This paper verifies a result of [9] concerning graphoidal structure of Shenoy’s notion of independence for Dempster-Shafer theory of belief functions. Shenoy proved that his notion of independence has graphoidal properties for positive normal valuations. The requirement of strict positive normal valuations as prerequisite for application of graphoidal properties excludes a wide class of DS beli...

This paper introduces an algorithm for automatically acquiring the conceptual structure of each word from corpus. The concept of a word is defined within the probabilistic framework. A variation of Belief Net named as Collocation Map is used to compute the probabilities. The Belief Net captures the conditional independences of words, which is obtained from the cooccurrence relations. The comput...

This paper presents an abstract general model for representing the belief systems of resource-bounded reasoning agents. The intuition which underlies this new model is that it is possible to capture the key properties of many different types of belief system in a structure called a belief extension relation. The paper shows how such a relation may be derived for any system that satisfies some b...

There exist two general forms of exact algorithms for updating probabilities in Bayesian Networks. The first approach involves using a structure, usually a clique tree, and performing local message based calculation to extract the belief in each variable. The second general class of algorithm involves the use of non-serial dynamic programming techniques to extract the belief in some desired gro...

Belief networks are popular tools for encoding uncertainty in expert systems. These networks rely on inference algorithms to compute beliefs in the context of observed evidence. One established method for exact inference on belief networks is the Probability Propagation in Trees of Clusters (PPTC) algorithm, as developed by Lauritzen and Spiegelhalter and re ned by Jensen et al. [1, 2, 3] PPTC ...

Ranking measures are coarse-grained, quasi-probabilistic plausibility valuations measuring the degree of surprise. Since Spohn’s work on the subclass of natural conditional functions, they have been used to model epistemic states and their dynamics. The simplest instance may be elementary ranking revision, which is a non-parametrized version of Spohn-style revision based on minimal Jeffreycondi...

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper Friedman and Halpern 1995a], we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to e...

* This research was sponsored in part by the Office of Naval Research under grant no. N00014-03-1-0033. ‡ 0-7803-7952—7/03/$17.00 © 2003 IEEE Abstract – Existing methods of parameter and structure learning of probabilistic inference networks assume that the database is complete. If there are missing values, these values are assumed to be missing at random. This paper incorporates the concepts u...

Representing interactions between variables in large data sets in an understandable way is usually important and hard task. This article presents a methodology how a linear dependency structure between variables can be constructed from multivariate data. The dependencies between the variables are specified by multiple linear regression models. A sparse regression algorithm and bootstrap based r...