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Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function.…

Machine Learning · Computer Science 2012-06-18 Jarno Vanhatalo , Aki Vehtari

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing…

Machine Learning · Computer Science 2023-11-20 Alexandre Capone , Geoff Pleiss , Sandra Hirche

Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…

Machine Learning · Statistics 2014-12-04 James Hensman , Neil D. Lawrence

While the great capability of Transformers significantly boosts prediction accuracy, it could also yield overconfident predictions and require calibrated uncertainty estimation, which can be commonly tackled by Gaussian processes (GPs).…

Machine Learning · Computer Science 2024-05-29 Yingyi Chen , Qinghua Tao , Francesco Tonin , Johan A. K. Suykens

Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…

Machine Learning · Statistics 2021-06-10 William J. Wilkinson , Arno Solin , Vincent Adam

Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…

Signal Processing · Electrical Eng. & Systems 2026-01-05 Jeongwoo Park , Seongkyu Jung , Kaiming Shen , Jeonghun Park

We present a general framework for classification of sparse and irregularly-sampled time series. The properties of such time series can result in substantial uncertainty about the values of the underlying temporal processes, while making…

Machine Learning · Statistics 2016-11-01 Steven Cheng-Xian Li , Benjamin Marlin

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…

Machine Learning · Statistics 2024-09-20 Qiuxian Meng , Yongyou Zhang

We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…

Machine Learning · Statistics 2020-06-05 Trefor W. Evans , Prasanth B. Nair

In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &…

Machine Learning · Statistics 2014-10-01 Yarin Gal , Mark van der Wilk

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…

Methodology · Statistics 2021-11-30 Mengyang Gu , Hanmo Li

Sparse, knot-based Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Certain sparse models can be derived through specific variational approximations to the true posterior, and knots…

Machine Learning · Statistics 2020-04-15 Nathaniel Garton , Jarad Niemi , Alicia Carriquiry

The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…

Computation · Statistics 2018-10-24 Shinichiro Shirota , Sudipto Banerjee

Approximate inference techniques are the cornerstone of probabilistic methods based on Gaussian process priors. Despite this, most work approximately optimizes standard divergence measures such as the Kullback-Leibler (KL) divergence, which…

Machine Learning · Computer Science 2020-11-06 Rui Zhang , Christian J. Walder , Edwin V. Bonilla , Marian-Andrei Rizoiu , Lexing Xie

This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…

Statistics Theory · Mathematics 2010-10-13 Nicolas Verzelen

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

Numerical Analysis · Mathematics 2024-05-01 Paolo Villani , Jörg Unger , Martin Weiser

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Machine Learning · Statistics 2023-02-10 Tapio Helin , Andrew Stuart , Aretha Teckentrup , Konstantinos Zygalakis

We present a method to approximate Gaussian process regression models for large datasets by considering only a subset of the data. Our approach is novel in that the size of the subset is selected on the fly during exact inference with…

Machine Learning · Computer Science 2023-05-01 Simon Bartels , Kristoffer Stensbo-Smidt , Pablo Moreno-Muñoz , Wouter Boomsma , Jes Frellsen , Søren Hauberg

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…

Robotics · Computer Science 2017-05-18 Jing Dong , Byron Boots , Frank Dellaert