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.

翻译：最大化对数似然是学习潜变量模型的关键环节，变分推断是其中常用的方法。然而在处理复杂后验分布时，变分推断可能难以实现高对数似然值。针对这一局限，我们提出了一种新型变分重要性采样方法，可直接估计并最大化对数似然值。该方法通过最小化正向 $\chi^2$ 散度来获得最优建议分布，从而改进对数似然估计。我们将所提方法应用于多种主流潜变量模型，包括混合模型、变分自编码器及部分可观测广义线性模型。实验结果表明，无论是在对数似然值还是模型参数估计方面，我们的方法始终优于现有最优基线方法。