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This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…

Despite the crucial need for formal safety and security verification of programs, discovering loop invariants remains a significant challenge. Static analysis is a primary technique for inferring loop invariants but often relies on…

Feature screening is useful and popular to detect informative predictors for ultrahigh-dimensional data before developing proceeding statistical analysis or constructing statistical models. While a large body of feature screening procedures…

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…

Reliable outlier detection in high-dimensional data is crucial in modern science, yet it remains a challenging task. Traditional methods often break down in these settings due to their reliance on asymptotic behaviors with respect to sample…

This paper develops novel conformal methods to test whether a new observation was sampled from the same distribution as a reference set. Blending inductive and transductive conformal inference in an innovative way, the described methods can…

Outlier detection amounts to finding data points that differ significantly from the norm. Classic outlier detection methods are largely designed for single data type such as continuous or discrete. However, real world data is increasingly…

Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this…

We study the design of iterative combinatorial auctions (ICAs). The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, recent work has proposed machine learning (ML)-based…

The computational cost of searching for new pulsars is a limiting factor for upcoming radio telescopes such as SKA. We introduce four new algorithms: an optimal constant-period search, a coherent tree search which permits optimal searching…

The state estimation problem can be solved through different methods. In terms of robustness, an effective approach is represented by the Least Absolute Value (LAV) estimator, though vulnerable to leverage points. Based on a previously…

Categorization is one of the basic tasks in machine learning and data analysis. Building on formal concept analysis (FCA), the starting point of the present work is that different ways to categorize a given set of objects exist, which…

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

Ensemble methods for classification and clustering have been effectively used for decades, while ensemble learning for outlier detection has only been studied recently. In this work, we design a new ensemble approach for outlier detection…

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA).…

In this paper, we define probabilistic measures for venture portfolio performance based on individual outlier probability for each investment and the dependence across investments. This work is inspired by loan portfolio modeling against…