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Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…

Methodology · Statistics 2023-02-20 Jackson Zhou , Clara Grazian , John Ormerod

Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…

Methodology · Statistics 2022-05-13 Alessandro Casa , Andrea Cappozzo , Michael Fop

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

Statistics Theory · Mathematics 2022-12-29 Bryon Aragam , Ruiyi Yang

Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…

Methodology · Statistics 2020-12-22 Xiao Chen

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

Statistics Theory · Mathematics 2019-07-09 Ankit Pensia , Varun Jog , Po-Ling Loh

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

Methodology · Statistics 2008-02-05 K. Triantafyllopoulos

We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…

Computation · Statistics 2020-07-31 Mauricio Nascimento , Benjamin A. Shaby

In this paper, a scale mixture of Normal distributions model is developed for classification and clustering of data having outliers and missing values. The classification method, based on a mixture model, focuses on the introduction of…

Machine Learning · Statistics 2017-11-23 G. Revillon , A. Djafari , C. Enderli

We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…

Econometrics · Economics 2025-04-22 Richard Spady , Sami Stouli

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

Computer Vision and Pattern Recognition · Computer Science 2023-04-05 Krzysztof Byrski , Przemysław Spurek , Jacek Tabor

Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…

Machine Learning · Computer Science 2025-01-14 Vladimir Jaćimović

In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…

Methodology · Statistics 2014-12-19 Pedro L. Ramos , Francisco Louzada

This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…

Analysis of PDEs · Mathematics 2011-08-12 Claudia Garetto , Michael Oberguggenberger

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…

Machine Learning · Statistics 2017-08-10 Alexandre K. W. Navarro , Jes Frellsen , Richard E. Turner

Motivated by problems in high-dimensional statistics such as mixture modeling for classification and clustering, we consider the behavior of radial densities as the dimension increases. We establish a form of concentration of measure, and…

Statistics Theory · Mathematics 2016-09-13 Ery Arias-Castro , Xiao Pu

Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…

Machine Learning · Statistics 2024-04-12 Shuangping Li , Tselil Schramm

Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…

Methodology · Statistics 2010-01-26 Abel Rodriguez , Alex Lenkoski , Adrian Dobra

We propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the…

Machine Learning · Statistics 2020-05-21 Gustav Zickert , Can Evren Yarman

We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or…

Applications · Statistics 2015-01-27 Gianluca Mastrantonio , Antonello Maruotti , Giovanna Jona Lasinio

In hyperbolic background geometry, we investigate a generalized circle packing (including circles, horocycles and hypercycles) with conical singularities on a surface with boundary, which has a total geodesic curvature on each generalized…

Differential Geometry · Mathematics 2024-09-02 Guangming Hu , Ziping Lei , Yi Qi , Puchun Zhou