Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses

Abstract

This paper focuses on optimal unimodal transformation of the score outputs of a univariate learning model under linear loss functions. We demonstrate that the optimal mapping between score values and the target region is a rectangular function. To produce this optimal rectangular fit for the observed samples, we propose a sequential approach that can its estimation with each incoming new sample. Our approach has logarithmic time complexity per iteration and is optimally efficient.