Learning reliable rules under class imbalance

Abstract

We are interested in learning rules under class imbalance. In this direction we extend the traditional model of probably approximately correct (PAC) learning to also include explicitly among its goals high recall and high precision at the end of the learning process. We establish relationships for the recall and the precision of a learned hypothesis as a function of its risk and the rate of the minority class. We then show that we can PAC learn a concept class with high recall and high precision by allowing a polynomial increase in the time and space complexity of traditional PAC learning algorithms that generate hypotheses with low risk. In sequence, by introducing a pre-processing phase on such algorithms, with a constant-size overhead on the overall sample complexity, we are able, with high probability, to compute a lower bound of the true unknown rate p of the minority class, in the interval [p/8, p). Thus, we extend our positive results on PAC learning with high recall and high precision by also waiving the requirement that such a lower bound on the rate of the minority class is given to the learners by some oracle ahead of time. We conclude our work by exploring two popular PAC learning algorithms for monotone conjunctions.