数似然估计，我们引入了一种称为变分重要性抽样（VIS）的新方法，实现了直接估计和最大化对数似然。将VIS应用于各种流行的潜变量模型，包括混合模型、变分自编码器和部分可观测广义线性模型，结果显示我们的方法在对数似然和模型参数估计方面始终优于最先进的基准模型。

基于$χ^2$散度的变分重要采样