# Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation

arXiv: https://arxiv.org/abs/2404.09113 · HTML: https://mlsanity.com/paper/2404.09113/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2024.

## Built on by (most cited first, 4 of 4)

- [Vertical Consensus Inference for High-Dimensional Random Partition](https://mlsanity.com/paper/2603.27864/) (2026)
- [Mode Collapse of Mean-Field Variational Inference](https://mlsanity.com/paper/2510.17063/) (2025)
- [Anchored Variational Inference for Personalized Sequential Latent-State Models](https://mlsanity.com/paper/2604.23454/) (2026)
- [Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexity](https://mlsanity.com/paper/2608.11486/) (2026)

## Abstract (arXiv)

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as Xi-variational inference (Xi-VI). Xi-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that Xi-variational posteriors effectively recover the true posterior dependency, where the dependence is downweighted by the regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of Xi-variational approximation and how it affects computational considerations, providing a rough characterization of the statistical-computational trade-off in Xi-VI. We also investigate the frequentist properties of Xi-VI and establish results on consistency, asymptotic normality, high-dimensional asymptotics, and algorithmic stability. We provide sufficient criteria for achieving polynomial-time approximate inference using the method. Finally, we demonstrate the practical advantage of Xi-VI over mean-field variational inference on simulated and real data.