## Dieter Jaksch awarded with the 2018 Thomas Young Medal and Prize

for "his contributions to theoretical proposals enabling the study of non-equilibrium quantum many-body dynamics with unprecedented microscopic control in ultra-cold atoms, and establishing them as a quantum technologies platform".

Read more## Jean-Marc Triscone awarded a honorary doctorate

by the Norwegian University of Science and Technology (NTNU)

Read more# Publication Detail / Abstract

## Exact Inference on Gaussian Graphical Models of Arbitrary Topology using Path-Sums

published in the Journal of Machine Learning Research, April 2016

> Full text via publisher
We present the path-sum formulation for exact statistical inference of marginals on Gaussian graphical models of arbitrary topology. The path-sum formulation gives the covariance between each pair of variables as a branched continued fraction of finite depth and breadth. Our method originates from the closed- form resummation of infinite families of terms of the walk-sum representation of the covariance matrix. We prove that the path- sum formulation always exists for models whose covariance matrix is positive definite: i.e. it is valid for both walk-summable and non-walk-summable graphical models of arbitrary topology. We show that for graphical models on trees the path-sum formulation is equivalent to Gaussian belief propagation. We also recover, as a corollary, an existing result that uses determinants to calculate the covariance matrix. We show that the path-sum formulation formulation is valid for arbitrary partitions of the inverse covariance matrix. We give detailed examples demonstrating our results.

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