相关论文: Robust Hierarchical-Optimization RLS Against Spars…

In this study, we tackle the challenge of outlier-robust predictive modeling using highly expressive neural networks. Our approach integrates two key components: (1) a transformed trimmed loss (TTL), a computationally efficient variant of…

This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…

We consider online convex optimization when a number k of data points are outliers that may be corrupted. We model this by introducing the notion of robust regret, which measures the regret only on rounds that are not outliers. The aim for…

Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…

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…

National statistical institutes in many countries are now mandated to produce reliable statistics for important variables such as population, income, unemployment, health outcomes, etc. for small areas, defined by geography and/or…

We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…

We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…

Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…

The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…

The rotation search problem aims to find a 3D rotation that best aligns a given number of point pairs. To induce robustness against outliers for rotation search, prior work considers truncated least-squares (TLS), which is a non-convex…

Traditional recursive least square (RLS) adaptive filtering is widely used to estimate the impulse responses (IR) of an unknown system. Nevertheless, the RLS estimator shows poor performance when tracking rapidly time-varying systems. In…

This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Reverse Unrestricted MIxed DAta Sampling (RU-MIDAS) regressions are used to model high-frequency responses by means of low-frequency variables. However, due to the periodic structure of RU-MIDAS regressions, the dimensionality grows quickly…

We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to…