Machine Learning in Montpellier, Theory & Practice – Batiste Le Bars (Inria)
Conformal Prediction has recently been considered as one of the state-of-art technique to construct distribution-free prediction sets satisfying probabilistic coverage guarantees. In this talk, we study the question of volume optimality in split conformal regression. Using the fact that the calibration step can be seen as an empirical volume minimization problem, we first derive a finite-sample upper-bound on the excess volume loss of the interval returned by the classical split method. This quantity measures the difference in length between the interval obtained with the split method and the shortest oracle prediction interval. Then, we introduce EffOrt, a methodology that modifies the learning step so that the base prediction function minimizes the length of the returned intervals. In particular, our theoretical analysis of the excess volume loss of the prediction sets produced by EffOrt reveals the links between the learning and calibration steps, and notably the impact of the function class of the base predictor. We also introduce Ad-EffOrt, an extension of the previous method, which produces intervals whose size adapts to the value of the covariate.
