Loss-Controlling Calibration for Predictive Models

We propose a learning framework for calibrating predictive models to make loss-controlling prediction for exchangeable data, which extends our recently proposed conformal loss-controlling prediction for more general cases. By comparison, the predictors built by the proposed loss-controlling approach are not limited to set predictors, and the loss function can be any measurable function without the monotone assumption. To control the loss values in an efficient way, we introduce transformations preserving exchangeability to prove finite-sample controlling guarantee when the test label is obtained, and then develop an approximation approach to construct predictors. The transformations can be built on any predefined function, which include using optimization algorithms for parameter searching. This approach is a natural extension of conformal loss-controlling prediction, since it can be reduced to the latter when the set predictors have the nesting property and the loss functions are monotone. Our proposed method is tested empirically for high-impact weather forecasting and the experimental results demonstrate its effectiveness for controlling the non-monotone loss related to false discovery.

Conformal Loss-Controlling Prediction

Conformal prediction is a learning framework controlling prediction coverage of prediction sets, which can be built on any learning algorithm for point prediction. This work proposes a learning framework named conformal loss-controlling prediction, which extends conformal prediction to the situation where the value of a loss function needs to be controlled. Different from existing works about risk-controlling prediction sets and conformal risk control with the purpose of controlling the expected values of loss functions, the proposed approach in this paper focuses on the loss for any test object, which is an extension of conformal prediction from miscoverage loss to some general loss. The controlling guarantee is proved under the assumption of exchangeability of data in finite-sample cases and the framework is tested empirically for classification with a class-varying loss and statistical postprocessing of numerical weather forecasting applications, which are introduced as point-wise classification and point-wise regression problems. All theoretical analysis and experimental results confirm the effectiveness of our loss-controlling approach.