On computable learning of continuous features
This work addresses theoretical foundations for computable learning in continuous domains, which is incremental but important for ensuring algorithmic feasibility in machine learning.
The paper tackles the problem of defining and analyzing computable PAC learning for binary classification in computable metric spaces, establishing conditions under which empirical risk minimizers are computable and providing a counterexample of a PAC-learnable class without a proper computable learner.
We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong Weihrauch degree of an ERM learner under more general conditions. We also give a presentation of a hypothesis class that does not admit any proper computable PAC learner with computable sample function, despite the underlying class being PAC learnable.