Understanding the Bethe Approximation: When and How Can It Go Wrong?
Abstract
Belief propagation is a remarkably effective tool for inference, even when applied to networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free energy, though with no convergence guarantee in general. A variational perspective shows that, compared to exact inference, this minimization employs two forms of approximation: (i) the true entropy is approximated by the Bethe entropy, and (ii) the minimization is performed over a relaxation of the marginal polytope termed the local polytope. Here we explore when and how the Bethe ap-proximation can fail for binary pairwise models by examining each aspect of the approximation, deriving results both analytically and with new experimental methods. 1
Cite
Text
Weller et al. "Understanding the Bethe Approximation: When and How Can It Go Wrong?." Conference on Uncertainty in Artificial Intelligence, 2014.Markdown
[Weller et al. "Understanding the Bethe Approximation: When and How Can It Go Wrong?." Conference on Uncertainty in Artificial Intelligence, 2014.](https://mlanthology.org/uai/2014/weller2014uai-understanding/)BibTeX
@inproceedings{weller2014uai-understanding,
title = {{Understanding the Bethe Approximation: When and How Can It Go Wrong?}},
author = {Weller, Adrian and Tang, Kui and Jebara, Tony and Sontag, David A.},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2014},
pages = {868-877},
url = {https://mlanthology.org/uai/2014/weller2014uai-understanding/}
}