Structured Nonparametric Variational Inference for Dependent Latent Modeling

2026-06-13

AI Summary

Traditional variational inference is constrained by the mean-field assumption, which fails to capture complex dependencies among latent variables and cannot accurately approximate posterior distributions with arbitrary shapes and bounded support. This work proposes a Structured Nonparametric Variational Inference (SN-VI) framework that, for the first time, integrates multivariate splines with nonparametric variational inference. By doing so, SN-VI overcomes the limitations of the mean-field approximation while automatically identifying the dependency structure among latent variables, thereby enabling flexible, dependency-preserving approximations of complex posteriors. The method enjoys theoretical asymptotic consistency guarantees and demonstrates significant improvements in generative model performance on both synthetic and real high-dimensional data—such as in computer vision and spatial transcriptomics—effectively uncovering coupled biological signals.

Abstract

Variational inference (VI) is a core engine of modern AI, enabling scalable approximate Bayesian learning and uncertainty-aware training of large probabilistic and generative models. In this paper, we propose Structured Nonparametric Variational Inference (SN-VI), a novel framework for modeling complex dependencies among latent variables in posterior approximation, leveraging multivariate spline techniques. Unlike traditional methods that rely on the mean-field assumption, SN-VI preserves intricate latent variable dependencies, providing a flexible and accurate approximation of posteriors with arbitrary shapes. We establish rigorous theoretical guarantees, including the derivation of the lower bound for the variational objective and proof of asymptotic consistency in posterior estimation. To facilitate practical implementation, we develop an algorithm that automatically identifies dependent latent variables and their underlying dependence structure, without requiring manual specification. Simulation studies validate the effectiveness of SN-VI in approximating posterior distributions with bounded support and complex dependencies. The proposed method has been successfully applied to high-dimensional structured data, including computer vision datasets and spatial transcriptomics. In these applications, SN-VI demonstrates improved generative model performance and effectively uncovers coupled biological signals through the learned dependency structure.

Problem

• variational inference
• latent variable dependencies
• posterior approximation
• nonparametric methods
• structured data

Innovation

• Structured Nonparametric Variational Inference
• latent variable dependencies
• multivariate splines
• asymptotic consistency
• posterior approximation