English
Related papers

Related papers: Robust mixture modelling using sub-Gaussian stable…

200 papers

q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…

Data Analysis, Statistics and Probability · Physics 2017-03-21 Wagner S. de Lima , Emerson L. de Santa Helena

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…

Applications · Statistics 2014-07-08 Abhik Ghosh

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

Methodology · Statistics 2024-02-12 Philippe Gagnon , Yuxi Wang

We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the…

Probability · Mathematics 2017-05-16 Leonardo Rojas-Nandayapa , Wangyue Xie

This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that allow for integrating robustness and skewness into a single unified cluster analysis framework. Non-symmetrically…

Signal Processing · Electrical Eng. & Systems 2021-07-05 Christian A. Schroth , Michael Muma

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

Methodology · Statistics 2024-07-02 Qingyang Liu , Xianzheng Huang , Haiming Zhou

We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to…

Statistics Theory · Mathematics 2020-12-04 Mariia Vladimirova , Stephane Girard , Hien Nguyen , Julyan Arbel

A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…

Methodology · Statistics 2014-08-15 Rose Baker , Dan Jackson

This article proposes a distributed multi-task learning (MTL) algorithm based on supervised principal component analysis (SPCA) which is: (i) theoretically optimal for Gaussian mixtures, (ii) computationally cheap and scalable. Supporting…

Machine Learning · Computer Science 2021-10-12 Sami Fakhry , Romain Couillet , Malik Tiomoko

Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where…

Machine Learning · Computer Science 2025-03-18 Qingshi Sun , Nathan Justin , Andres Gomez , Phebe Vayanos

We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…

Methodology · Statistics 2023-05-23 Bikramjit Das

Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an…

Statistics Theory · Mathematics 2023-01-05 Haoxiang Li , Qian Qin , Galin L. Jones

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…

Machine Learning · Computer Science 2020-01-15 Chiwoo Park , David J. Borth , Nicholas S. Wilson , Chad N. Hunter , Fritz J. Friedersdorf

We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…

Methodology · Statistics 2025-05-29 Marco Bee , Flavio Santi

Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid control. State-of-the-art algorithms have focused on data-driven…

Systems and Control · Electrical Eng. & Systems 2021-11-15 Hany Abdulsamad , Tim Dorau , Boris Belousov , Jia-Jie Zhu , Jan Peters

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…

Machine Learning · Statistics 2014-04-30 Jianqing Fan , Han Liu , Yang Ning , Hui Zou

Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…

Optimization and Control · Mathematics 2020-12-08 Andrey Tremba

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…

Statistics Theory · Mathematics 2023-11-28 Pavol Ševera

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…

Statistics Theory · Mathematics 2019-06-12 Gabor Lugosi , Shahar Mendelson

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…

Methodology · Statistics 2019-03-12 Yuan Ke , Stanislav Minsker , Zhao Ren , Qiang Sun , Wen-Xin Zhou