Abstract: We introduce novel results for approximate
inference on planar graphicalmodels using
the loop calculus framework. The loop cal-
culus (Chertkov and Chernyak, 2006b) allows
to express the exact partition function Z of
a graphical model as a finite sum of terms
that can be evaluated once the belief prop-
agation (BP) solution is known. In general,
full summation over all correction terms is
intractable. We develop an algorithm for
the approach presented in Chertkov et al.
(2008) which represents an efficient trunca-
tion scheme on planar graphs and a new rep-
resentation of the series in terms of Pfaffians
of matrices. We analyze in detail both the
loop series and the Pfaffian series for mod-
els with binary variables and pairwise in-
teractions, and show that the first term of
the Pfaffian series can provide very accurate
approximations. The algorithm outperforms
previous truncation schemes of the loop series
and is competitive with other state-of-the-art
methods for approximate inference.

Abstract: This paper discusses inference problems in probabilistic graphicalmodels that often occur in a machine learning setting. In particular it presents a unified view of several recently proposed approximation schemes. Expectation consistent approximations and expectation propagation are both shown to be related to Bethe free energies with weak consistency constraints, i.e. free energies where local approximations are only required to agree on certain statistics instead of full marginals.

Abstract: Probabilistic graphicalmodels, and in particular Bayesian networks, are nowa-
days well established as a modeling tool for domains with uncertainty. The capability of dealing with uncertainty is essential for any intelligent system. With BayesLib, we provide a JAVA library for creating, editing and querying Bayesian networks in software applications. Comparing to our previous Bayesian-net libraries, one important difference is that it is now implemented in Java. Therefore, it can be run on any platform with an installed Java Runtime Environment (jre) without recompilation. It has an internal xml parser to parse xml formatted files. This XML format is based on Microsoft Research’s XBN (for "Bayesian network in XML") standard format, and therefore facilitates communication with other systems. Thus, with this software, the Bayesian net can now be easily embedded in an Enterprise or web application stacks, and can be used in a multi user environment.

Abstract: libDAI is a free/open source C++ library (licensed under GPL) that provides
implementations of various (deterministic) approximate inference methods for
discrete graphicalmodels. libDAI supports arbitrary factor graphs with
discrete variables (this includes discrete Markov Random Fields and Bayesian
Networks).

Abstract: Probabilistic graphicalmodels, and in particular Bayesian networks, are nowadays well established as a modeling tool for domains with
uncertainty. In the SHELL outreach project, we have build a Bayesian network model for petrophysical decision support: the system estimates mineral composition based on borehole estimates. The system uses advanced hybrid Monte Carlo methods for inference. Unfortunately, we cannot disclose the system for Shell. Therefore, to demonstrate the method we have built a demonstrator for similar kind of inference in a toy-domain. What is the chemical composition of wine, given taste observations?
Note that this is a toy model for demonstration purposes. The model does not pretend to be realistic in any way.

Abstract: We propose a method for improving approximate inference methods that corrects for the influence of loops in the graphical model. The method is applicable to arbitrary factor graphs, provided that the size of the Markov blankets is not too large. It is an alternative implementation of an idea introduced recently by Montanari and Rizzo (2005). In its simplest form, which amounts to the assumption that no loops are present, the method reduces to the minimal Cluster Variation Method approximation (which uses maximal factors as outer clusters). On the other hand, using estimates of the effect of loops (obtained by some approximate inference algorithm) and applying the Loop Correcting (LC) method usually gives significantly better results than applying the approximate inference algorithm directly without loop corrections. Indeed, we often observe that the loop corrected error is approximately the square of the error of the approximate inference method used to estimate the effect of loops. We compare different variants of the Loop Correcting method with other approximate inference methods on a variety of graphicalmodels, including "real world" networks, and conclude that the LC approach generally obtains the most accurate results.

Abstract: We propose a method to improve approximate inference methods by correcting for the influence of
loops in the graphical model. The method is a generalization and alternative implementation of a recent idea from Montanari and Rizzo (2005). It is applicable to arbitrary factor graphs, provided that
the size of the Markov blankets is not too large. It consists of two steps: (i) an approximate infer-
ence method, for example, belief propagation, is used to approximate cavity distributions for each
variable (i.e., probability distributions on the Markov blanket of a variable for a modified graphical
model in which the factors involving that variable have been removed); (ii) all cavity distributions
are improved by a message-passing algorithm that cancels out approximation errors by imposing
certain consistency constraints. This loop correction (LC) method usually gives significantly better
results than the original, uncorrected, approximate inference algorithm that is used to estimate the
effect of loops. Indeed, we often observe that the loop-corrected error is approximately the square
of the error of the uncorrected approximate inference method. In this article, we compare different
variants of the loop correction method with other approximate inference methods on a variety of
graphicalmodels, including “real world” networks, and conclude that the LC method generally
obtains the most accurate results

Abstract: Probabilistic graphicalmodels, and in particular Bayesian networks, are nowadays well established as a modeling tool for domains with
uncertainty. A drawback is that large, complex graphicalmodels are intractable for exact computation. Therefore there is a lot of research interest in approximate inference.
The lack of open source "reference" implementations hampers progress in research on approximate inference. Methods differ widely in terms of quality and performance characteristics, which also depend in different ways on various properties of the graphicalmodels. Finding the best approximate inference method for a particular application therefore often requires empirical comparisons. However, implementing and debugging these methods takes a lot of time which could otherwise be spent on research. Therefore we have developed libDAI. libDAI is a free/open source C++ library (licensed under GPL) that provides implementations of various (deterministic) approximate inference methods for discrete graphicalmodels. libDAI supports arbitrary `factor graphs` with discrete variables (this includes discrete Markov Random Fields and Bayesian Networks).
This release is an additional contribution to the LibDAI library. This code implements the Z2 algorithm, a particular way of correcting the Belief Propagation (BP) solution, developed in the ICIS project SNN1 (see Gomez (2009), Approximate inference on planar graphs using Loop Calculus and Belief Propagation).

Abstract: Optimal control theory is a mathematical description of how to act optimally
to gain future rewards. In this paper I give an introduction to
deterministic and stochastic control theory; partial observability,
learning and the combined problem of inference and control. Subsequently, I
discuss a new class of non-linear stochastic
control problems for which the Bellman equation becomes linear in the
control and that can be efficiently solved using a path integral.
In this control formalism the central concept of cost-to-go becomes a
free energy and methods and concepts from probabilistic graphicalmodels and statistical physics can be readily applied. I illustrate the
theory with a number of examples.

Abstract: We introduce a computationally efﬁcient method to estimate the validity of the BP method as a function of graph topology, the connectivity strength, frustration and network size. We present numerical results
that demonstrate the correctness of our estimates for the uniform random
model and for a real-world network (“C. Elegans”). Although the method
is restricted to pair-wise interactions, no local evidence (zero “biases”)
and binary variables, we believe that its predictions correctly capture the
limitations of BP for inference and MAP estimation on arbitrary graphicalmodels. Using this approach, we ﬁnd that BP always performs better
than MF. Especially for large networks with broad degree distributions
(such as scale-free networks) BP turns out to signiﬁcantly outperform
MF.