A conceptual regression method

which the nodes are tests. The leaves, instead of indicating This paper presents a "conceptual regression method". classes, indicate i~tervals of values or single values with Given a set of examples whose representations are symbolic confide~ce coefficIents. The oldest (1960? re'i!jTession tree and which are attached to a real value, the method learns the meth~ IS A.I.D [22] (~ descendant of WhICh IS ID3 [20]). link between the representation and this value (or explains Very Important theore~cal developments on these methods this value). What is learned enables the value attached to a have been done by Breiman et al. [8]. new example to be predicted. Our method may be applied to These methods may be seen as symbolic because they attribute-value representations as well as to structural present a real ability to learn from attribute-value representations. Because it is based on statistical criteria representation and, most importantly, because they produce optimization, it has good noise immunity. trees which are symbolic objects (a tree with n leaves is We present: (1) the basic features of the problem' equivalent to a set of n rules). However, they have two (2) the statistical criteria which are used for selecting th; limitations: good descriptors (a descriptor is a rule left-hand side); (1) Their ability to learn from structural representations (3) the branch-and-bound algorithm which is used for is very limited. This has been demonstrated by Blythe [7] in searching the descriptor space (or rule space); (4) how the framework of classification tree methods. The problem selected descriptors are used for predictions. is that each time a node has to be split there are a great A simple regression problem derived from METAnumber of possible tests. For generating and evaluating DENDRAL [9] is used throughout this paper for these tests, Blythe proposed combining these methods with illustration. an AQ-like method. (2) They perform a very particular and limited search of