2008-07-09-cseke08a.md

abstract	title	year	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	note	address	container-title	volume	genre	issued	pdf	extras
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an upper and lower bound for it. We give necessary conditions for the Gaussian fractional Bethe free energies to be bounded from below. It turns out that the bounding condition is the same as the pairwise normalizability condition derived by Malioutov et al. (2006) as a sufficient condition for the convergence of the message passing algorithm. By giving a counterexample, we disprove the conjecture in Welling and Teh (2001): even when the Bethe free energy is not bounded from below, it can possess a local minimum to which the minimization algorithms can converge.	Bounds on the Bethe free energy for Gaussian networks	2008	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	cseke08a	0	Bounds on the Bethe free energy for Gaussian networks	97	104	97-104	97	false	Cseke, Botond and Heskes, Tom	given family Botond Cseke given family Tom Heskes	2008-07-09	Reissued by PMLR on 09 October 2024.		Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence	R6	inproceedings	date-parts 2008 7 9	https://raw.githubusercontent.com/mlresearch/r6/main/assets/cseke08a/cseke08a.pdf