Related papers: Cauchy-Gaussian Overbound for Heavy-tailed GNSS Me…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
Anomaly detection is crucial in industrial applications for identifying rare and unseen patterns to ensure system reliability. Traditional models, trained on a single class of normal data, struggle with real-world distributions where normal…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…
This paper focuses on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. Unfortunately, no closed-form expression is available for the statistical distribution of the…
We develop a new upper bound on the capacity of the relay channel that is tighter than previously known upper bounds. This upper bound is proved using traditional weak converse techniques involving mutual information inequalities and…
We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus…
We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and…
We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with exponent $\tau-1$, where $\tau\in (3,4)$. The…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Effective cross-modal retrieval requires robust alignment of heterogeneous data types. Most existing methods focus on bi-modal retrieval tasks and rely on distributional alignment techniques such as Kullback-Leibler divergence, Maximum Mean…
GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding…
Low internal friction coatings are key components of advanced technologies such as optical atomic clocks and high-finesse optical cavity and often lie at the forefront of the most advanced experiments in Physics. Notably, increasing the…
We present a statistical framework for estimating global navigation satellite system (GNSS) non-ionospheric differential time delay bias. The biases are estimated by examining differences of measured line integrated electron densities (TEC)…
Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…
We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is…
Synthetic aperture radar (SAR) imagery can provide useful information in a multitude of applications, including climate change, environmental monitoring, meteorology, high dimensional mapping, ship monitoring, or planetary exploration. In…