MERCI: A NEW METRIC TO EVALUATE THE CORRELATION BETWEEN PREDICTIVE UNCERTAINTY AND TRUE ERROR

As deep learning applications are becoming more and more pervasive, the question of evaluating the reliability of a prediction becomes a central question in the machine learning community. This domain, known as predictive uncertainty, has come under the scrutiny of research groups developing Bayesian approaches to deep learning such as Monte Carlo Dropout. Unfortunately, for the time being, the real goal of predictive uncertainty has been swept under the rug. Indeed, Bayesian approaches are solely evaluated in terms of raw performance of the prediction, while the quality of the estimated uncertainty is not assessed. One contribution of this article is to draw attention on existing metrics developed in the forecast community, designed to evaluate both the sharpness and the calibration of predictive uncertainty. Sharpness refers to the concentration of the predictive distributions and calibration to the consistency between the predicted uncertainty level and the actual errors. We further analyze the behavior of these metrics on regression problems when deep convolutional networks are involved and for several current predictive uncertainty approaches. A second contribution of this article is to propose an alternative metric that is more adapted to the evaluation of relative uncertainty assessment and directly applicable to regression with deep learning. This metric is evaluated and compared with existing ones on a toy dataset as well as on the problem of monocular depth estimation.