Improving Variational Methods via Pairwise Linear Response Identities
Abstract
Inference methods are often formulated as variational approximations: these approxima- tions allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the variational parameters, and in so doing inference of marginal probability distributions is improved. For the Bethe approximation and its generalizations, improvements are achieved with simple choices of the constraints. The approximations are presented as variational frameworks; iterative procedures related to message passing are provided for finding the minima.
Cite
Text
Raymond and Ricci-Tersenghi. "Improving Variational Methods via Pairwise Linear Response Identities." Journal of Machine Learning Research, 2017.Markdown
[Raymond and Ricci-Tersenghi. "Improving Variational Methods via Pairwise Linear Response Identities." Journal of Machine Learning Research, 2017.](https://mlanthology.org/jmlr/2017/raymond2017jmlr-improving/)BibTeX
@article{raymond2017jmlr-improving,
title = {{Improving Variational Methods via Pairwise Linear Response Identities}},
author = {Raymond, Jack and Ricci-Tersenghi, Federico},
journal = {Journal of Machine Learning Research},
year = {2017},
pages = {1-36},
volume = {18},
url = {https://mlanthology.org/jmlr/2017/raymond2017jmlr-improving/}
}