相关论文: Robust matrix completion via Novel M-estimator Fun…

Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers…

To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…

The asymmetric objective function is proposed as an alternative to Huber objective function to model skewness and obtain robust estimators for the location, scale and skewness parameters. The robustness and asymptotic properties of the…

We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…

This paper delves into the challenging issues in uncertain multi-objective optimization, where uncertainty permeates nonsmooth nonconvex objective and constraint functions. In this context, we investigate highly robust (weakly efficient)…

Reinforcement Learning is a powerful framework for training agents to navigate different situations, but it is susceptible to changes in environmental dynamics. However, solving Markov Decision Processes that are robust to changes is…

We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…

We propose a robust variable selection procedure using a divergence based M-estimator combined with a penalty function. It produces robust estimates of the regression parameters and simultaneously selects the important explanatory…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…

A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…

We introduce a novel class of regularization functions, called Cauchy-Schwarz (CS) regularizers, which can be designed to induce a wide range of properties in solution vectors of optimization problems. To demonstrate the versatility of CS…

We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…

This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…

Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…