Optimizing Epistemic Model Checking Using Conditional Independence (Extended Abstract)

This paper shows that conditional independence reasoning can be applied to optimize epistemic model checking, in which one verifies that a model for a number of agents operating with imperfect information satisfies a formula expressed in a modal multi-agent logic of knowledge. The optimization has been implemented in the epistemic model checker MCK. The paper reports experimental results demonstrating that it can yield multiple orders of magnitude performance improvements.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Independence, Conditionality and Structure of Dempster-Shafer Belief Functions

Several approaches of structuring (factorization, decomposition) of Dempster-Shafer joint belief functions from literature are reviewed with special emphasis on their capability to capture independence from the point of view of the claim that belief functions generalize bayes notion of probability. It is demonstrated that Zhu and Lee's {Zhu:93} logical networks and Smets' {Smets:93} directed acyclic graphs are unable to capture statistical dependence/independence of bayesian networks {Pearl:88}. On the other hand, though Shenoy and Shafer's hypergraphs can explicitly represent bayesian network factorization of bayesian belief functions, they disclaim any need for representation of independence of variables in belief functions. Cano et al. {Cano:93} reject the hypergraph representation of Shenoy and Shafer just on grounds of missing representation of variable independence, but in their frameworks some belief functions factorizable in Shenoy/Shafer framework cannot be factored. The approach in {Klopotek:93f} on the other hand combines the merits of both Cano et al. and of Shenoy/Shafer approach in that for Shenoy/Shafer approach no simpler factorization than that in {Klopotek:93f} approach exists and on the other hand all independences among variables captured in Cano et al. framework and many more are captured in {Klopotek:93f} approach.%Comment: 1994 internal repor

Lazy Evaluation of Symmetric Bayesian Decision Problems

Solving symmetric Bayesian decision problems is a computationally intensive task to perform regardless of the algorithm used. In this paper we propose a method for improving the efficiency of algorithms for solving Bayesian decision problems. The method is based on the principle of lazy evaluation - a principle recently shown to improve the efficiency of inference in Bayesian networks. The basic idea is to maintain decompositions of potentials and to postpone computations for as long as possible. The efficiency improvements obtained with the lazy evaluation based method is emphasized through examples. Finally, the lazy evaluation based method is compared with the hugin and valuation-based systems architectures for solving symmetric Bayesian decision problems.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Probabilistic Argumentation and Information Algebras of Probability Potentials on Families of Compatible Frames

Probabilistic argumentation is an alternative to causal modeling with Bayesian networks. Probabilistic argumentation structures (PAS) are defined on families of compatible frames (f.c.f). This is a generalization of the usual multivariate models based on families of variables. The crucial relation of conditional independence between frames of a f.c.f is introduced and shown to form a quasi-separoid, a weakening of the well-known structure of a separoid. It is shown that PAS generate probability potentials on the frames of the f.c.f. The operations of aggregating different PAS and of transport of a PAS from one frame to another induce an algebraic structure on the family of potentials on the f.c.f, an algebraic structure which is similar to valuation algebras related to Bayesian networks, but more general. As a consequence the well-known local computation architectures of Bayesian networks for inference apply also for the potentials on f.c.f. Conditioning and conditionals can be defined for potentials and it is shown that these concepts satisfy similar properties as conditional probability distributions. Finally a max/prod algebra between potentials is defined and applied to find most probable configurations for a factorization of potentials

Possibilistic Conditioning and Propagation

We give an axiomatization of confidence transfer - a known conditioning scheme - from the perspective of expectation-based inference in the sense of Gardenfors and Makinson. Then, we use the notion of belief independence to "filter out" different proposal s of possibilistic conditioning rules, all are variations of confidence transfer. Among the three rules that we consider, only Dempster's rule of conditioning passes the test of supporting the notion of belief independence. With the use of this conditioning rule, we then show that we can use local computation for computing desired conditional marginal possibilities of the joint possibility satisfying the given constraints. It turns out that our local computation scheme is already proposed by Shenoy. However, our intuitions are completely different from that of Shenoy. While Shenoy just defines a local computation scheme that fits his framework of valuation-based systems, we derive that local computation scheme from II(,8) = tI(,8 I a) * II(a) and appropriate independence assumptions, just like how the Bayesians derive their local computation scheme.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Testing Implication of Probabilistic Dependencies

Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation may require exponential time in some cases, this technique is a powerful tool for establishing nontrivial theoretical results. More importantly, this approach provides valuable insight into the intriguing connection between relational databases and probabilistic reasoning systems.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Optimizing compilation with preservation of structural code coverage metrics to support software testing

Code-coverage-based testing is a widely-used testing strategy with the aim of providing a meaningful decision criterion for the adequacy of a test suite. Code-coverage-based testing is also mandated for the development of safety-critical applications; for example, the DO178b document requires the application of the modified condition/decision coverage. One critical issue of code-coverage testing is that structural code coverage criteria are typically applied to source code whereas the generated machine code may result in a different code structure because of code optimizations performed by a compiler. In this work, we present the automatic calculation of coverage profiles describing which structural code-coverage criteria are preserved by which code optimization, independently of the concrete test suite. These coverage profiles allow to easily extend compilers with the feature of preserving any given code-coverage criteria by enabling only those code optimizations that preserve it. Furthermore, we describe the integration of these coverage profile into the compiler GCC. With these coverage profiles, we answer the question of how much code optimization is possible without compromising the error-detection likelihood of a given test suite. Experimental results conclude that the performance cost to achieve preservation of structural code coverage in GCC is rather low.Peer reviewedSubmitted Versio

Toward a Market Model for Bayesian Inference

We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and producers trade in uncertain propositions. We demonstrate the correspondence between the equilibrium prices of goods in this economy and the probabilities represented by the Bayesian network. A computational market model such as this may provide a useful framework for investigations of belief aggregation, distributed probabilistic inference, resource allocation under uncertainty, and other problems of decentralized uncertainty.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Conditional Plausibility Measures and Bayesian Networks

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures. It is shown that algebraic conditional plausibility measures can be represented using Bayesian networks

Reasoning in evidential networks with conditional belief functions

AbstractIn the existing evidential networks applicable to belief functions, the relations among the variables are always represented by joint belief functions on the product space of the variables involved. In this paper, we use conditional belief functions to represent such relations in the network and show some relations between these two kinds of representations. We also present a propagation algorithm for such networks. By analyzing the properties of some special networks with conditional belief functions, called networks with partial dependency, we show that the computation for reasoning can be simplified