Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses
This provides an efficient solution for real-time unimodal fitting in sequential data processing applications.
The paper tackles the problem of optimally transforming univariate model scores into unimodal predictions under linear loss functions, showing the optimal mapping is a rectangular function and proposing a sequential algorithm with logarithmic time per iteration.
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.