Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimator

Autor:	Dalalyan, Arnak S., Thompson, Philip
Rok vydání:	2019
Předmět:	Mathematics - Statistics Theory Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\ell_1$-penalized Huber's $M$-estimator based on $n$ samples attains the optimal rate of convergence $(s/n)^{1/2} + (o/n)$, up to a logarithmic factor. For more general design matrices, our results highlight the importance of two properties: the transfer principle and the incoherence property. These properties with suitable constants are shown to yield the optimal rates, up to log-factors, of robust estimation with adversarial contamination. Comment: This is a follow up paper of arXiv:1805.08020
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.06288 Zobrazit plný text záznamu View this record from Arxiv