Improved Copula-based conformal prediction for uncertainty quantification of multi-output regression

Abstract

Though machine learning-based prediction techniques have been widely applied in industrial production, how to quantify their uncertainty remains a major challenge. Conformal prediction is a framework for uncertainty quantification that can be combined with arbitrary machine learning methods. Based on the existing methods, an improved conformal prediction multi-output method is proposed in this paper in order to obtain more effective prediction region. Firstly, a multi-output regression model is used as the underlying model and the Copula function is estimated by the calibration set; Secondly, given the global confidence level, the volume of the prediction region obtained from the calibration set is used as the optimization objective function, and the Differential Evolution (DE) algorithm is used to calculate different individual confidence levels for each output variable; Then, the uncertainty of the test set is calculated based on the individual confidence level obtained from the optimization solution. Finally, the experiments and analysis of the data from the iron production process show that the proposed method improves the efficiency of prediction region under the guarantee of coverage.