This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the sum-product Belief Propagation (BP) algorithm of artificial intelligence. The Bethe approximation reduces the problem of computing the partition function in a graphical model to that of solving a set of non-linear equations, so-called the Bethe equation. On the other hand, the BP algorithm is...

Recently, simplified graphical modeling approaches based on low-order conditional (in-)dependence calculations have received attention because of their potential to model gene regulatory networks. Such methods are able to reconstruct large-scale gene networks with a small number of experimental measurements, at minimal computational cost. However, unlike Bayesian networks, current low-order gra...

Last time we discussed the Chow-Liu algorithm, which uses mutual information estimation to learn the best tree graphical model representing data. Recall that, in each iteration, the Chow-Liu algorithm greedily adds an edge between the pair of unconnected variables exhibiting the greatest (estimated) mutual information. Because we only add edges between unconnected variables, (unconditional) mut...

This paper studies precision matrix estimation for multiple related Gaussian graphical models from a dataset consisting of different classes, based upon the formulation of this problem as group graphical lasso. In particular, this paper proposes a novel hybrid covariance thresholding algorithm that can effectively identify zero entries in the precision matrices and split a large joint graphical...

Introduction: This research was meant to provide a model for COPD diagnosis and to classify the cases into phenotypes; General COPD, Chronic bronchitis, Emphysema, and the Asthmatic COPD using a Bayesian Network (BN). Methods: The model was constructed through developing the Bayesian Network structure and instantiating the parameters for each of the variables. In order to validate the achiev...

We propose a new stochastic search algorithm for Gaussian graphical models called the mode oriented stochastic search. Our algorithm relies on the existence of a method to accurately and efficiently approximate the marginal likelihood associated with a graphical model when it cannot be computed in closed form. To this end, we develop a new Laplace approximation method to the normalizing constan...

The Stationary Subspace Analysis (SSA) algorithm linearly factorizes a high-dimensional time series into stationary and non-stationary components. The SSA Toolbox is a platform-independent efficient stand-alone implementation of the SSA algorithm with a graphical user interface written in Java, that can also be invoked from the command line and from Matlab. The graphical interface guides the us...

Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two character­ izations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal graphical representation of any given decom­ posable model. We also propose an algorithm for le...

Universal Akers Arrays (UAA) allow to realize arbitrary Boolean function directly in cellular layout but are very area-ine cient. This paper presents an extension of UAAs, called \Lattice Diagrams" in which Shannon, Positive and Negative Davio expansions are used in nodes. An e cient method of mappig arbitrary multi-output incompletely speci ed functions to them is presented. We prove that with...