S. K. Michael Wong

On Information-Theoretic Measures of Attribute Importance

An attribute is deemed important in data mining if it partitions the database such that previously unknown regularities are observable. Many information-theoretic measures have been applied to quantify the importance of an attribute. In this paper, we summarize and critically analyze these measures.

Upper and Lower Entropies of Belief Functions Using Compatible Probability Functions

This paper uses the compatible probability functions to define the notion of upper entropy and lower entropy of a belief function as a generalization of the Shannon entropy. The upper entropy measures the amount of information conveyed by the evidence currently available. The lower entropy measures the maximum possible amount of information that can be obtained if further evidence becomes available. This paper also analyzes the different characteristics of these entropies and the computational aspect. The study demonstrates usefulness of compatible probability functions to apply various notions from the probability theory to the theory of belief functions.

Interval Approaches for Uncertain Reasoning

This paper presents a framework for reasoning using intervals. Two interpretations of intervals are examined, one treats intervals as bounds of a truth evaluation function, and the other treats end points of intervals as two truth evaluation functions. They lead to two different reasoning approaches, one is based on interval computations, and the other is based on interval structures. A number of interval based reasoning methods are reviewed and compared within the proposed framework.

Triangulation of Bayesian Networks: A Relational Database Perspective

In this paper, we study the problem of triangulation of Bayesian networks from a relational database perspective. We show that the problem of triangulating a Bayesian network is equivalent to the problem of identifying a maximal subset of conflict free conditional independencies. Several interesting theoretical results regarding triangulating Bayesian networks are obtained from this perspective.

Granular Information Retrieval

There are three main problems when designing an information retrieval (IR) system, namely, uncertainty in the representation of documents and queries, computational complexity, and the diversity of users. An IR system may be designed to be adaptive by allowing the modification of document and query representation. As well, different retrieval methods can be used for different users. The combina-tion of multi-representation of documents and multi-strategy retrieval may provide a Solution for the diversity of users. A widely used Solution for reducing computational costs is cluster-based retrieval. However, the use of document clustering only reduces the dimensionality of documents. The same number of terms is used for the representation of the Clusters. One may reduce the dimensionality of terms by constructing a term hierarchy in parallel to the construction of a document hierarchy. The proposed framework of granular IR enables us to incorporate multi-representation of documents and multi-strategy retrieval. Hence, granular IR may provide a method for developing knowledge based intelligent IR Systems.

Probabilistic reasoning in Bayesian networks: a relational database approach

Probabilistic reasoning in Bayesian networks is normally conducted on a junction tree by repeatedly applying the local propagation whenever new evidence is observed. In this paper, we suggest to treat probabilistic reasoning as database queries. We adapt a method for answering queries in database theory to the setting of probabilistic reasoning in Bayesian networks. We show an effective method for probabilistic reasoning without repeated application of local propagation whenever evidence is observed.

An Algebraic Characterization of Equivalent Bayesian Networks

In this paper, we propose an algebraic characterization for equivalent classes of Bayesian networks. Unlike the other characterizations which are based on the graphical structure of the Bayesian network, our algebraic characterization is derived from its intrinsic algebraic structure, i.e., the factorization of its joint probability distribution. The new proposed algebraic characterization not only provides us with a new perspective to look into equivalent Bayesian networks, but also suggests simple and efficient methods for determining equivalence of Bayesian networks and identifying compelled edges in Bayesian networks.

A Structural Characterization of DAG-Isomorphic Dependency Models

Graphical models have been extensively used in probabilistic reasoning for representing conditionali ndependency (CI) information. Among them two of the well known models are undirected graphs (UGs), and directed acyclic graphs (DAGs). Given a set of CIs, it woul d be desirable to know whether this set can be perfectly represented by a UG or DAG. A necessary and sufficient condition using axioms has been found for a set of CIs that can be perfectly represented by a UG; while negative result has been shown for DAGs, i.e., there does not exist a finite set of axioms which can characterize a set of CIs having a perfect DAG. However, this does not exclude other possible ways for such a characterization. In this paper, by studying the relationship between CIs and factorizations of a joint probability distribution, we show that there does exist such a characterization for DAGs in terms of the structure of the given set of CIs. More precisely, we demonstrate that if the given set of CIs satisfies certain constraints, then it has a perfect DAG representation.

Rough Sets for Uncertainty Reasoning

Rough sets have traditionally been applied to decision (classification) problems. We suggest that rough sets are even better suited for reasoning. It has already been shown that rough sets can be applied for reasoning about knowledge. In this preliminary paper, we show how rough sets provide a convenient framework for uncertainty reasoning. This discussion not only presents a new topic for future research, but further demonstrates the flexibility of rough sets.

The marginal factorization of Bayesian networks and its application

A Bayesian network consists of a directed acyclic graph (DAG) and a set of conditional probability distributions (CPDs); they together define a joint probability distribution (jpd). The structure of the DAG dictates how a jpd can be factorized as a product of CPDs. This CPD factorization view of Bayesian networks has been well recognized and studied in the uncertainty community. In this article, we take a different perspective by studying a marginal factorization view of Bayesian networks. In particular, we propose an algebraic characterization of equivalent DAGs based on the marginal factorization of a jpd defined by a Bayesian network. Moreover, we show a simple method to identify all the compelled edges in a DAG.