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

Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses