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线性最小二乘的精确极小极大风险与样本协方差矩阵的下尾AI 解读

We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order d/n in dimension d with n samples. Here, we study the minimax expected excess risk over the full linear class, depending on the distribution of covariates. First, the least squares estimator is exactly minimax optimal in the well-specified case, for every distribution of covariates. We express…

AMF：用于在线学习的聚合 Mondrian 森林AI 解读

Abstract Random forest (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes from a combination of several characteristics: a remarkable accuracy in a variety of tasks, a small number of parameters to tune, robustness with respect to features scaling, a reasonable computational cost for training and prediction, and their suitability in high-dimensional settings. The…

Mondrian 树与森林的极小极大最优速率AI 解读

Introduced by Breiman (Mach. Learn. 45 (2001) 5–32), Random Forests are widely used classification and regression algorithms. While being initially designed as batch algorithms, several variants have been proposed to handle online learning. One particular instance of such forests is the Mondrian forest (In Adv. Neural Inf. Process. Syst. (2014) 3140–3148; In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS) (2016)), whose…