Related papers: Theoretical properties of angular halfspace depth

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…

We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on…

We introduce a new method for the estimation of the angular parameters [i.e., central directions of arrival (DOAs) and angular spreads] of multiple non-circular and incoherently-distributed (ID) sources and thoroughly analyze its…

Geometric (also known as spatial) quantiles, introduced by Chaudhury and representing one of the three principal approaches to defining multivariate quantiles, have been well studied in the literature. In this work, we focus on the extremal…

We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on…

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…

Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Recently, it has been shown that the trajectories of iterative…

The inability of deep learning models to handle data drawn from unseen distributions has sparked much interest in unsupervised out-of-distribution (U-OOD) detection, as it is crucial for reliable deep learning models. Despite considerable…

Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of…

The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining…

The Atiyah-Drinfeld-Hitchin-Manin (ADHM) transform and its various generalizations are examples of non-linear integral transforms between finite-dimensional moduli spaces. This note describes a natural infinite-dimansional generalization,…

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more…

Anomaly detection suffered from the lack of anomalies due to the diversity of abnormalities and the difficulties of obtaining large-scale anomaly data. Semi-supervised anomaly detection methods are often used to solely leverage normal data…

Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of…

Statistical tools which satisfy rigorous privacy guarantees are necessary for modern data analysis. It is well-known that robustness against contamination is linked to differential privacy. Despite this fact, using multivariate medians for…

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental…

The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…