Conformal prediction for regression models with asymmetrically distributed errors: application to aircraft navigation during landing maneuver

Abstract

Semi-autonomous aircraft navigation is a high-risk domain where confidence on the prediction is required. For that, this paper introduces the use of conformal predictions strategies for regression problems. While standard approaches use an absolute nonconformity scores, we aim at introducing a signed version of the nonconformity scores. Experimental results on synthetic data have shown their interest for non-centered errors. Moreover, in order to reduce the width of the prediction interval, we introduce an optimization procedure which learn the optimal alpha risks for the lower and upper bounds of the interval. In practice, we show that a line search algorithm can be employed to solve it. Practically, this novel adaptive conformal prediction strategy has revealed to be well adapted for skew distributed errors. In addition, an extension of these conformal prediction strategies is introduced to incorporate numeric and categorical auxiliary variables describing the acquisition context. Based on a quantile regression model, they allow to maintain the coverage for each metadata value. All these strategies have then been applied on a real use case of runway localization from data acquired by an aircraft during landing maneuver. Extensive experiments on multiple airports have shown the interest of the proposed conformal prediction strategies, in particular for runways equipped with a very long ramp approach where asymmetric angular deviation error are observed.