Loss functions for finite sets
Loss functions for finite sets
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DOI：
10.1007/s10589-022-00420-9
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发表时间：
2021-12
影响因子：
2.2
通讯作者：
Jiawang Nie;Suhan Zhong
中科院分区：
文献类型：
--
作者：
Jiawang Nie;Suhan Zhong
本文研究了有限集的损失函数。对于给定的有限集S，我们给出了最小次数的平方和型损失函数。当是一个标准单纯形的顶点集时，我们证明了这样的损失函数没有虚假的最小值（即，每个局部最小值都是全局最小值）。到变换，我们给出了类似的损失函数没有虚假的一般有限集的极小。当S由样本集T近似给定时，我们给出了如何通过求解一个二次优化问题来得到损失函数。数值实验和应用表明，这些损失函数的有效性。
This paper studies loss functions for finite sets. For a given finite setS, we give sum-of-square type loss functions of minimum degree. WhenSis the vertex set of a standard simplex, we show such loss functions have no spurious minimizers (i.e., every local minimizer is a global one). Up to transformations, we give similar loss functions without spurious minimizers for general finite sets. WhenSis approximately given by a sample setT, we show how to get loss functions by solving a quadratic optimization problem. Numerical experiments and applications are given to show the efficiency of these loss functions.