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.

A significant problem in designing mobile robot control systems involves coping with the uncertainty that arises in moving about in an unknown or partially unknown environment and relying on noisy or ambiguous sensor data to acquire knowledge about that environment. We describe a control system that chooses what activity to engage in next on the basis of expectations about how the information re- turned as a result of a given activity will improve 2 its knowledge about the spatial layout of its environment. Certain of the higher-level components of the control system are specified in terms of probabilistic decision models whose output is used to mediate the behavior of lower-level control components responsible for movement and sensing.

Many Artificial Intelligence systems depend on the agent's updating its beliefs about the world on the basis of experience. Experiments constitute one type of experience, so scientific methodology offers a natural environment for examining the issues attendant to using this class of evidence. This paper presents a framework which structures the process of using scientific data from research reports for the purpose of making decisions, using decision analysis as the basis for the structure and using medical research as the general scientific domain. The structure extends the basic influence diagram for updating belief in an object domain parameter of interest by expanding the parameter into four parts: those of the patient, the population, the study sample, and the effective study sample. The structure uses biases to perform the transformation of one parameter into another, so that, for instance, selection biases, in concert with the population parameter, yield the study sample parameter. The influence diagram structure provides decision theoretic justification for practices of good clinical research such as randomized assignment and blindfolding of care providers. The model covers most research designs used in medicine: case-control studies, cohort studies, and controlled clinical trials, and provides an architecture to separate clearly between statistical knowledge and domain knowledge. The proposed general model can be the basis for clinical epidemiological advisory systems, when coupled with heuristic pruning of irrelevant biases; of statistical workstations, when the computational machinery for calculation of posterior distributions is added; and of meta-analytic reviews, when multiple studies may impact on a single population parameter.

Influence diagrams are a directed graph representation for uncertainties as probabilities. The graph distinguishes between those variables which are under the control of a decision maker (decisions, shown as rectangles) and those which are not (chances, shown as ovals), as well as explicitly denoting a goal for solution (value, shown as a rounded rectangle.