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.

研究了在高斯设计和加性噪声的线性模型中，估计一个 p - 维 s - 稀疏向量的问题，证明当标签受到至多 o 个敌对异常数据的污染时，基于 n 个样本的 L1 惩罚 Huber's M - 估计量达到最优的收敛速率 (s /n)^ {1/2} +（o /n），更一般的设计矩阵结果强调了转移原则和无相干性质的重要性，并证明适当的常数加上这些属性可以实现最优的强鲁棒估计率，最高可达对数因子，具有敌对扰动。