Top-Down Induction of Relational Model Trees in Multi-instance Learning

(Multi-)relational regression consists of predicting continuous response of target objects called reference objects by taking into account interactions with other objects called task-relevant objects. In relational databases, reference objects and task-relevant objects are stored in distinct data relations. Interactions between objects are expressed by means of (many-to-one) foreign key constraints which may allow linking explanatory variables of a task-relevant object in several alternative ways to the response variable. By materializing multiple assignments in distinct attribute-value vectors, a reference object is represented as a bag of multiple instances, although there is only one response value for the entire bag. This works points out the same assumption of multi-instance learning that is a primary instance is responsible for the observed response value of a reference object. We propose a top-down induction multi-relational model tree system which navigates foreign key constraints according to a divide-and-conquer strategy, derives a representation of reference objects as bags of attribute-value vectors and then, for each bag, constructs a primary instance as main responsible of the response value. Coefficients of local hyperplane are estimated in an EM implementation of the stepwise least square regression. Experiments confirm the improved accuracy of our proposal with respect to traditional attribute-value and relational model tree learners.