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Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…

Methodology · Statistics 2025-04-29 Blake Hansen , Alejandra Avalos-Pacheco , Massimiliano Russo , Roberta De Vito

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Machine Learning · Computer Science 2012-06-22 Samuel Gershman , Matt Hoffman , David Blei

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Methodology · Statistics 2024-09-25 Anwesha Chakravarti , Naveen N. Narishetty , Feng Liang

Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…

Machine Learning · Statistics 2024-03-20 Dionissios T. Hristopulos

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…

Machine Learning · Statistics 2019-06-14 Alessandro Davide Ialongo , Mark van der Wilk , James Hensman , Carl Edward Rasmussen

This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…

Machine Learning · Computer Science 2019-03-25 Haibin Yu , Trong Nghia Hoang , Kian Hsiang Low , Patrick Jaillet

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Machine Learning · Computer Science 2025-07-10 Jihao Andreas Lin

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional…

Machine Learning · Statistics 2011-11-01 Andrea Schirru , Simone Pampuri , Giuseppe De Nicolao , Sean McLoone

Modern approximations to Gaussian processes are suitable for "tall data", with a cost that scales well in the number of observations, but under-performs on ``wide data'', scaling poorly in the number of input features. That is, as the…

Machine Learning · Statistics 2022-10-17 Martin Jørgensen , Michael A. Osborne

In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…

Machine Learning · Statistics 2023-03-28 Anant Mathur , Sarat Moka , Zdravko Botev

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…

Machine Learning · Computer Science 2022-07-19 Pashupati Hegde , Çağatay Yıldız , Harri Lähdesmäki , Samuel Kaski , Markus Heinonen

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

Machine Learning · Computer Science 2018-09-11 Linfeng Liu , Liping Liu

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

Statistics Theory · Mathematics 2025-04-29 Botond Szabo , Amine Hadji , Aad van der Vaart

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…

Machine Learning · Statistics 2021-07-21 Gia-Lac Tran , Dimitrios Milios , Pietro Michiardi , Maurizio Filippone

We address three key challenges in learning continuous kernel representations: computational efficiency, parameter efficiency, and spectral bias. Continuous kernels have shown significant potential, but their practical adoption is often…

Machine Learning · Computer Science 2024-09-17 Clayton Harper , Luke Wood , Peter Gerstoft , Eric C. Larson

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but…

Machine Learning · Statistics 2015-07-29 Chris Lloyd , Tom Gunter , Michael A. Osborne , Stephen J. Roberts

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Machine Learning · Computer Science 2010-02-23 Yuan Qi , Ahmed H. Abdel-Gawad , Thomas P. Minka

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

Machine Learning · Computer Science 2013-09-27 James Hensman , Nicolo Fusi , Neil D. Lawrence

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar