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 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 …
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.
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.
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.
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.
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.
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.
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…
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.
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…
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.
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.
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of models. An attractive feature of these models is that they can admit analytic pr…
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.
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.
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.
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 depend on a set of globally relevant inducing variables which factorize the model …
Projection pursuit model improves Gaussian process regression for high-dimensional data.
problem Scalability issues with traditional Gaussian process models in high dimensions.
method Additive Gaussian process regression with dimension expansion and gradient descent.
result The proposed method approximates more complex functions and outperforms traditional models.
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.
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.
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.
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.
Deep Transformed Gaussian Processes extend TGPs with variational inference for scalable multi-layer modeling.
problem Flexible modeling of complex data distributions.
method DTGPs are a multi-layer model of TGPs using variational inference for scalability.
result DTGPs achieve good scalability and performance in multiple regression datasets.
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.
Combines additivity and active subspaces for high-dimensional Gaussian process modeling.
problem High-dimensional Gaussian process modeling challenges due to the curse of dimensionality.
method Combines additivity and active subspaces with a multi-fidelity strategy.
result Shows advantages through experiments on synthetic functions and datasets.
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). Improved Gaussian Process model for predicting trajectories without independence assumption errors.
problem Incorrect independence assumption in previous work on Gaussian Process uncertainty propagation.
method Proposed a novel piecewise linear approximation to correct the independence assumption in continuous models.
result Corrected the independence assumption in Gaussian Process models for predicting trajectories.
Extends Gaussian process regression for non-Gaussian data.
problem Inadequate modeling of uncertainty and over-smoothing in non-Gaussian datasets.
method Time-changed Gaussian processes with Lévy processes.
result Improved modeling of heavy-tailed non-Gaussian behaviors.
The paper introduces a method to probabilistically select inducing points in sparse Gaussian processes.
problem The challenge is selecting the optimal number of inducing points in sparse Gaussian processes.
method A point process prior is applied to the inducing points, and the posterior is approximated using stochastic variational inference.
result The model learns which and how many inducing points to use, leading to fewer inducing points being preferred as they become less informative.
Flexible Hawkes model with Gaussian process self-effects for time-dependent data.
problem Modeling time-dependent point processes with history dependence and self-effects.
method Extended Hawkes process with Gaussian process self-effects for both excitatory and inhibitory types, using Bayesian inference and mean-field variational approximation.
result Efficient approximate Bayesian inference achieved via data augmentation and mean-field variational approach.
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of …
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.
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 …
Combines boosting with Gaussian process and mixed effects models.
problem Model misspecifications and independence assumptions in boosting.
method Relaxes zero or linearity assumption in Gaussian process and mixed effects models, and independence assumption in boosting.
result Increased prediction accuracy compared to existing approaches.
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.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
New method for global optimization of Gaussian processes reduces computational time.
problem Nonconvex optimization problems with Gaussian processes trained on few data points.
method Reduced-space formulation with branch-and-bound solver and McCormick relaxations.
result Significantly reduced computational time compared to state-of-the-art methods.
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
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.
Distributed Quantum Gaussian Processes improve modeling in multi-agent systems.
problem Limited expressivity of classical kernels in complex domains.
method Distributed Quantum Gaussian Process (DQGP) with DR-ADMM algorithm.
result Enhanced modeling capabilities and scalability in multi-agent systems.
The chapter compares Gaussian process models for stochastic simulators with varying noise.
problem Modeling stochastic simulators with varying noise.
method Various Gaussian process models are compared, including input varying noise variance, non-Gaussian noise, and quantile modeling.
result Sequential design procedures are adapted for these 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.
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.
Enhances Gaussian process models for handling variable error variances and multiple responses.
problem Limited ability of Gaussian process models to capture abrupt changes and heteroscedastic errors.
method Introduces a novel heteroscedastic Gaussian process (HeGP) framework coupled with variational inference and EM algorithm.
result Effective modeling of multivariate responses with varying error variances.
In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration. The parallelization scheme arises naturally from the modular computational structure w.r.t. datapoints in the sparse Gaussian process formulation. Additionally, the computational bottleneck is …
GNP models predictive correlations and outperforms NPs.
problem Training and understanding of Neural Processes.
method Proposed a new model, Gaussian Neural Process (GNP), which incorporates translation equivariance and provides universal approximation guarantees.
result Demonstrates encouraging performance and provides universal approximation guarantees.