Abstract

Automated inductive learning is a vital part of machine intelligence and the design of intelligent agents. A useful formalization of inductive learning is the model of PAC-learnability. Nevertheless, the ability to learn every target concept expressible in a given representation, as required in the PAC-learnability model, is highly demanding and leads to many negative results for interesting concept classes. A new model of learnability, called Universal Learnability or U-learnability, recently has been proposed as a less demanding, average-case variant of PAC-learnability. This paper uses the U-learnability model to analyze a top-down decision tree induction algorithm. Specifically, this paper proves that an idealized variant of the well-known decision tree learning algorithm CART---one of the most successful existing machine learning algorithms---is a U-learner under a natural set of assumptions regarding target hypotheses. (The motivation and description of these assumptions is best...

Citations