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.

翻译：本文研究在线性损失函数下的单变量学习模型的最佳单调转换。我们证明了分数值和目标区域之间的最优映射是一个矩形函数。为了在观察到的样本中产生这种最优矩形拟合，我们提出了一种序贯方法，可以在每个新样本到来时进行估计。我们的方法具有每次迭代的对数时间复杂度，是最优高效的解决方案。