Related papers: Robust Sparse Reduced Rank Regression in High Dime…
High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
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…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
In this paper, we propose robust stochastic algorithms for solving convex compositional problems of the form $f(\E_\xi g(\cdot; \xi)) + r(\cdot)$ by establishing {\bf sub-Gaussian confidence bounds} under weak assumptions about the tails of…
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
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…
We consider a standard distributed optimization problem in which networked nodes collaboratively minimize the sum of their locally known convex costs. For this setting, we address for the first time the fundamental problem of design and…
We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…
This paper considers the problem of asynchronous stochastic nonconvex optimization with heavy-tailed gradient noise and arbitrarily heterogeneous computation times across workers. We propose an asynchronous normalized stochastic gradient…
In this manuscript, we research on the behaviors of surrogates for the rank function on different image processing problems and their optimization algorithms. We first propose a novel nonconvex rank surrogate on the general rank…
Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…
In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…
This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…
We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…
Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…