# Gauging Variational Inference

## Abstract

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 meanfield (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.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Korea Advanced Inst. Science and Technology (KAIST), Daejeon (Korea, Republic of)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- OSTI Identifier:
- 1360686

- Report Number(s):
- LA-UR-17-24280

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Computer Science

### Citation Formats

```
Chertkov, Michael, Ahn, Sungsoo, and Shin, Jinwoo.
```*Gauging Variational Inference*. United States: N. p., 2017.
Web. doi:10.2172/1360686.

```
Chertkov, Michael, Ahn, Sungsoo, & Shin, Jinwoo.
```*Gauging Variational Inference*. United States. doi:10.2172/1360686.

```
Chertkov, Michael, Ahn, Sungsoo, and Shin, Jinwoo. Thu .
"Gauging Variational Inference". United States.
doi:10.2172/1360686. https://www.osti.gov/servlets/purl/1360686.
```

```
@article{osti_1360686,
```

title = {Gauging Variational Inference},

author = {Chertkov, Michael and Ahn, Sungsoo and Shin, Jinwoo},

abstractNote = {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 meanfield (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.},

doi = {10.2172/1360686},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu May 25 00:00:00 EDT 2017},

month = {Thu May 25 00:00:00 EDT 2017}

}