English
Related papers

Related papers: A Mixture of Generalized Hyperbolic Distributions

200 papers

We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The…

Machine Learning · Statistics 2011-05-05 Stevenn Volant , Marie-Laure Martin Magniette , Stéphane Robin

Joint modelling of longitudinal observations and event times continues to remain a topic of considerable interest in biomedical research. For example, in HIV studies, the longitudinal bio-marker such as CD4 cell count in a patient's blood…

Methodology · Statistics 2024-07-19 Srimanti Dutta , Arindom Chakraborty , Dipankar Bandyopadhyay

Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…

Machine Learning · Statistics 2026-02-11 Haoyuan Chen , Rui Tuo

Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…

Probability · Mathematics 2022-03-11 Sami Davies , Arya Mazumdar , Soumyabrata Pal , Cyrus Rashtchian

With the progress of information technology, large amounts of asymmetric, leptokurtic and heavy-tailed data are arising in various fields, such as finance, engineering, genetics and medicine. It is very challenging to model those kinds of…

Methodology · Statistics 2024-01-26 Chengdi Lian , Yaohua Rong , Weihu Cheng

Azzalini (1985) introduced a skew-normal distribution of which normal distribution is a special case. Recently Kundu (2014) introduced a geometric skew-normal distribution and showed that it has certain advantages over Azzalini's…

Methodology · Statistics 2017-06-26 Debasis Kundu

Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and…

Machine Learning · Statistics 2019-05-31 Charles W. L. Gadd , Sara Wade , Alexis Boukouvalas

The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…

Optimization and Control · Mathematics 2021-05-19 Sarthak Chatterjee , Orlando Romero , Sérgio Pequito

We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…

Probability · Mathematics 2019-07-10 V. Yu. Korolev , A. K. Gorshenin , A. I. Zeifman

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…

Methodology · Statistics 2015-06-15 Utkarsh J. Dang , Ryan P. Browne , Paul D. McNicholas

There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…

Statistics Theory · Mathematics 2018-07-23 Yuichi Hirose , Ivy Liu

A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…

Statistical Mechanics · Physics 2023-01-11 Massimiliano Giona , Chiara Pezzotti , Giuseppe Procopio

We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly…

Methodology · Statistics 2020-07-28 C. R. B. Cabral , N. L. de Souza , J. Leão

Gaussian mixture models are central to classical statistics, widely used in the information sciences, and have a rich mathematical structure. We examine their maximum likelihood estimates through the lens of algebraic statistics. The MLE is…

Statistics Theory · Mathematics 2019-04-19 Carlos Améndola , Mathias Drton , Bernd Sturmfels

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…

Methodology · Statistics 2024-07-02 Raffaele Argiento , Edoardo Filippi-Mazzola , Lucia Paci

Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also…

Machine Learning · Statistics 2021-01-28 Alessio Benavoli , Dario Azzimonti , Dario Piga

When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions…

Methodology · Statistics 2018-02-07 Anna Kiriliouk , Holger Rootzén , Johan Segers , Jennifer L. Wadsworth

We extend the stochastic reconstruction theorem to a setting where the underlying family of distributions satisfies some natural conditions involving rectangular increments. This allows us to prove the well-posedness of a new class of mixed…

Probability · Mathematics 2025-11-13 Carlo Bellingeri , Hannes Kern

We propose a Stein characterization of the Kummer distribution on (0, $\infty$). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the…

Probability · Mathematics 2018-08-07 Essomanda Konzou , Angelo Koudou

Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class of location-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying generalized hyperbolic…

Statistics Theory · Mathematics 2023-03-13 Yuki Fujinaga , Hiroki Masuda