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If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…

General Mathematics · Mathematics 2017-07-03 Andrej Liptaj

We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…

Probability · Mathematics 2016-01-07 Archil Gulisashvili , Peter Tankov

We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected…

Machine Learning · Statistics 2018-04-17 Nikitas Rontsis , Michael A. Osborne , Paul J. Goulart

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…

Machine Learning · Statistics 2023-05-04 Aapo Hyvärinen , Ilyes Khemakhem , Ricardo Monti

The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Hanns L. Harney

In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…

Machine Learning · Computer Science 2024-04-03 Marzieh Ajirak , Daniel Waxman , Fernando Llorente , Petar M. Djuric

Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in…

Methodology · Statistics 2023-12-19 Shunsuke Horii , Yoichi Chikahara

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Artificial Intelligence · Computer Science 2013-01-30 Kevin Murphy

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…

Machine Learning · Computer Science 2012-04-04 Matthias Scholz

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…

Numerical Analysis · Mathematics 2019-09-04 Chen Zhang , Simon Arridge , Bangti Jin

In this work an approximated path integral model describing the dynamics of a inextensible chain is presented. To this purpose, the nonlinear constraints which enforce the property of inextensibility of the chain are relaxed and are just…

Statistical Mechanics · Physics 2010-09-20 Franco Ferrari , Maciej Pyrka

This paper derives the analytic form of the $h$-step ahead prediction density of a GARCH(1,1) process under Gaussian innovations, with a possibly asymmetric news impact curve. The contributions of the paper consists both in the derivation…

Statistics Theory · Mathematics 2021-03-05 Karim M. Abadir , Alessandra Luati , Paolo Paruolo

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…

Methodology · Statistics 2013-01-04 George Karabatsos , Stephen G. Walker

The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the…

Methodology · Statistics 2019-02-11 Krzysztof Domino

Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to…

Methodology · Statistics 2021-02-02 Rou Zhong , Shishi Liu , Jingxiao Zhang , Haocheng Li

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

Machine Learning · Statistics 2022-03-22 Hossein Mohammadi , Peter Challenor , Marc Goodfellow

In this work we present a rigorous application of the Expectation Maximization algorithm to determine the marginal distributions and the dependence structure in a Gaussian copula model with missing data. We further show how to circumvent a…

Machine Learning · Statistics 2022-01-17 Maximilian Kertel , Markus Pauly

Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of…

Computation · Statistics 2016-11-16 Alexis Roche

Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in…

Systems and Control · Electrical Eng. & Systems 2022-09-22 Alexander von Rohr , Matthias Neumann-Brosig , Sebastian Trimpe

Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained…

Machine Learning · Computer Science 2021-09-21 Mingxuan Liang , Kai Zhou