Gaussian processes model geospatial trajectories with uncertainty.
problem Interpolating and predicting complex spatiotemporal data.
method Gaussian process models trajectories as multidimensional Gaussian distributions.
result Gaussian processes provide a flexible and probabilistic way to interpolate geospatial data.
Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.
problem Gaussian process regression struggles with compositional functions.
method We study information-theoretic lower bounds for posterior contraction rates in Gaussian process regression for a continuous regression model.
result Posterior based on any mean-zero Gaussian process can only recover the truth at a rate strictly slower than the minimax rate for generalized additive functions.
New sparse Gaussian process method tackles unconstrained regression problems.
problem Dealing with physical systems that satisfy inequality constraints.
method Extends constrained Gaussian process by redefining hat basis functions.
result Reduces computational complexity from O(n3) to O(nm2). Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance conditioned on observed data depends only on the locations of those data, not the assoc…
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to …
This note explains when neural networks can be seen as Gaussian processes.
problem Understanding the relationship between neural networks and Gaussian processes.
method Formulating a Gaussian process regression based on neural network outputs and analyzing the resulting posterior mean functions.
result The posterior mean functions of neural networks follow a Gaussian process in certain cases, providing an interpretation of reproducing kernel Hilbert spaces.
Graph Gaussian processes use Matérn models for better function learning.
problem Lack of Gaussian process models for graph input spaces.
method Stochastic partial differential equation characterization of Matérn Gaussian processes.
result Graph Matérn Gaussian processes inherit properties of Euclidean and Riemannian models and can be trained efficiently.
Gaussian processes adapted for non-Euclidean spaces enhance decision-making.
problem Applying Gaussian processes in non-Euclidean spaces.
method Developed pathwise conditioning and Gaussian process models over non-Euclidean spaces.
result Efficient Gaussian process models for non-Euclidean spaces.
A new method combines Gaussian Processes to optimize under uncertainty.
problem Bayesian Optimization's weakness in fitting Gaussian Processes.
method Wasserstein Barycenter Gaussian Process (WBGP) approach.
result WBGP-BO converges to the optimum, improving on vanilla BO.
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
Elliptical processes extend Gaussian models with heavier tails.
problem Regression and classification with non-Gaussian likelihoods or heavy tails.
method Spline normalizing flow for variational inference of elliptical distributions.
result Elliptical processes outperform Gaussian processes in non-Gaussian settings.
This paper speeds up Gaussian process regression for autocorrelated data.
problem Temporal overfitting in Gaussian process models for autocorrelated data.
method Modifying existing Gaussian process approximations to handle blocked, de-correlated data.
result Proposed methods accelerate Gaussian process regression on autocorrelated data without sacrificing performance.
A new algorithm splits Gaussian processes for efficient streaming data.
problem Poor scaling of Gaussian processes in streaming data.
method Sequential partitioning of input space and localized Gaussian process fitting.
result The algorithm achieves linear memory complexity and superior time and space complexity.
Optimizes Gaussian process hyperparameters using Bayesian autoregression.
problem Optimizing hyperparameters for Matérn kernel temporal Gaussian processes.
method Recursive Bayesian estimation for autoregressive parameters.
result Outperforms traditional optimization methods in runtime and accuracy.
This work improves Gaussian process inference using mixtures of experts and nested SMC samplers.
problem High computational and memory costs of Gaussian processes.
method Mixtures of Gaussian process experts with nested SMC samplers.
result Significantly improved inference compared to importance sampling.
Deep Gaussian Processes with polynomial kernels can collapse rapidly without proper hyperparameter tuning.
problem The collapse of Deep Gaussian Processes with polynomial kernels without careful hyperparameter tuning.
method Analysis using the Berry-Esseen Theorem and observation of prior behavior.
result The prior of a Deep Gaussian Process collapses rapidly towards zero or places negligible mass on low norm functions without proper hyperparameter tuning.
Gaussian processes adapted for Riemannian manifolds using gauge-independent kernels.
problem Deploying Gaussian processes on non-Euclidean domains like Riemannian manifolds.
method Developed techniques to generalize Gaussian processes to vector fields on Riemannian manifolds using gauge-independent kernels.
result Enabled training of vector-valued Gaussian processes on Riemannian manifolds using standard Gaussian process methods.
The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of t…
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.
problem Extending classical Gaussian min-max theorems to non-i.i.d. Gaussian matrices.
method Identifying a new pair of Gaussian processes that satisfy comparison inequalities.
result New Gaussian min-max and convex Gaussian min-max theorems with applications in multi-source Gaussian regression and binary classification.
This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.
problem Approximating non-Gaussian likelihoods in Gaussian Processes.
method Proposes a piece-wise constant approximation for the inverse-link function.
result Yields a closed form solution for the SVGP lower bound.
This paper shows how infinitely wide Tensor Networks converge to Gaussian Processes.
problem Understanding the relationship between Tensor Networks and Gaussian Processes.
method Analyzing the infinite-width limit of Tensor Networks and comparing them to Gaussian Processes.
result Infinitely wide Tensor Networks converge to Gaussian Processes, proving their equivalence.
We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image classification. We demonstrate greatly improved image classification performance compared …
Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.
problem Efficiently implementing Gaussian process acquisition functions for expensive simulations.
method Proposed a truncated eigenbasis representation for closed-form evaluation of IMSE acquisition function.
result Significantly lower prediction error and reduced computation time compared to benchmarks.
New Gaussian processes for Riemannian manifolds enable uncertainty quantification.
problem Modeling functions on Riemannian manifolds with uncertainty.
method Generalized Matérn Gaussian processes on compact manifolds via spectral theory.
result Efficient training of Riemannian Matérn Gaussian processes using scalable techniques.
