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We introduce a software generator for a class of colored (self-correlated) and non-Gaussian noise, whose statistics and spectrum depend on two parameters, $q$ and $\tau$. Inspired by Tsallis' nonextensive formulation of statistical physics,…

Statistical Mechanics · Physics 2022-09-01 J Ignacio Deza , Hisham Ihshaish

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…

General Relativity and Quantum Cosmology · Physics 2016-03-04 Christopher J. Moore , Christopher P. L. Berry , Alvin J. K. Chua , Jonathan R. Gair

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with…

Networking and Internet Architecture · Computer Science 2007-05-23 Vern Paxson

Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…

Machine Learning · Computer Science 2025-02-25 Juliusz Ziomek , Masaki Adachi , Michael A. Osborne

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to…

Machine Learning · Statistics 2022-01-12 Takuo Matsubara , Chris J. Oates , François-Xavier Briol

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…

Methodology · Statistics 2020-04-21 Laurentiu Catalin Hinoveanu , Fabrizio Leisen , Cristiano Villa

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…

Machine Learning · Statistics 2019-07-16 Simo Särkkä

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Numerical Analysis · Mathematics 2025-04-24 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Machine Learning · Statistics 2018-01-23 Ching-An Cheng , Byron Boots

Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data,…

Numerical Analysis · Mathematics 2024-01-23 Yuhuang Meng , Yue Qiu

We compute the expected randomized benchmarking sequence fidelity for a system subject to Gaussian time-correlated noise. For single qubit benchmarking we show that the expected sequence fidelity is given by the partition function of a…

Quantum Physics · Physics 2017-03-30 Bryan H. Fong , Seth T. Merkel

Generative models (GMs) such as Generative Adversary Network (GAN) and Variational Auto-Encoder (VAE) have thrived these years and achieved high quality results in generating new samples. Especially in Computer Vision, GMs have been used in…

Machine Learning · Computer Science 2018-04-27 Honggang Zhou , Yunchun Li , Hailong Yang , Wei Li , Jie Jia

We address the task of simultaneous feature fusion and modeling of discrete ordinal outputs. We propose a novel Gaussian process(GP) auto-encoder modeling approach. In particular, we introduce GP encoders to project multiple observed…

Machine Learning · Statistics 2016-09-07 Stefanos Eleftheriadis , Ognjen Rudovic , Marc P. Deisenroth , Maja Pantic

In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…

Analysis of PDEs · Mathematics 2014-05-30 Ngoc-Cuong Nguyen , Jaime Peraire

We explore the use of non homogenous noise kernels in Gaussian process modelling to improve the potential energy curve models describing stochastic electronic structure data. We use the same noise kernels on energy curves describing…

Chemical Physics · Physics 2023-01-02 Fabio E. A. Albertani , Alex J. W. Thom

Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., image understanding, data fusion, medical diagnosis, fraud detection). This paper concerns inference in…

Artificial Intelligence · Computer Science 2019-05-21 Cheol Young Park , Kathryn Blackmond Laskey , Paulo C. G. Costa , Shou Matsumoto

The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…

Statistics Theory · Mathematics 2025-03-19 Conor Osborne , Aretha L. Teckentrup

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

Methodology · Statistics 2017-11-21 Hassan Maatouk

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…

Machine Learning · Computer Science 2019-03-15 Shengyang Sun , Guodong Zhang , Jiaxin Shi , Roger Grosse