Fundamenta Informaticae - Volume 30, issue 3-4

Authors: Wierzchoń, S.T. | Kłopotek, M.A. | Michalewicz, M.

Article Type: Research Article

Abstract: In the literature, the optimization problem to identify a set of composite hypotheses H, which will yield the k largest P(H|Se ) where a composite hypothesis is an instantiation of all the nodes in the network except the evidence nodes [17] is of significant interest. This problem is called “finding the k Most Plausible Explanation (MPE) of a given evidence Se in a Bayesian belief network”. The problem of finding k most probable hypotheses is generally NP-hard [2]. Therefore in the past various simplifications of the task by restricting k (to 1 or 2), restricting the structure (e.g. to …singly connected networks), or shifting the complexity to spatial domain have been investigated. A genetic algorithm is proposed in this paper to overcome some of these restrictions while stepping out from probabilistic domain onto the general Valuation based System (VBS) framework is also proposed by generalizing the genetic algorithm approach to the realm of Dempster-Shafer belief calculus. Show more

Keywords: Genetic algorithm, most plausible explanation, graphoidal expert systems

DOI: 10.3233/FI-1997-303410

Citation: Fundamenta Informaticae, vol. 30, no. 3-4, pp. 359-371, 1997

Authors: Ziarko, Wojciech | Shan, Ning

Article Type: Research Article

Abstract: This paper presents an approach to incremental concept learning in attribute-value systems. The main characteristic feature of this approach is adaptive creation of a complete decision table rather than classification rules. The approach involves gradual accumulation of atomic class descriptions followed by subsequent analysis and simplification of the learned decision table using the ideas of rough sets. Both deterministic and probabilistic aspects of learning are discussed. The basic learning procedure is presented. The convergence of the learning process is illustrated with a computational example using the Thyroid data collection.

DOI: 10.3233/FI-1997-303411

Citation: Fundamenta Informaticae, vol. 30, no. 3-4, pp. 373-382, 1997

Authors: Żytkow, Jan M. | Zembowicz, Robert

Article Type: Research Article

Abstract: We analyze relationships between different forms of knowledge that can be discovered in the same data matrix (relational table): contingency tables, equations, concept definitions, concept hierarchies, and rules. We argue that contingency tables are the basic form of knowledge because other forms can be derived from their various special cases. We analyze the relationship between contingency tables and rules and present advantages of knowledge expressed in contingency tables. We show that special cases of contingency tables lead to concepts with empirical contents. In our view, concepts should be accepted as a by-product of knowledge discovery, as instruments justified by knowledge …they express. The same applies to taxonomies (concept hierarchies). They should be created in the right circumstances, to express specific empirical knowledge. We discuss several types of knowledge that are not conducive to taxonomy formation. Then we demonstrate how concepts generated from contingency tables which approximate logical equivalence can be combined to construct concept hierarchies: (1) each of those regularities leads to a hierarchy element (mini-hierarchy), (2) the elements are merged to increase their empirical contents, and (3) they are combined into multi-level hierarchy. This method has been implemented as a part of database discovery system 49er. We illustrate our algorithm by an application on the soybean database, and we show how our results go beyond those obtained by the COBWEB approach. Show more

DOI: 10.3233/FI-1997-303412

Citation: Fundamenta Informaticae, vol. 30, no. 3-4, pp. 383-399, 1997