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在变量模型的关键环节，变分推断（VI）是常用的方法。然而，当处理复杂后验分布时，VI在实现高对数似然方面可能面临挑战。针对这一局限，我们提出了一种新的变分重要性采样（VIS）方法，该方法能直接估计并最大化对数似然。VIS通过最小化前向$\chi^2$散度，利用最优提议分布来增强对数似然估计。我们将VIS应用于多种流行的潜在变量模型，包括混合模型、变分自动编码器和部分可观测广义线性模型。结果表明，无论是在对数似然还是模型参数估计方面，我们的方法均持续优于最先进的基线方法。