论文标题
最大值方程的稀疏近似解决方案，并应用于多元凸回归
Sparse Approximate Solutions to Max-Plus Equations with Application to Multivariate Convex Regression
论文作者
论文摘要
在这项工作中，我们研究了发现近似值的问题，最低支持集，用于矩阵最大方程的解决方案，我们称之为稀疏的近似解决方案。我们向任何$ \ ell_p $近似错误显示如何有效地和多项式时间内获得此类解决方案。基于这些结果，我们提出了一种新型方法，用于凸多变量函数的分段线性拟合，并为模型参数提供最佳保证，并且仿射区域数量大约最少。
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial time for any $\ell_p$ approximation error. Based on these results, we propose a novel method for piecewise-linear fitting of convex multivariate functions, with optimality guarantees for the model parameters and an approximately minimum number of affine regions.
