Title: Quasi-Monte Carlo Methods Enable Extremely Low-Dimensional Deep Generative Models
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: representation learning, quasi monte-carlo integration, generative modeling, variational autoencoder

Abstract: 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, lattice-LVMs 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 latent variable models.
Empirical results on a range of datasets show that QLVMs consistently outperform conventional variational autoencoders (VAEs) with matched latent dimensionality, and even rival VAEs with larger latent spaces.
The resulting embeddings enable transparent visualization and *post hoc* analyses such as nonparametric density estimation, clustering, and geodesic path computation, which are nontrivial in higher-dimensional spaces.
While our approach is limited by computational requirements and struggles to generate fine-scale details in complex datasets, it offers a compelling solution for applications prioritizing interpretability and latent space analysis.

TL;DR: We introduce a new latent variable model that allows easy exploration of scientific datasets