Deep Gaussian Processes

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8 papers0 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Generalized Splines and Gaussian Processes
Aug 28, 2026Michael UnserDeep Gaussian Processes Gaussian Processes
Biomedical Imaging Group, École polytechnique fédérale de Lausanne (EPFL), Station 17, CH-1015, Lausanne, Switzerland
Enhancing Bayesian Optimization and Active Learning Through Kernel Diversity
Aug 25, 2026Heng Zhang, Haotian Xiang, Konstantinos D. Polyzos +2Bayesian Optimization Deep Gaussian Processes
University of Georgia, Athens, GA, USA · University of California San Diego, La Jolla, CA, USA
A Bayesian Framework for Built-in Input Dimension Reduction for Gaussian Process Modeling
Jul 21, 2026Eric Herrison Gyamfi, Emily L. Kang, Bledar A. Konomi +1Bayesian Inference Deep Gaussian Processes
Division of Statistics and Data Science, Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH · Department of Mathematics, Purdue University, West Lafayette, IN
Deep Gaussian Processes on Directed Acyclic Graphs
Jul 10, 2026Federico L. Perlino, Oliver Hamelijnck, Adam M. Johansen +1Surrogate Modeling Deep Gaussian Processes
Department of Statistics, University of Warwick · 2AI Team, Unilink Software Ltd · Department of Computer Science, University of Warwick
An Analysis of Posterior Collapse, Parameterization and Initialization in Variational Deep Gaussian Processes
Jun 24, 2026Francisco Javier Sáez-Maldonado, Juan Maroñas, Daniel Hernández-LobatoDeep Learning Optimization Posterior Collapse
Department of Computer Science and Artificial Intelligence Universidad de Granada Granada, Spain · Department of Quantitative Methods CUNEF Universidad Madrid, Spain · Machine Learning Group at Universidad Autónoma de Madrid +1
How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs
Jun 6, 2026Mark Kozdoba, Shie MannorDeep Gaussian Processes Gaussian Processes
Technion, IIT · NVIDIA
Onsager-Machlup Posterior Transport for Deep Gaussian Processes
May 22, 2026Jian Xu, Delu Zeng, John Paisley +1Deep Gaussian Processes Gaussian Processes
RIKEN iTHEMS · RIKEN AIP · South China University of Technology +1
Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions
Oct 24, 2025Yang Xu, Chiwoo ParkDeep Gaussian Processes Surrogate Modeling
Industrial & Systems Engineering, University of Washington, Seattle, WA, USA

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Generalized Splines and Gaussian Processes

Michael Unser

Biomedical Imaging Group, École polytechnique fédérale de Lausanne (EPFL), Station 17, CH-1015, Lausanne, Switzerland

Deep Gaussian Processes Gaussian Processes Bayesian Inverse Problems

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For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least-squares data fit. In this chapter, we show that this equivalence extends to a much broader infinite-dimensional setting where generalized splines take the role of linear regressors and generalized Gaussian processes on a nuclear space

S

are the counterpart of Gaussian random vectors. The scope of this extension is of the same nature as the switch from the classic notion of function to that of a distribution, also known as a "generalized function." Our formalism involves a whitening/regularization operator

L: S\to S'

whose continuous extension induces a native Hilbert space

H\subset S'

that plays a central role in our characterization. The presentation is self-contained for the most part and remarkably general and powerful. It allows for the recovery of all known instances of such equivalences; in particular, the methods involving innovations and reproducing-kernel Hilbert spaces developed by Kailath and his students, and the mathematical correspondence between fractional splines and Mandelbrot's fractional Brownian motion (fractals), with the former being the optimal estimators of the latter. It also covers general Bayesian methods for the resolution of infinite-dimensional inverse problems.