Related papers: Classification of Heavy-tailed Features in High Di…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…

We describe a general reduction technique for analyzing learning algorithms that are subject to light-tailed (but not necessarily bounded) randomness, a scenario that is often the focus of theoretical analysis. We show that the analysis of…

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

Gradient clipping is a commonly used technique to stabilize the training process of neural networks. A growing body of studies has shown that gradient clipping is a promising technique for dealing with the heavy-tailed behavior that emerged…

Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax…

This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…

Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…

Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper,…

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

We propose statistically robust and computationally efficient linear learning methods in the high-dimensional batch setting, where the number of features $d$ may exceed the sample size $n$. We employ, in a generic learning setting, two…

In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

Experiments involving the two-dimensional passive diffusion of colloidal boomerangs tracked off their centre of mobility have shown striking non-Gaussian tails in their probability distribution function [Chakrabarty et al., Soft Matter 12,…

Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution.…

We propose a bootstrap procedure for data that may exhibit clustering in two or more dimensions. We use insights from the theory of generalized U-statistics to analyze the large-sample properties of statistics that are sample averages from…

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…