Constraint Based Induction of Multi-objective Regression Trees

Constrained based inductive systems are a key component of inductive databases and responsible for building the models that satisfy the constraints in the inductive queries. In this paper, we propose a constraint based system for building multi-objective regression trees. A multi-objective regression tree is a decision tree capable of predicting several numeric variables at once. We focus on size and accuracy constraints. By either specifying maximum size or minimum accuracy, the user can trade-off size (and thus interpretability) for accuracy. Our approach is to first build a large tree based on the training data and to prune it in a second step to satisfy the user constraints. This has the advantage that the tree can be stored in the inductive database and used for answering inductive queries with different constraints. Besides size and accuracy constraints, we also briefly discuss syntactic constraints. We evaluate our system on a number of real world data sets and measure the size versus accuracy trade-off.