# Principled Parallel Mean-Field Inference for Discrete Random Fields

arXiv: https://arxiv.org/abs/1511.06103 · HTML: https://mlsanity.com/paper/1511.06103/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2015.

## Built on by (most cited first, 6 of 6)

- [Data Pruning by Information Maximization](https://mlsanity.com/paper/2506.01701/) (2025)
- [Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyond](https://mlsanity.com/paper/2110.14759/) (2021)
- [Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization](https://mlsanity.com/paper/2602.07632/) (2026)
- [Monotone deep Boltzmann machines](https://mlsanity.com/paper/2307.04990/) (2023)
- [Benchmarking Performance of Deep Learning Model for Material Segmentation on Two HPC Systems](https://mlsanity.com/paper/2307.14921/) (2023)
- [UnfoldCRF: Structured Mask Refinement with Image-Conditioned Latent Regions](https://mlsanity.com/paper/2609.33996/) (2026)

## Abstract (arXiv)

Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice, various parallel techniques are used, which either rely on ad-hoc smoothing with heuristically set parameters, or put strong constraints on the type of models. In this paper, we propose a novel proximal gradient-based approach to optimizing the variational objective. It is naturally parallelizable and easy to implement. We prove its convergence, and then demonstrate that, in practice, it yields faster convergence and often finds better optima than more traditional mean-field optimization techniques. Moreover, our method is less sensitive to the choice of parameters.