Related papers: Statistical consistency and asymptotic normality f…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
We introduce a robust and fully adaptive method for pointwise estimation in heteroscedastic regression. We allow for noise and design distributions that are unknown and fulfill very weak assumptions only. In particular, we do not impose…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional asymptotic regime where the sample size $n$ and the number…
``Localization'' has proven to be a valuable tool in the Statistical Learning literature as it allows sharp risk bounds in terms of the problem geometry. Localized bounds seem to be much less exploited in the Stochastic Optimization…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex…
Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper,…
We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…
High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…