论文标题
平稳地凸回归
Smooth Strongly Convex Regression
论文作者
论文摘要
凸回归（CR）是将凸函数拟合到有限数量的基础凸函数的有限数量的问题。 CR在许多域中很重要，其工作主场之一是非参数最小成方估计器（LSE）。当前，LSE仅提供非平滑的非凸出凸功能估计。在本文中，利用了凸插值的最新结果，我们将LSE推广到强烈的凸回归问题。由此产生的算法依赖于凸的四边形二次程序。我们还提出了一个并行实施，该实施利用ADMM，将整体计算复杂性降低到$ n $观测值的紧密$ O（n^2）$。数值结果支持我们的发现。
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.
