In recent years, we have witnessed fast advancement of data-acquisition techniques in many areas, including biological domains, engineering and social sciences. As a result, new statistical and machine learning techniques are needed to help us develop a better understanding of complexities underlying large, noisy data sets. Networks have been commonly used to abstract noisy data and provide an insight into regularities and dependencies between observed variables. For example, in a biological study, nodes of the network can represent genes in one organism and edges can represent associations or regulatory dependencies among genes. In a social domain, nodes of a network can represent actors and edges can represent interactions between actors. Recent popular techniques for modeling and exploring networks are based on the structure estimation in the probabilistic graphical models, specifically, Markov Random Fields (MRFs).

In recent years extreme value mixture models have been proposed as a combination of a distribution with a "bulk part" below threshold and a generalized Pareto distribution (GPD) in the tail. Different distributions have been proposed for modelling the "bulk part" where the threshold is a parameter to be estimated. The first approach which allow us a transition between the bulk and tail parts is provided by Frigessi, Haug & Harvard (2003). Frigessi et al. (2003) uses a Weibull distribution in the bulk part, a GPD for the tail and the location-scale Cauchy cdf in the transition function and the authors use maximum likelihood estimation. However in the Frigessi et al. (2003) approach maximum likelihood estimation in the bulk part could produce multiple modes and hence some identifiability problems. Behrens, Lopez & Gammerman (2004) and Carreu & Bengio (2009) consider Gamma and Normal distributions respectively in the bulk part.

This article presents the state-of-the-art in optimal solution methods for decentralized partially observable Markov decision processes (Dec-POMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A* (GMAA*) algorithm, which reduces the problem to a tree of one-shot collaborative Bayesian games (CBGs), we describe several advances that greatly expand the range of Dec-POMDPs that can be solved optimally. First, we introduce lossless incremental clustering of the CBGs solved by GMAA*, which achieves exponential speedups without sacrificing optimality. Second, we introduce incremental expansion of nodes in the GMAA* search tree, which avoids the need to expand all children, the number of which is in the worst case doubly exponential in the node's depth. This is particularly beneficial when little clustering is possible. In addition, we introduce new hybrid heuristic representations that are more compact and thereby enable the solution of larger Dec-POMDPs. We provide theoretical guarantees that, when a suitable heuristic is used, both incremental clustering and incremental expansion yield algorithms that are both complete and search equivalent. Finally, we present extensive empirical results demonstrating that GMAA*-ICE, an algorithm that synthesizes these advances, can optimally solve Dec-POMDPs of unprecedented size.

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form decisions from incomplete data in diagnostic problems has highlighted probabilistic methods [5] which compute posterior probabilities from prior distributions in a way similar to Bayes Rule, and thus are called Bayesian methods. This paper documents the use of a Bayesian method in a real time problem which is similar to medical diagnosis in that there is a need to form decisions and take some action without complete knowledge of conditions in the problem domain. This particular method has a limitation which is discussed.

We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final probabilities of interest with the allocation of a complete resource fraction. The approach allows a reasoner to exchange arbitrary quantities of computational resource for incremental gains in inference quality. As such, bounded conditioning holds promise as a useful inference technique for reasoning under the general conditions of uncertain and varying reasoning resources. The algorithm solves a probabilistic bounding problem in complex belief networks by breaking the problem into a set of mutually exclusive, tractable subproblems and ordering their solution by the expected effect that each subproblem will have on the final answer. We introduce the algorithm, discuss its characterization, and present its performance on several belief networks, including a complex model for reasoning about problems in intensive-care medicine.

This paper describes a generalization of previous methods for constructing tree-structured belief network with hidden variables. The major new feature of the described method is the ability to produce a tree decomposition even when there are errors in the correlation data among the input variables. This is an important extension of existing methods since the correlational co efficients usually cannot be measured with precision. The technique involves using a greedy search algorithm that locally minimizes an error function.

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the conclusions are much weaker than those computed from complete probability distributions, they are still valuable for suggesting potential actions, eliminating obviously inferior plans, identifying important tradeoffs, and explaining probabilistic models.

The JIEDDO Analytic Decision Engine (JADE) is a flexible software toolkit for studying the performance of sensor configurations for the detection of person-borne explosive compounds and other threat substances. JADE is designed to enable performance and tradeoff analyses between different, user-specified scenarios with given sensor placements and data fusion networks. JADE contains fundamental physics-based models of several sensor technologies of interest, such as nonlinear acoustic and radar-based detectors, along with a data fusion system that we focus on in this paper. The fusion system consists of a static component that combines the decisions of individual sensors at a fixed point in time, and a dynamic, time-dependent component that in turn fuses the outputs of the static structure at different times. The static component is based on a probabilistic graphical model, or Bayesian network, and accepts probability matrices from the physicsbased sensor models as inputs (the details of which are abstracted from the fusion system). Its outputs are fed into the dynamic fusion framework, which is based on sequential hypothesis testing and produces performance metrics for the entire, fused sensor configuration. The purpose of the system is to determine the performance of a given fusion structure, as opposed to doing fusion on actual measurements.

We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors, and the residual scale. Using a factorized posterior approximation we derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse linear models. The approach enables flexible definition of weight priors with different sparseness properties such as independent Laplace priors with a common scale parameter or Gaussian automatic relevance determination (ARD) priors with different relevance parameters for all inputs. The approach can be extended beyond standard activation functions and NN model structures to form flexible nonlinear predictors from multiple sparse linear models. The effects of the hierarchical priors and the predictive performance of the algorithm are assessed using both simulated and real-world data. Comparisons are made to two alternative models with ARD priors: a Gaussian process with a NN covariance function and marginal maximum a posteriori estimates of the relevance parameters, and a NN with Markov chain Monte Carlo integration over all the unknown model parameters.

In this paper, the feasibility of using finite totally ordered probability models under Alelinnas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how these problems arise. The investigation shows that a finite probability model may be of very limited usage.