Combining Learning Constraints and Numerical Regression

Abstract

Usual numerical learning methods are primarily concerned with finding a good numerical fit to data and often make predictions that do not correspond to qualitative laws in the domain of modelling or expert intuition. In contrast, the idea of Q2 learning is to induce qualitative constraints from training data, and use the constraints to guide numerical regression. The resulting numerical predictions are consistent with a learned qualitative model which is beneficial in terms of explanation of phenomena in the modelled domain, and can also improve numerical accuracy. This paper proposes a method for combining the learning of qualitative constraints with an arbitrary numerical learner and explores the accuracy and explanation benefits of learning monotonic qualitative constraints in a number of domains. We show that Q2 learning can correct for errors caused by the bias of the learning algorithm and discuss the potentials of similar hierarchical learning schemes.