基于非结构化核的m估计的结构学习

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY Electronic Journal of Statistics Pub Date : 2023-01-01 DOI:10.1214/23-ejs2153
Xin He, Yeheng Ge, Xingdong Feng
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引用次数: 0

摘要

在统计学习中,基于观测数据识别真实目标函数的底层结构对于后续建模和分析至关重要。与现有的大多数方法不同,本文提出了一种利用再现核希尔伯特空间(RKHS)中的非结构化m估计来恢复目标函数真实结构的通用框架。该框架的灵感来自于梯度函数可以作为一种有效的工具来学习底层结构,包括稀疏学习、交互选择和模型识别,并且通过利用RKHS的一些很好的特性很容易实现。更重要的是,它允许广泛的损失函数,因此包括许多常用的方法作为特殊情况,如均值回归、分位数回归、基于似然的分类、基于边缘的分类,这些方法通过求解凸优化任务也具有计算效率。该框架的渐近结果建立在一个丰富的损失函数族中,不需要任何显式的模型规范。通过各种仿真实例和实际案例研究,证明了该框架的优越性能。
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Structure learning via unstructured kernel-based M-estimation
In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some specific settings under certain model assumptions, a general and novel framework is proposed for recovering the true structures of target functions by using unstructured M-estimation in a reproducing kernel Hilbert space (RKHS) in this paper. This framework is inspired by the fact that gradient functions can be employed as a valid tool to learn underlying structures, including sparse learning, interaction selection and model identification, and it is easy to implement by taking advantage of some nice properties of the RKHS. More importantly, it admits a wide range of loss functions, and thus includes many commonly used methods as special cases, such as mean regression, quantile regression, likelihood-based classification, and margin-based classification, which is also computationally efficient by solving convex optimization tasks. The asymptotic results of the proposed framework are established within a rich family of loss functions without any explicit model specifications. The superior performance of the proposed framework is also demonstrated by a variety of simulated examples and a real case study.
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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