First-Order Regression Tree

Synonyms

Logical regression tree; Relational regression tree

Definition

A first-order regression tree can be defined as follows:

Definition 1 (First-Order Regression Tree).

A first-order regression tree is a binary tree in which

• Every internal node contains a test which is a conjunction of first-order literals.

• Every leaf (terminal node) of the tree contains a real valued prediction.

An extra constraint placed on the first-order literals that are used as tests in internal nodes is that a variable that is introduced in a node (i.e., it does not occur in higher nodes) does not occur in the right subtree of the node.

Figure 1gives an example of a first-order regression tree. The test in a node should be read as the existentially quantified conjunction of all literals in the nodes in the path from the root of the tree to that node. In the left subtree of a node, the test of the node is added to the conjunction, for the right subtree, the negation of the test should be added. For the...