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The objective of reliability sensitivity analysis is to determine input variables that mostly contribute to the variability of the failure probability. In this paper, we study a recently introduced method for the reliability sensitivity…

Statistics Theory · Mathematics 2013-04-02 Ekaterina Sergienko , Paul Lemaître , Aurélie Arnaud , Daniel Busby , Fabrice Gamboa

We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…

Methodology · Statistics 2017-12-14 Sutanoy Dasgupta , Debdeep Pati , Anuj Srivastava

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

Methodology · Statistics 2018-07-03 Beatriz Bueno-Larraz , Johannes Klepsch

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

Statistics Theory · Mathematics 2021-06-01 Liyan Xie , Rui Gao , Yao Xie

Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling,…

Machine Learning · Computer Science 2024-03-12 Werner Zellinger , Stefan Kindermann , Sergei V. Pereverzyev

The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…

Machine Learning · Statistics 2023-08-07 Ambrus Tamás , Dániel Ágoston Bálint , Balázs Csanád Csáji

Detecting changes in high-dimensional vectors presents significant challenges, especially when the post-change distribution is unknown and time-varying. This paper introduces a novel robust algorithm for correlation change detection in…

Methodology · Statistics 2024-10-07 Assma Alghamdi , Taposh Banerjee , Jayant Rajgopal

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…

Statistics Theory · Mathematics 2023-09-29 Liyan Xie , Yuchen Liang , Venugopal V. Veeravalli

Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a…

Statistics Theory · Mathematics 2023-09-18 Marta Catalano , Hugo Lavenant , Antonio Lijoi , Igor Prünster

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. RDC is defined in terms…

Machine Learning · Statistics 2013-06-04 David Lopez-Paz , Philipp Hennig , Bernhard Schölkopf

In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…

Statistics Theory · Mathematics 2024-10-15 Suprio Bhar , Subhra Sankar Dhar

This paper presents a new efficient black-box attribution method based on Hilbert-Schmidt Independence Criterion (HSIC), a dependence measure based on Reproducing Kernel Hilbert Spaces (RKHS). HSIC measures the dependence between regions of…

Computer Vision and Pattern Recognition · Computer Science 2022-09-28 Paul Novello , Thomas Fel , David Vigouroux

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…

Machine Learning · Statistics 2016-11-03 Adrián Pérez-Suay , Gustau Camps-Valls

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

Machine Learning · Statistics 2022-08-29 Yuan Mao , Lei Shi , Zheng-Chu Guo

This paper draws distinctions among various concepts related to tipping points, robustness, path dependence, and other properties of system dynamics. For each concept a formal definition is provided that utilizes Markov model…

Adaptation and Self-Organizing Systems · Physics 2008-11-06 Aaron L Bramson

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…

Machine Learning · Statistics 2025-06-19 Agnimitra Dasgupta , Javier Murgoitio-Esandi , Ali Fardisi , Assad A Oberai

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before…

Machine Learning · Computer Science 2026-03-25 Rodrigo F. L. Lassance , Jasper De Bock

We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence…

Methodology · Statistics 2013-02-22 Matthew Reimherr , Dan L. Nicolae

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…

Quantum Physics · Physics 2016-06-08 René Schwonnek , David Reeb , Reinhard F. Werner

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…

Mathematical Finance · Quantitative Finance 2020-05-27 Stephan Eckstein , Michael Kupper , Mathias Pohl