光滑强凸回归
Smooth Strongly Convex Regression
摘要：
凸回归（Convex Regression，CR）是将凸函数拟合到有限数量的底层凸函数的噪声观测值的问题。CR在许多领域都很重要，其中一个重要的工具是非参数最小二乘估计（LSE）。目前，LSE仅提供非光滑非强凸函数估计。本文利用凸插值的最新结果，将最小二乘估计推广到光滑强凸回归问题。由此产生的算法依赖于一个凸二次约束二次规划。我们还提出了一个并行实现，它利用ADMM，减少了整体的计算复杂性，一个紧密的$O(n^2)$的$n$的意见。数值结果支持我们的研究结果。
英文摘要：
Convex regression (CR) is the problem of fitting a convex function to a finite number of noisy observations of an underlying convex function. CR is important in many domains and one of its workhorses is the non-parametric least square estimator (LSE). Currently, LSE delivers only non-smooth non-strongly convex function estimates. In this paper, leveraging recent results in convex interpolation, we generalize LSE to smooth strongly convex regression problems. The resulting algorithm relies on a convex quadratically constrained quadratic program. We also propose a parallel implementation, which leverages ADMM, that lessens the overall computational complexity to a tight $O(n^2)$ for $n$ observations. Numerical results support our findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
