Combining Learning Constraints and Numerical Regression

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 Q 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 Q learning can correct for errors caused by the bias of the learning algorithm and discuss the potentials of similar hierarchical learning schemes.