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An infinitely wide model is a weighted integration $\int \varphi(x,v) d \mu(v)$ of feature maps. This model excels at handling an infinite number of features, and thus it has been adopted to the theoretical study of deep learning. Kernel…

Machine Learning · Statistics 2020-07-08 Sho Sonoda

Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, compared to many classical cubature methods, comes at a…

Methodology · Statistics 2019-01-29 Toni Karvonen , Simo Särkkä , Chris. J. Oates

In this paper, we study error bounds for {\em Bayesian quadrature} (BQ), with an emphasis on noisy settings, randomized algorithms, and average-case performance measures. We seek to approximate the integral of functions in a {\em…

Machine Learning · Statistics 2023-02-13 Xu Cai , Chi Thanh Lam , Jonathan Scarlett

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

Statistics Theory · Mathematics 2022-07-27 Kelly R. Moran , Matthew W. Wheeler

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

Methodology · Statistics 2021-06-15 Edwin Fong , Chris Holmes

We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…

Machine Learning · Statistics 2020-03-20 Keiichi Kisamori , Motonobu Kanagawa , Keisuke Yamazaki

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

Applications · Statistics 2016-10-26 Federico Bassetti , Roberto Casarin , Francesco Ravazzolo

Parallelisation in Bayesian optimisation is a common strategy but faces several challenges: the need for flexibility in acquisition functions and kernel choices, flexibility dealing with discrete and continuous variables simultaneously,…

Machine Learning · Computer Science 2024-04-22 Masaki Adachi , Satoshi Hayakawa , Martin Jørgensen , Saad Hamid , Harald Oberhauser , Michael A. Osborne

To accelerate the scale-up of gaseous CO2 fermentation reactors, computational models need to predict gas-to-liquid mass transfer which requires capturing the bubble size dynamics, i.e. bubble breakup and coalescence. However, the…

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…

Machine Learning · Computer Science 2019-03-04 Henry Chai , Jean-Francois Ton , Roman Garnett , Michael A. Osborne

Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…

Computation · Statistics 2019-11-21 Michael Stanley Smith , Ruben Loaiza-Maya , David J. Nott

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…

Machine Learning · Statistics 2021-04-13 Mattias Åkesson , Prashant Singh , Fredrik Wrede , Andreas Hellander

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Computation · Statistics 2018-08-01 Xiaoyue Xi , François-Xavier Briol , Mark Girolami

We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…

Numerical Analysis · Mathematics 2025-03-28 P. Michael Kielstra , Michael Lindsey

In this work we propose a new matrix-free implementation of the Wiener sampler which is traditionally applied to high dimensional analysis when signal covariances are unknown. Specifically, the proposed method addresses the problem of…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-18 Jens Jasche , Guilhem Lavaux

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

Methodology · Statistics 2025-12-01 Angus Lewis , Antonio Parrella , John Maclean , Andrew J. Black

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…

Computer Vision and Pattern Recognition · Computer Science 2016-04-20 Sanjay Ghosh , Kunal N. Chaudhury

Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…

Methodology · Statistics 2017-05-10 Rui Tuo

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…

Statistics Theory · Mathematics 2014-06-03 Debdeep Pati , Anirban Bhattacharya , Natesh S. Pillai , David Dunson

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…

Methodology · Statistics 2021-05-12 Rajarshi Guhaniyogi , Aaron Scheffler