Performance of Empirical Risk Minimization for Linear Regression with Dependent Data

• Tác giả: Christian Brownlees, Guðmundur Stefán Guðmundsson
• Ngôn ngữ: eng
• Ký hiệu phân loại: 519.7 Programming
• Thông tin xuất bản: 2021
• Bộ sưu tập: Metadata
• ID: 166812

Tóm tắt

This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the cases of identically and heterogeneously distributed observations. Our analysis is nonparametric in the sense that the relationship between the regressand and the regressors is not specified. The main results of this paper show that the empirical risk minimizer achieves the optimal performance (up to a logarithmic factor) in a dependent data setting.