Scholarlink

In this chapter, we return to the noisy linear regression. Recall the sparse linear model \(Y = \mathbb {X} \beta ^* + \varepsilon \) , where \(\mathbb {X} \in \mathbb {R}^{n\times d}\) and \(\|\beta ^*\|_0 \le s\) . We estimate the high-dimensional linear model via the Lasso estimator \(\displaystyle \widehat \beta = \operatorname *{\text{arg min}}_{\beta }\frac {1}{2n} \|Y-\mathbb {X}\beta \|_2^2 + \lambda \|\beta \|_1. \) In this chapter, we will study the statistical properties of the Lasso estimator. Like the RIP condition for the basis pursuit, we also need conditions for Lasso.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Statistical Properties of Lasso

  • 章节

  • 发表日期：

    2025年

查看全文
  • Junwei Lu

摘要

In this chapter, we return to the noisy linear regression. Recall the sparse linear model \(Y = \mathbb {X} \beta ^* + \varepsilon \) , where \(\mathbb {X} \in \mathbb {R}^{n\times d}\) and \(\|\beta ^*\|_0 \le s\) . We estimate the high-dimensional linear model via the Lasso estimator \(\displaystyle \widehat \beta = \operatorname *{\text{arg min}}_{\beta }\frac {1}{2n} \|Y-\mathbb {X}\beta \|_2^2 + \lambda \|\beta \|_1. \) In this chapter, we will study the statistical properties of the Lasso estimator. Like the RIP condition for the basis pursuit, we also need conditions for Lasso.