Knowledge Discovery by Following Conditional Structures

Abstract

In many cases, knowledge bases for expert systems consist of rules, i.e., of conditional statements. In the previous chapters, we investigated in detail the formal properties of conditionals, how to represent them appropriately and how to handle them under change of beliefs. Solving these problems is a necessary prerequisite to arrive at a satisfactory representation and processing of knowledge. When designing an expert system, however, at first one has to face another crucial problem: Where do all the rules come from? How to find a set of rules representing relevant knowledge in an exhaustive way? Besides human expertise, also experimental data may be available. Incorporating the detailed experiences of an expert into the knowledge base usually is an indispensible task in knowledge acquisition. Extracting and providing information from databases, however, may essentially help to support, automate and improve this process.

Data mining and knowledge discovery, respectively, mean finding new and relevant information in databases. Usually, knowledge discovering is understood as the more comprehensive task, including preparing and cleaning the available data and interpreting the results revealed by the actual data mining process, aiming at discovering interesting patterns in data (cf. [FPSS96, FPSSU96, FU + 96]).

In this chapter, we will focus on this central part of knowledge discovery within a probabilistic framework, where we assume experimental data to be represented by a probability distribution. This means that we will deal with relatively “small” data mining problems with respect to the number of variables or propositions involved. By using clustering techniques (see, for instance, [AGGR98]) and considering LEG-networks as an appropriate tool to split up large probability distributions in a system of local distributions (see Chapter 9), however, the problem of discovering relevant relationships amongst variables can be reduced to mining manageable distributions.

Relationships amongst variables and sets of variables may be expressed by association rules (cf. [AIS93, MS98, AMS + 96, SA95, Bol96], and see below) which are a special kind of probabilistic conditionals. Relevance of such rules is usually measured by considering their confidence, which is nothing but a conditional probability, and their support, which is the number of cases in the database that a rule is based upon (cf. [AIS93]). These are certainly plausible indicators for a rule to interest the user. If, for instance, the manager of a supermarket wants to improve the layout of his store, he will be interested in knowing how many customers buying product A also buy product B, and which percentage of total sales those transactions constitute.