Tube Loss: A Novel Approach for Prediction Interval Estimation

ArXi:2412.06853v4 Announce Type: replace-cross This paper proposes a novel loss function, called 'Tube Loss', for simultaneous estimation of bounds of a Prediction Interval (PI) in the regression setup. The PIs obtained by minimizing the empirical risk based on the Tube Loss are shown to be of better quality than the PIs obtained by the existing methods in the following sense. First, it yields intervals that attain the prespecified confidence level t $\in$ (0,1) asymptotically. A theoretical proof of this fact is given.