标题： 带有锚点正则化的快速局部线性回归 显示英文标题

标题： Fast local linear regression with anchor regularization

摘要： 回归是机器学习和数据挖掘中的一个重要任务。 它在多个领域有各种应用，包括金融、生物医学和计算机视觉。 最近，提出了一种称为网络Lasso的方法，该方法通过使用网络信息进行聚类来估计局部模型，并展示了其优越的性能。 在本研究中，我们提出了一种简单而有效的局部模型训练算法，称为快速锚定正则化局部线性方法（FALL）。 更具体地说，我们通过用预先计算的锚定模型对每个样本进行正则化来训练一个局部模型。 所提出算法的关键优势是我们可以通过仅矩阵乘法获得闭式解；此外，所提出的算法易于解释、计算速度快且可并行化。 通过在合成和真实世界数据集上的实验，我们证明了FALL在准确性方面优于最先进的网络Lasso算法，且训练时间显著减少（两个数量级）。 显示英文摘要

摘要： Regression is an important task in machine learning and data mining. It has several applications in various domains, including finance, biomedical, and computer vision. Recently, network Lasso, which estimates local models by making clusters using the network information, was proposed and its superior performance was demonstrated. In this study, we propose a simple yet effective local model training algorithm called the fast anchor regularized local linear method (FALL). More specifically, we train a local model for each sample by regularizing it with precomputed anchor models. The key advantage of the proposed algorithm is that we can obtain a closed-form solution with only matrix multiplication; additionally, the proposed algorithm is easily interpretable, fast to compute and parallelizable. Through experiments on synthetic and real-world datasets, we demonstrate that FALL compares favorably in terms of accuracy with the state-of-the-art network Lasso algorithm with significantly smaller training time (two orders of magnitude).