标题： 平滑强凸回归 显示英文标题

标题： Smooth Strongly Convex Regression

摘要： 凸回归（CR）是将一个凸函数拟合到一个底层凸函数的有限噪声观测值的问题。 CR在许多领域都很重要，其中一种常用方法是非参数最小二乘估计器（LSE）。 目前，LSE仅能提供非光滑的非强凸函数估计。 在本文中，利用凸插值的最新成果，我们将LSE推广到平滑的强凸回归问题。 该算法依赖于一个凸二次约束二次规划。 我们还提出了一种并行实现方法，利用ADMM，将总体计算复杂度降低到对于$O(n^2)$个$n$观测值的紧密复杂度。 数值结果支持我们的发现。 显示英文摘要

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.