# Gauging Variational Inference

arXiv: https://arxiv.org/abs/1703.01056 · HTML: https://mlsanity.com/paper/1703.01056/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2017.

## Built on by (most cited first, 2 of 2)

- [Unsupervised Anomaly Detection in Multivariate Time Series across Heterogeneous Domains](https://mlsanity.com/paper/2503.23060/) (2025)
- [On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks](https://mlsanity.com/paper/2609.23774/) (2026)

## Abstract (arXiv)

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular and successful approaches of a variational type. In this paper, we propose two new variational schemes, coined Gauged-MF (G-MF) and Gauged-BP (G-BP), improving MF and BP, respectively. Both provide lower bounds for the partition function by utilizing the so-called gauge transformation which modifies factors of GM while keeping the partition function invariant. Moreover, we prove that both G-MF and G-BP are exact for GMs with a single loop of a special structure, even though the bare MF and BP perform badly in this case. Our extensive experiments, on complete GMs of relatively small size and on large GM (up-to 300 variables) confirm that the newly proposed algorithms outperform and generalize MF and BP.