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Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

Statistics Theory · Mathematics 2021-03-18 Yifan Chen , Houman Owhadi , Andrew M. Stuart

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Computation · Statistics 2026-01-09 Elliot Maceda , Emily C. Hector , Amanda Lenzi , Brian J. Reich

Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…

Statistics Theory · Mathematics 2023-09-04 Deborah Sulem , Vincent Rivoirard , Judith Rousseau

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

Machine Learning · Statistics 2022-09-07 Joel Janek Dabrowski , Daniel Edward Pagendam

Because researchers typically do not have the time or space to present more than a few evaluation metrics in any published study, it can be difficult to assess relative effectiveness of prior methods for unreported metrics when baselining a…

Information Retrieval · Computer Science 2018-02-02 Mucahid Kutlu , Vivek Khetan , Matthew Lease

Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly.…

Machine Learning · Statistics 2018-10-15 Marko Järvenpää , Michael U. Gutmann , Arijus Pleska , Aki Vehtari , Pekka Marttinen

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…

Methodology · Statistics 2016-12-05 Shonosuke Sugasawa , Tatsuya Kubokawa , Kota Ogasawara

Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…

Methodology · Statistics 2024-08-15 M-Z. Spyropoulou , J. Hopker , J. E. Griffin

Parametric empirical Bayes (EB) estimators have been widely used in variety of fields including small area estimation, disease mapping. Since EB estimator is constructed by plugging in the estimator of parameters in prior distributions, it…

Methodology · Statistics 2017-04-28 Shonosuke Sugasawa

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

Statistics Theory · Mathematics 2018-08-21 Chao Gao , Aad W. van der Vaart , Harrison H. Zhou

This paper reviews past and ongoing efforts in using high-throughput ab-inito calculations in combination with machine learning models for materials design. The primary focus is on bulk materials, i.e., materials with fixed, ordered,…

Materials Science · Physics 2020-07-08 Rickard Armiento

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate…

Machine Learning · Statistics 2025-08-18 Stefano Cortinovis , François Caron

Domain experts often possess valuable physical insights that are overlooked in fully automated decision-making processes such as Bayesian optimisation. In this article we apply high-throughput (batch) Bayesian optimisation alongside…

Machine Learning · Computer Science 2023-12-06 Tom Savage , Ehecatl Antonio del Rio Chanona

Most active learning research has focused on methods which perform well when many labels are available, but can be dramatically worse than random selection when label budgets are small. Other methods have focused on the low-budget regime,…

Machine Learning · Computer Science 2025-02-28 Wonho Bae , Gabriel L. Oliveira , Danica J. Sutherland

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

Statistics Theory · Mathematics 2018-10-12 Stéphane Guerrier , Mucyo Karemera , Samuel Orso , Maria-Pia Victoria-Feser

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

Machine Learning · Statistics 2017-12-19 Alexandre Lacoste , Thomas Boquet , Negar Rostamzadeh , Boris Oreshkin , Wonchang Chung , David Krueger

Approximate Bayesian Computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by…

Methodology · Statistics 2024-03-11 Sanjay Chaudhuri , Subhroshekhar Ghosh , Kim Cuc Pham

The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…

Methodology · Statistics 2024-12-30 Jungeum Kim , Veronika Rockova

Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…

Methodology · Statistics 2017-09-08 Arnab Kumar Laha , Somak Dutta , Vivekananda Roy

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Machine Learning · Statistics 2019-09-12 Tomasz Kuśmierczyk , Joseph Sakaya , Arto Klami