Related papers: Choosing among notions of multivariate depth stati…
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
In the past decade, various exact balancing-based weighting methods were introduced to the causal inference literature. Exact balancing alleviates the extreme weight and model misspecification issues that may incur when one implements…
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
Tukey depth function is one of the most famous multivariate tools serving robust purposes. It is also very well known for its computability problems in dimensions $p \ge 3$. In this paper, we address this computing issue by presenting two…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
We give the first polynomial time and sample $(\epsilon, \delta)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm…
We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…
Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
This article studies statistical estimation of $\pi$ based on the fact that the ratio of the volumes of a $d$-dimensional hypersphere and a $d$-dimensional hypercube is a certain function of $\pi$, and the function depends on the dimension…
Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and…
Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…
For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…
A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of…
Classical discriminant analysis (DA) is based on the mean and empirical covariance matrix of each class, both of which are sensitive to outliers in the data. In the past the focus was on casewise outliers, that is, datapoints that lie far…
We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…