BayesNDE: Bayesian Generative Modeling for Neural Density Estimation

2026-09-30

AI Summary

This study addresses the limitations of existing neural density estimation methods, which rely on invertible network architectures and computationally expensive Jacobian determinant calculations, thereby constraining model flexibility and scalability. To overcome these challenges, this work proposes a Jacobian-free density estimation framework grounded in Bayesian generative modeling. By employing variational inference to approximate latent variable posteriors for constructing adaptive proposal distributions, and integrating bridge sampling techniques for precise density estimation, the approach directly transforms generative models into flexible density estimators. A key contribution is that this method entirely eliminates the dependence on invertible networks. Experimental results demonstrate significant improvements in both density estimation accuracy and structural recovery on synthetic datasets, while also exhibiting superior performance in anomaly detection tasks across real-world scenarios.

Abstract

Density estimation is a fundamental problem in statistics and machine learning. In this work, we introduce BayesNDE, a neural density estimator based on Bayesian generative modeling. BayesNDE learns a Bayesian generative model and evaluates its density without requiring invertible networks or Jacobian-determinant computation. For each observation, it infers a sample-specific latent posterior to construct an adaptive proposal that focuses computation on regions contributing most to its density. Bridge sampling then combines samples from this proposal with separate posterior samples to estimate the density. Experiments on nonlinear and multimodal synthetic datasets show improved estimation of density values and better recovery of the density structure compared to the state-of-the-art neural density estimators. Applications to real-world datasets further demonstrate improved anomaly detection. Together, these results highlight BayesNDE as a flexible and effective neural density estimator, demonstrating how posterior inference can turn generative models into tools for density estimation. The code and tutorials are available at https://github.com/liuq-lab/BayesNDE.

Problem

• Density Estimation
• Neural Density Estimation
• Bayesian Generative Modeling
• Anomaly Detection

Innovation

• Bayesian generative modeling
• Neural density estimation
• Latent posterior inference
• Adaptive proposal
• Bridge sampling