Conformal predictor combination using Neyman–Pearson Lemma

The problem of how to combine advantageously Conformal Predictors (CP) has attracted the interest of many researchers in recent years. The challenge is to retain validity, while improving efficiency. In this article a very generic method is proposed which takes advantage of a well-established result in Classical Statistical Hypothesis Testing, the Neyman–Pearson Lemma, to combine CP with maximum efficiency. The merits and the limits of the method are explored on synthetic data sets under different levels of correlation between NonConformity Measures (NCM). CP Combination via Neyman–Pearson Lemma generally outperforms other combination methods when an accurate and robust density ratio estimation method, such as the V-Matrix method, is used.