Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture transient dependencies, such as, gene regulatory dependencies throughout a developmental cycle of an organism. Kolar et al (2010b) proposed a method based on kernel-smoothing l1-penalized logistic regression for estimating time-varying networks from nodal observations collected from a time-series of observational data. In this paper, we establish conditions under which the proposed method consistently recovers the structure of a time-varying network. This work complements previous empirical findings by providing sound theoretical guarantees for the proposed estimation procedure. For completeness, we include numerical simulations in the paper.

In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible allowing us posterior density estimation and posterior inference for high quantiles. The model works well even for small sample sizes and in the absence of prior information. We evaluate the performance of the proposed model through a simulation study. Finally, the proposed model is applied to a real environmental data.

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 present a new algorithm for finding maximum a-posterior) (MAP) assignments of values to belief networks. The belief network is compiled into a network consisting only of nodes with boolean (i.e. only 0 or 1) conditional probabilities. The MAP assignment is then found using a best-first search on the resulting network. We argue that, as one would anticipate, the algorithm is exponential for the general case, but only linear in the size of the network for poly trees.

One of the most important aspects in any treatment of uncertain information is the rule of combination for updating the degrees of uncertainty. The theory of belief functions uses the Dempster rule to combine two belief functions defined by independent bodies of evidence. However, with limited dependency information about the accumulated belief the Dempster rule may lead to unsatisfactory results. The present study suggests a method to determine the accumulated belief based on the premise that the information gain from the combination process should be minimum. This method provides a mechanism that is equivalent to the Bayes rule when all the conditional probabilities are available and to the Dempster rule when the normalization constant is equal to one. The proposed principle of minimum information gain is shown to be equivalent to the maximum entropy formalism, a special case of the principle of minimum cross-entropy. The application of this principle results in a monotonic increase in belief with accumulation of consistent evidence. The suggested approach may provide a more reasonable criterion for identifying conflicts among various bodies of evidence.

We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson [14]. We develop a variety of logical notions for probabilistic reasoning, including soundness, completeness justification; and convergence: reduction of a theory to a simpler logical class. We argue that a bound view is especially useful for describing the semantics of probabilistic knowledge representation and for describing intermediate states of probabilistic inference and updating. We show that the Dempster-Shafer theory of evidence is formally identical to a special case of our generalized probabilistic logic. Our paradigm thus incorporates both Bayesian "rule-based" approaches and avowedly non-Bayesian "evidential" approaches such as MYCIN and DempsterShafer. We suggest how to integrate the two "schools", and explore some possibilities for novel synthesis of a variety of ideas in probabilistic reasoning.

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.

We describe a methodology for modeling the performance of decision-level data fusion between different sensor configurations, implemented as part of the JIEDDO Analytic Decision Engine (JADE). We first discuss a Bayesian network formulation of classical probabilistic data fusion, which allows elementary fusion structures to be stacked and analyzed efficiently. We then present an extension of the Wald sequential test for combining the outputs of the Bayesian network over time. We discuss an algorithm to compute its performance statistics and illustrate the approach on some examples. This variant of the sequential test involves multiple, distinct stages, where the evidence accumulated from each stage is carried over into the next one, and is motivated by a need to keep certain sensors in the network inactive unless triggered by other sensors.

The intelligent reformulation or restructuring of a belief network can greatly increase the efficiency of inference. However, time expended for reformulation is not available for performing inference. Thus, under time pressure, there is a tradeoff between the time dedicated to reformulating the network and the time applied to the implementation of a solution. We investigate this partition of resources into time applied to reformulation and time used for inference. We shall describe first general principles for computing the ideal partition of resources under uncertainty. These principles have applicability to a wide variety of problems that can be divided into interdependent phases of problem solving. After, we shall present results of our empirical study of the problem of determining the ideal amount of time to devote to searching for clusters in belief networks. In this work, we acquired and made use of probability distributions that characterize (1) the performance of alternative heuristic search methods for reformulating a network instance into a set of cliques, and (2) the time for executing inference procedures on various belief networks. Given a preference model describing the value of a solution as a function of the delay required for its computation, the system selects an ideal time to devote to reformulation.

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.