Evaluating Influence Diagrams using LIMIDs

We present a new approach to the solution of decision problems formulated as influence diagrams. The approach converts the influence diagram into a simpler structure, the LImited Memory Influence Diagram (LIMID), where only the requisite information for the computation of optimal policies is depicted. Because the requisite information is explicitly represented in the diagram, the evaluation procedure can take advantage of it. In this paper we show how to convert an influence diagram to a LIMID and describe the procedure for finding an optimal strategy. Our approach can yield significant savings of memory and computational time when compared to traditional methods.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

Diagnosis of Multiple Faults: A Sensitivity Analysis

We compare the diagnostic accuracy of three diagnostic inference models: the simple Bayes model, the multimembership Bayes model, which is isomorphic to the parallel combination function in the certainty-factor model, and a model that incorporates the noisy OR-gate interaction. The comparison is done on 20 clinicopathological conference (CPC) cases from the American Journal of Medicine-challenging cases describing actual patients often with multiple disorders. We find that the distributions produced by the noisy OR model agree most closely with the gold-standard diagnoses, although substantial differences exist between the distributions and the diagnoses. In addition, we find that the multimembership Bayes model tends to significantly overestimate the posterior probabilities of diseases, whereas the simple Bayes model tends to significantly underestimate the posterior probabilities. Our results suggest that additional work to refine the noisy OR model for internal medicine will be worthwhile.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

An Anytime Algorithm for Decision Making under Uncertainty

We present an anytime algorithm which computes policies for decision problems represented as multi-stage influence diagrams. Our algorithm constructs policies incrementally, starting from a policy which makes no use of the available information. The incremental process constructs policies which includes more of the information available to the decision maker at each step. While the process converges to the optimal policy, our approach is designed for situations in which computing the optimal policy is infeasible. We provide examples of the process on several large decision problems, showing that, for these examples, the process constructs valuable (but sub-optimal) policies before the optimal policy would be available by traditional methods.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998

Evaluating influence diagrams with decision circuits

Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we introduce decision circuits as a means to exploit the local structure usually found in decision problems and to improve the performance of influence diagram analysis. This work builds on the probabilistic inference algorithms using arithmetic circuits to represent Bayesian belief networks [Darwiche, 2003]. Once compiled, these arithmetic circuits efficiently evaluate probabilistic queries on the belief network, and methods have been developed to exploit both the global and local structure of the network. We show that decision circuits can be constructed in a similar fashion and promise similar benefits.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007

Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians

The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG Bayesian networks, and there exists a commercial implementation of this algorithm. However, this algorithm can only be used for MoG BNs. Some limitations of such networks are as follows. All continuous chance variables must have conditional linear Gaussian distributions, and discrete chance nodes cannot have continuous parents. The methods described in this paper will enable us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This includes networks with continuous chance nodes with non-Gaussian distributions, networks with no restrictions on the topology of discrete and continuous variables, networks with conditionally deterministic variables that are a nonlinear function of their continuous parents, and networks with continuous chance variables whose variances are functions of their parents.Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006

A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables

In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is value in the unit interval [0,1] which denotes a lower bound on the belief on A in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all many-valued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy propositional variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy propositional variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

Neural-Symbolic Learning and Reasoning: A Survey and Interpretation

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.Comment: 58 pages, work in progres

Management of Uncertainty in the Multi-Level Monitoring and Diagnosis of the Time of Flight Scintillation Array

We present a general architecture for the monitoring and diagnosis of large scale sensor-based systems with real time diagnostic constraints. This architecture is multileveled, combining a single monitoring level based on statistical methods with two model based diagnostic levels. At each level, sources of uncertainty are identified, and integrated methodologies for uncertainty management are developed. The general architecture was applied to the monitoring and diagnosis of a specific nuclear physics detector at Lawrence Berkeley National Laboratory that contained approximately 5000 components and produced over 500 channels of output data. The general architecture is scalable, and work is ongoing to apply it to detector systems one and two orders of magnitude more complex.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991

Probabilistic State-Dependent Grammars for Plan Recognition

Techniques for plan recognition under uncertainty require a stochastic model of the plan-generation process. We introduce Probabilistic State-Dependent Grammars (PSDGs) to represent an agent's plan-generation process. The PSDG language model extends probabilistic context-free grammars (PCFGs) by allowing production probabilities to depend on an explicit model of the planning agent's internal and external state. Given a PSDG description of the plan-generation process, we can then use inference algorithms that exploit the particular independence properties of the PSDG language to efficiently answer plan-recognition queries. The combination of the PSDG language model and inference algorithms extends the range of plan-recognition domains for which practical probabilistic inference is possible, as illustrated by applications in traffic monitoring and air combat.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

An Uncertainty Framework for Classification

We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain classifiers that optimize the cross-entropy function. In the possibilistic framework, we obtain classifiers that maximize the interclass margin. Furthermore, we show that the support vector machine is a sub-class of these maximum-margin classifiers.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000