Develops intrinsic Gaussian process regression for manifold-valued data.
problem Lack of intrinsic Gaussian process methods for manifold-valued response variables.
method Proposes an intrinsic covariance structure and a novel intrinsic Gaussian process regression model.
result Establishes asymptotic properties and shows posterior consistency.
Ens-CGP synthesizes ensemble-based inference with Gaussian processes.
problem Ensemble-based inference and Gaussian process modeling.
method Formulates Ens-CGP as a conditional Gaussian process for ensemble moments.
result Ens-CGP provides a unified probabilistic foundation for Kalman-type methods.
This thesis tackles Gaussian Process challenges in low dimensions.
problem Constructing models for large datasets and selecting optimal models.
method Samplet-based approach to efficiently construct and train Gaussian Processes.
result Reduces cubic computational complexity to log-linear scale.
This study connects Gaussian processes and RKHS, bridging two machine learning communities.
problem Understanding the relationship between Gaussian processes and RKHS.
method Examining connections and equivalences in regression, interpolation, and other topics.
result Established the equivalence between Gaussian Hilbert space and RKHS.
Meta-learn sparse Gaussian process inference for faster predictions.
problem Cubic computational cost of exact Gaussian process inference for many observations.
method Meta-learn sparse Gaussian process inference.
result Rapid prediction on new tasks with sparse Gaussian processes.
Develops a new method for functional regression that works with non-Gaussian data.
problem Limited models for regression in function spaces with Gaussian process priors.
method Introduces Neural Operator Flows (OpFlow) for non-Gaussian function spaces.
result OpFlow enables robust and accurate uncertainty quantification for functional regression.
Develops Gaussian processes on non-Euclidean spaces with symmetries.
problem Invariance to symmetries in non-Euclidean spaces.
method Constructive techniques for stationary Gaussian processes on compact and non-compact spaces.
result Makes non-Euclidean Gaussian processes compatible with standard software.
Develops Gaussian processes on non-compact Lie groups.
problem Invariance to symmetries in non-Euclidean spaces.
method Constructive techniques for stationary Gaussian processes.
result Makes non-Euclidean Gaussian processes compatible with standard software.
Paper introduces robust Gaussian process regression without sacrificing computational efficiency.
problem Violation of independent and identically distributed Gaussian observation noise assumption in Gaussian process regression.
method Proves robust and conjugate Gaussian process regression (RCGP) at no additional cost using generalised Bayesian inference.
result RCGP enables exact conjugate closed form updates in all settings where standard GPs admit them.
Advanced kernels improve Gaussian process accuracy by incorporating domain knowledge.
problem Improving function approximation accuracy in Gaussian processes.
method Advanced kernel designs that enforce specific function properties (symmetry, periodicity) and non-stationarity.
result Advanced kernels significantly enhance function approximation accuracy and relevance.
Improved Gaussian process experts model for complex data.
problem Limitations of standard Gaussian processes: scalability and predictive performance.
method Proposes a new mixture model of Gaussian process experts based on kernel stick-breaking processes.
result Improved predictive performance compared to existing models.
Survey on Gaussian processes and their deep variants.
problem Limitations of Gaussian processes and their derivatives.
method Comprehensive review of existing methods and research themes.
result Advancements in Deep Gaussian Processes over the past decade.
Study Gaussian-process limits of neural networks using tensor programs.
problem Understanding the behavior of neural networks as they approach infinite width.
method Quantitative analysis through tensor programs and Wasserstein distance.
result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.
New method optimizes processes under constraints using bivariate Gaussian models.
problem Optimizing processes with constraints using traditional methods.
method Developed a constrained expected improvement acquisition function using bivariate Gaussian process models.
result Demonstrated improved performance in a manufacturing cure process optimization.
Efficiently trains deep Gaussian processes with sparse approximations.
problem High computational complexity in training and inference for DGP models.
method Tensor Markov Gaussian Processes (TMGP) and hierarchical expansion to create DTMGP model.
result DTMGP model achieves superior computational efficiency compared to existing DGP models.
Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.
problem Modeling multiple heterogeneous correlated tasks jointly.
method Data augmentation and mean-field approximation for non-conjugate Bayesian inference.
result Demonstrates improved performance and inference on synthetic and real data.
Improved Gaussian process models for interpretable predictions.
problem Complex responses require high-dimensional interaction terms in additive Gaussian processes.
method Orthogonal additive kernel (OAK) with orthogonality constraint on additive functions.
result OAK models achieve similar or better predictive performance with fewer terms, retaining interpretability.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
GGMPs improve non-Gaussian conditional density estimation.
problem Multimodality, heteroscedasticity, and strong non-Gaussianity in conditional density estimation.
method GGMP combines local Gaussian mixture fitting, cross-input component alignment, and per-component heteroscedastic GP training.
result GGMPs improve distributional approximation on synthetic and real-world datasets.
A scalable Gaussian process clustering method for large datasets.
problem Infeasibility of Gaussian process clustering on large grids.
method Embedding Vecchia approximation in EM algorithm for scalability.
result Efficient Gaussian process clustering for large environmental applications.
This tutorial simplifies Gaussian process regression for beginners.
problem Understanding Gaussian process regression for machine learning.
method Explains basic concepts, provides a concise GPR description, and reviews implementation packages.
result Clear understanding of Gaussian process regression fundamentals.
Extends Gaussian process theory to Banach spaces.
problem Extending Gaussian process theory to Banach spaces.
method Investigates the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces.
result Characterizes positive definite functions that arise from covariance operators in Banach space setting.