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The Classical Tukey-Huber Contamination Model (CCM) is a usual framework to describe the mechanism of outliers generation in robust statistics. In a data set with $n$ observations and $p$ variables, under the CCM, an outlier is a unit, even…

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,…

The development of effective knowledge discovery techniques has become in the recent few years a very active research area due to the important impact it has in several relevant application areas. One interesting task thereof is that of…

Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…

We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust…

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…

This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis (PCA) problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this…

Outlier detection refers to the identification of anomalous samples that deviate significantly from the distribution of normal data and has been extensively studied and used in a variety of practical tasks. However, most unsupervised…

Outliers have been widely observed in Large Language Models (LLMs), significantly impacting model performance and posing challenges for model compression. Understanding the functionality and formation mechanisms of these outliers is…

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which…

The product moment covariance is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately the product moment covariance and the…

Clustering and outlier detection are two important tasks in data mining. Outliers frequently interfere with clustering algorithms to determine the similarity between objects, resulting in unreliable clustering results. Currently, only a few…

The problem of identifying the most discriminating features when performing supervised learning has been extensively investigated. In particular, several methods for variable selection in model-based classification have been proposed.…

In this work, we revisit outlier hypothesis testing and propose exponentially consistent, low-complexity fixed-length tests that achieve a better tradeoff between detection performance and computational complexity than existing…

The presence of outliers can prevent clustering algorithms from accurately determining an appropriate group structure within a data set. We present outlierMBC, a model-based approach for sequentially removing outliers and clustering the…

We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus…

Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…

Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…

In this paper, we propose a novel conceptual framework to detect outliers using optimal transport with a concave cost function. Conventional outlier detection approaches typically use a two-stage procedure: first, outliers are detected and…

In this paper, an outlier elimination algorithm for ellipse/ellipsoid fitting is proposed. This two-stage algorithm employs a proximity-based outlier detection algorithm (using the graph Laplacian), followed by a model-based outlier…