This paper introduces quasi-Monte Carlo latent variable models (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard approaches, which rely on a learned encoder and variational lower bounds, QLVMs directly approximate the marginal likelihood by randomized quasi-Monte Carlo integration. While this brute force approach has drawbacks in higher-dimensional spaces, we find that it excels in fitting one, two, and three dimensional deep latent variable models. Empirical results on a range of datasets show that QLVMs consistently outperform conventional variational autoencoders (VAEs) and importance weighted autoencoders (IWAEs) with matched latent dimensionality. The resulting embeddings enable transparent visualization and post hoc analyses such as nonparametric density estimation, clustering, and geodesic path computation, which are nontrivial to validate in higher-dimensional spaces. While our approach is compute-intensive and struggles to generate fine-scale details in complex datasets, it offers a compelling solution for applications prioritizing interpretability and latent space analysis.

翻译：本文提出准蒙特卡洛隐变量模型（QLVM）：一类专门用于发现高维数据集极低维可解释嵌入表示的深度生成模型。与依赖学习编码器和变分下界的标准方法不同，QLVM通过随机化准蒙特卡洛积分直接逼近边缘似然。虽然这种暴力方法在高维空间中存在缺陷，但我们发现其在拟合一维、二维和三维深度隐变量模型时表现卓越。在多个数据集上的实证结果表明，在隐变量维度匹配的情况下，QLVM始终优于传统变分自编码器（VAE）和重要性加权自编码器（IWAE）。所得嵌入表示支持透明的可视化及事后分析，如非参数密度估计、聚类和测地路径计算——这些分析在高维空间中难以有效验证。尽管我们的方法计算密集且在复杂数据集的精细细节生成方面存在局限，但其为优先考虑可解释性和隐空间分析的应用提供了极具价值的解决方案。