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Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…

Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…

Outlier detection (also known as anomaly detection or deviation detection) is a process of detecting data points in which their patterns deviate significantly from others. It is common to have outliers in industry applications, which could…

When neural networks are employed for high-stakes decision-making, it is desirable that they provide explanations for their prediction in order for us to understand the features that have contributed to the decision. At the same time, it is…

Circle fitting methods are extensively utilized in various industries, particularly in quality control processes and design applications. The effectiveness of these algorithms can be significantly compromised when the point sets to be…

Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified…

Geometric perception problems are fundamental tasks in robotics and computer vision. In real-world applications, they often encounter the inevitable issue of outliers, preventing traditional algorithms from making correct estimates. In this…

Cox and Kartsonaki proposed a simple outlier test for a vector of p-values based on the R\'enyi transformation that is fast for large $p$ and numerically stable for very small p-values -- key properties for large data analysis. We propose…

In this paper, we propose a novel approach for outlier detection, called local projections, which is based on concepts of Local Outlier Factor (LOF) (Breunig et al., 2000) and RobPCA (Hubert et al., 2005). By using aspects of both methods,…

The $K$-means algorithm remains one of the most widely-used clustering methods due to its simplicity and general utility. The performance of $K$-means depends upon location of minima low in cost function, amongst a potentially vast number…

Observations in data which are significantly different from its neighbouring points but cannot be classified as noise are known as anomalies or outliers. These anomalies are a cause of concern and a timely warning about their presence could…

We consider functional outlier detection from a geometric perspective, specifically: for functional data sets drawn from a functional manifold which is defined by the data's modes of variation in amplitude and phase. Based on this manifold,…

The combination of the Internet of Things and the Edge Computing gives many opportunities to support innovative applications close to end users. Numerous devices present in both infrastructures can collect data upon which various processing…

We revisit sequential outlier hypothesis testing and derive bounds on achievable exponents when both the nominal and anomalous distributions are unknown. The task of outlier hypothesis testing is to identify the set of outliers that are…

Aleatoric and Epistemic uncertainty have achieved recent attention in the literature as different sources from which uncertainty can emerge in stochastic modeling. Epistemic being intrinsic or model based notions of uncertainty, and…

The Residual Congruent Subset (RCS) is a new method for finding outliers in the linear regression setting. Like many other outlier detection procedures, RCS searches for a subset which minimizes a criterion. The difference is that the new…

'Optimal cutpoints' for binary classification tasks are often established by testing which cutpoint yields the best discrimination, for example the Youden index, in a specific sample. This results in 'optimal' cutpoints that are highly…

Unsupervised learning methods are well established in the area of anomaly detection and achieve state of the art performances on outlier datasets. Outliers play a significant role, since they bear the potential to distort the predictions of…

A new method for outlier detection and generation is introduced by lifting data into the space of probability distributions which are not analytically expressible, but from which samples can be drawn using a neural generator. Given a…