Abstract: We propose a novel bound on single-variable marginal probabilitydistributions in
factor graphs with discrete variables. The bound is obtained by propagating local
bounds (convex sets of probabilitydistributions) over a subtree of the factor graph,
rooted in the variable of interest. By construction, the method not only bounds
the exact marginal probability distribution of a variable, but also its approximate
Belief Propagation marginal (“belief”). Thus, apart from providing a practical
means to calculate bounds on marginals, our contribution also lies in providing
a better understanding of the error made by Belief Propagation. We show that
our bound outperforms the state-of-the-art on some inference problems arising in
medical diagnosis.

Abstract: We propose a method for improving Belief Propagation (BP) that takes into account the influence of loops in the graphical model. The method is a variation on and generalization of the method recently introduced by Montanari and Rizzo [2005]. It consists of two steps: (i) standard BP is used to calculate cavity distributions for each variable (i.e. probabilitydistributions 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 combined by a messagepassing algorithm to obtain consistent single node marginals. The method is exact if the graphical model contains a single loop. The complexity of the method is exponential in the size of the Markov blankets. The results are very accurate in general: the error is often several orders of magnitude smaller than that of standard BP, as illustrated by numerical experiments.

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., probabilitydistributions 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
graphical models, including “real world” networks, and conclude that the LC method generally
obtains the most accurate results

Abstract: Generation algorithms allow for the generation of Virtual Neurons (VNs) from a small set of morphological properties. The set describes the morphological properties of real neurons in terms of statistical descriptors such as the number of branches and segment lengths (among others). The majority of reconstruction algorithms use the observed properties to estimate the parameters of a priori fixed probabilitydistributions in order to construct statistical descriptors that fit well with the observed data. In this article, we present a non-parametric generation algorithm based on kernel density estimators (KDEs). The new algorithm is called KDE-Neuron and has three advantages over parametric reconstruction algorithms: (1) no a priori specifications about the distributions underlying the real data, (2) peculiarities in the biological data will be reflected in the VNs, and (3) ability to reconstruct different cell types. We experimentally generated motor neurons and granule cells, and statistically validated the obtained results. Moreover, we assessed the quality of the prototype data set and observed that our generated neurons are as good as the prototype data in terms of the used statistical descriptors. The opportunities and limitations of data-driven algorithmic reconstruction of neurons are discussed.