用准蒙特卡洛方法实现极低维可解释生成模型
Quasi Monte Carlo methods enable extremely low-dimensional deep generative models
- 用准蒙特卡洛积分直接逼近边缘似然，跳过变分下界
- 在1~3维潜空间上优于标准VAE和IWAE
- 适合需要可解释性与可视化分析的场景
本文提出准蒙特卡洛潜在变量模型（QLVMs）：一类专为高维数据寻找极低维且可解释嵌入的深度生成模型。与依赖学习编码器和变分下界的常规方法不同，QLVMs通过随机准蒙特卡洛积分直接逼近边缘似然。尽管在高维空间中计算成本高，但在一维、二维和三维深层潜在变量模型中表现优异。多种数据集上的实验表明，QLVMs在相同潜空间维度下持续优于标准变分自编码器（VAEs）和重要性加权自编码器（IWAEs）。所得嵌入支持透明可视化及后验分析，如非参数密度估计、聚类和测地线路径计算，这些在高维空间中难以验证。虽然该方法计算密集且在复杂数据上难以生成精细细节，但为强调可解释性和潜空间分析的应用提供了有力解决方案。
原文摘要 · Abstract (English)
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.
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