Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses

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 observe...

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Hauptverfasser:	Gokcesu, Kaan, Gokcesu, Hakan
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Sprache:	eng
Schlagworte:	Computer Science - Data Structures and Algorithms Computer Science - Learning Mathematics - Optimization and Control Statistics - Machine Learning
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creator	Gokcesu, Kaan Gokcesu, Hakan
description	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.
doi_str_mv	10.48550/arxiv.2304.02141
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title	Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses
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