Title: Kullback-Leibler excess risk bounds for exponential weighted aggregation in Generalized linear models Show Chinese title

Title: 广义线性模型中指数加权聚合的Kullback-Leibler超额风险界

Abstract: Aggregation methods have emerged as a powerful and flexible framework in statistical learning, providing unified solutions across diverse problems such as regression, classification, and density estimation. In the context of generalized linear models (GLMs), where responses follow exponential family distributions, aggregation offers an attractive alternative to classical parametric modeling. This paper investigates the problem of sparse aggregation in GLMs, aiming to approximate the true parameter vector by a sparse linear combination of predictors. We prove that an exponential weighted aggregation scheme yields a sharp oracle inequality for the Kullback-Leibler risk with leading constant equal to one, while also attaining the minimax-optimal rate of aggregation. These results are further enhanced by establishing high-probability bounds on the excess risk. Show Chinese abstract

Abstract: 聚合方法作为统计学习中一种强大且灵活的框架应运而生，在回归、分类和密度估计等多种问题中提供统一的解决方案。 在广义线性模型（GLMs）的背景下，其中响应变量服从指数族分布，聚合提供了一种有吸引力的经典参数化建模的替代方案。 本文研究了GLMs中稀疏聚合的问题，旨在通过预测变量的稀疏线性组合来逼近真实的参数向量。 我们证明了一个指数加权聚合方案对于Kullback-Leibler风险给出了一个尖锐的oracle不等式，其主要常数等于一，同时达到了聚合的minimax最优速率。 这些结果进一步通过建立超额风险的高概率界得到增强。