A Bayesian belief network models a joint distribution over variables using a DAG to represent variable dependencies and network parameters to represent the conditional probability of each variable given an assignment to its immediate parents. Existing algorithms assume each network parameter is fixed. From a Bayesian perspective, however, these network parameters can be random variables that reflect uncertainty in parameter estimates, arising because the parameters are learned from data, or as they are elicited from uncertain experts. Belief networks are commonly used to compute responses to queriesi.e., return a number for P(H = h | E = e). Parameter uncertainty induces uncertainty in query responses, which are thus themselves random variables. This paper investigates this query response distribution, and shows how to accurately model it for any query and any network structure. In particular, we prove that the query response is asymptotically Gaussian and provide its mean value and asymptotic variance. Moreover, we present an algorithm for computing these quantities that has the same worst-case complexity as inference in general, and also describe straight-line code when the query includes all n variables. We provide empirical evidence that (1) our approximation of the variance is very accurate, and (2) a Beta distribution with these moments provides a very accurate model of the observed query response distribution. We also show how to use this to produce accurate error bars around these responsesi.e., to determine that the response to P(H = h | E = e) is x ± y with confidence 1 − δ.
Quickly detecting an unexpected pathogen can save many lives. In cases of bioterrorism or naturally occurring epidemics, accurate diagnoses may not be made until much of the population has already been jeopardized. The goal of syndromic surveillance is to detect early anomalies that emerge from patient data in a given population area and to note disease patterns before more individuals begin to experience definitive symptoms. We developed a syndromic surveillance approach for generating advance warnings of potential wide-spread diseases as well as identifying demographic attributes that are predictive of the diseases. We describe the Causal Reasoning Engine (CRE), a multipurpose decision support system for diagnosing causes from observed symptoms and predictors. The CRE uses Bayesian inference and machine learning methods and deploys an intuitive explanation-based framework for causal modeling. We also present a diagnostic decision support tool based on the CRE that allows emergency responders to analyze and interrogate findings.
We address the general problem of finding algorithms for efficient, qualitative, point-based temporal reasoning over a set of operations. We consider general reasoners tailored for temporal domains that exhibit a particular structure and introduce such a reasoner based on the series-parallel graph reasoner of Delgrande and Gupta; this reasoner is also an extension of the TimeGraph reasoner of Gerevini and Schubert. Test results indicate that for data with underlying structure, our reasoner performs better than other approaches. When there is no underlying structure in the data, our reasoner still performs better for query answering.
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