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.
Adaptive Gaussian process models for efficient Bayesian inference.
problem Expensive forward models in Bayesian inference.
method Fully Bayesian approach with adaptive training designs maximizing expected improvement.
result Adaptive designs lead to more accurate posterior estimation at lower cost.
Bayesian Optimization uses Deep Gaussian Processes for non-stationary functions.
problem Optimizing expensive non-stationary functions with classic Gaussian Processes.
method Deep Gaussian Processes as surrogate models for capturing non-stationarity.
result The proposed algorithm outperforms state-of-the-art methods on analytical and aerospace design problems.
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.
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.
Bayesian optimization sped up with scalable Gaussian processes.
problem Optimizing functions with derivative information and large datasets.
method Combines derivative acceleration and scalable Gaussian process models.
result Significant speedup in optimization convergence for large datasets.
VMGP extends Gaussian processes for Bayesian meta-learning, improving uncertainty prediction.
problem Bayesian meta-learning for few-shot tasks with non-Gaussian uncertainty.
method VMGP (Variational Meta-Gaussian Processes) extends Gaussian processes to model non-Gaussian predictive posteriors.
result VMGP significantly outperforms existing Bayesian meta-learning methods on complex tasks.
New method to assess uncertainty in Bayesian optimization.
problem Uncertainty quantification in Bayesian optimization.
method Constructing confidence regions of the maximum point or value of the objective function.
result Unified uncertainty quantification framework for various sampling policies and stopping criteria.
Bayesian deep learning on quantum computers using Gaussian process connections.
problem Training deep neural networks with Bayesian uncertainty estimates on quantum computers.
method Connecting deep neural networks to Gaussian processes, leveraging quantum algorithms for inversion.
result At least polynomial speedup over classical algorithms for Bayesian deep learning on quantum computers.
Proposes a Bayesian Autoencoder with sparse Gaussian process priors to capture data correlations.
problem Autoencoders' i.i.d. assumption of latent representations fails to capture data correlations.
method Imposes fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder and uses stochastic gradient Hamiltonian Monte Carlo for posterior estimation.
result Consistently outperforms alternatives relying on Variational Autoencoders on various tasks.
Deep convolutional Gaussian processes boost image classification accuracy.
problem Image classification with hierarchical feature combinations.
method Deep Gaussian process architecture with convolutional structure.
result Significantly improved image classification performance on MNIST and CIFAR-10 datasets.
This paper explores approximations for fully Bayesian Gaussian Process Regression.
problem Learning in Gaussian Process models through hyperparameter adaptation.
method Two approximation schemes: Hamiltonian Monte Carlo and Variational Inference.
result Predictive performance analysis on various benchmark datasets.
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.
Improved Bayesian optimisation method using randomised Gaussian process UCB.
problem Improving performance in Bayesian optimisation.
method Developed a modified Gaussian process upper confidence bound (GP-UCB) acquisition function.
result The method achieves better performance than GP-UCB in various problems.
The article explores Gaussian processes and Bayesian optimization in financial applications.
problem Modeling financial markets and optimizing strategies.
method Gaussian processes and Bayesian optimization methods.
result Gaussian processes and Bayesian optimization are effective in financial modeling and strategy construction.
Decentralized Gaussian processes for multi-agent systems.
problem Scalable and flexible learning solutions for multi-agent systems.
method Asymptotically exact decentralized solution to Gaussian processes, with online Bayesian model averaging for hyperparameter selection.
result Asymptotically exact decentralized Gaussian process approximation and online Bayesian model averaging.
Bayesian layer improves image segmentation and out-of-distribution detection.
problem Outlier detection in image segmentation.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates improve out-of-distribution detection.
Bayesian optimization selects experiments for causal structure learning in Gaussian process networks.
problem Discover causal relationships in non-linear systems with continuous variables.
method Bayesian active learning and Gaussian process priors combined with Bayesian optimization for experiment selection.
result Efficiently maximizes expected information gain in learning causal structure.
Bayesian method calibrates local volatility with Gaussian processes.
problem Calibrating local volatility models is challenging.
method Bayesian inference with Gaussian process priors.
result Rich probabilistic model of local volatility with uncertainty.
Optimizes parameter reconstruction for optical scatterometry using Gaussian process regression.
problem Efficiently reconstructing geometry parameters of micro/nanostructures from scatterometry measurements.
method Bayesian optimization with Gaussian-process regression to find optimal parameter values.
result Gaussian process regression accelerates the optimization process for numerical simulations.
Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.
problem Minimizing regret in Gaussian process bandit optimization.
method Gaussian process upper confidence bound (GP-UCB) algorithm with refined analysis.
result Achieves O ( T ln 2 T ) O(\sqrt{T \ln^2 T}) O ( T ln 2 T ) cumulative regret under squared exponential kernel. Bayesian approach to data association using Gaussian processes.
problem Separating data from different generating processes.
method Fully Bayesian approach with Gaussian process priors for structure encoding and doubly stochastic variational inference.
result Efficient learning scheme for deep Gaussian process priors.
RGPs connect predictive coding to Bayesian inference, providing a neural substrate.
problem Scalable implementations of Bayesian inference respecting neurobiological constraints.
method Formal connection between predictive coding and Recursive Gaussian Processes (RGPs).
result RGPs intrinsically implement hierarchical Bayesian inference and uncertainty propagation.
Bayesian model learns complex multivariate dependencies.
problem Learning dependency structures across multiple dimensions.
method Flexible Gaussian process priors and Dirichlet process for structure learning.
result Efficient variational inference for model parameters.
Bayesian ODEs with Gaussian processes infer unknown dynamics from data.
problem Estimating unknown continuous-time system dynamics from data.
method Bayesian nonparametric model using Gaussian processes, sparse variational inference, probabilistic shooting.
result Posterior predictive uncertainty scores outperform alternative methods on multiple ODE learning tasks.
Bayesian inference for wide neural networks using Edgeworth expansion.
problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.
method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.
result Derived non-Gaussian posterior distribution in Bayesian regression tasks.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
Bayesian framework improves uncertainty quantification in Gaussian process models.
problem High correlations between latent variables and hyperparameters in Gaussian process models.
method Uses pseudo-marginal method to estimate marginal likelihood and explore posterior of hyperparameters.
result Demonstrates improved uncertainty quantification and multimodality in hyperparameters compared to variational inference.
The paper improves Bayesian optimization by estimating unknown Gaussian process parameters.
problem The challenge of unknown parameters in Bayesian optimization.
method Adopting empirical Bayes to estimate Gaussian process prior and constructing unbiased estimators.
result Achieves near-zero regret bound, decreasing to a constant proportional to observational noise.
Bayesian framework reduces high-dimensional GP modeling costs.
problem Challenges in fitting Gaussian processes to high-dimensional inputs.
method Hierarchical Bayesian model with orthonormal projection matrix, incorporating Deep Gaussian Processes.
result Improves predictive performance and uncertainty quantification.
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
Finite-width neural networks use non-Gaussian priors, extending Gaussian process theory.
problem Understanding the behavior of neural networks with finite width.
method Perturbative extension of Gaussian process theory to finite-width neural networks, tracking preactivation distributions.
result Non-Gaussian processes as priors in finite-width neural networks.
Develops a new Gaussian process method for efficient Bayesian inference of plant root parameters in the Richards equation.
problem Estimating unknown parameters in nonlinear PDEs for agricultural studies.
method Gaussian process collocation with importance sampling and Bayesian optimization.
result Our method yields robust estimates with uncertainty quantification for plant root parameters.
Bayesian approach uses Gaussian process for reinforcement learning.
problem Robotic locomotion environments
method Bayesian actor-critic, model-free reinforcement learning with Gaussian process for exploration and policy optimization.
result Gaussian process method outperforms current algorithms in robotic locomotion environments.
Bayesian method learns network structure from Gaussian process priors.
problem Computational infeasibility of Bayesian structure learning in GPNs.
method Monte Carlo and MCMC methods for sampling network structures.
result Method outperforms state-of-the-art algorithms in recovering network structure.
Extends Gaussian Process regression for handling multiple prior distributions.
problem Handling multiple prior distributions in Bayesian Machine Learning models.
method Mixtures of Gaussian Processes with analytical and Sparse Variational approaches.
result Effective in accounting for prior misspecification in functional regression problems.
Bayesian neural networks use ridgelet prior for uncertainty quantification.
problem Combining strong predictive performance with uncertainty quantification in Bayesian neural networks.
method Proposes a ridgelet prior that approximates a Gaussian process covariance function in the output space of the network.
result Establishes universality property allowing Bayesian neural networks to approximate any Gaussian process.
New method for Bayesian neural networks with unbounded weights.
problem Posterior inference for Bayesian neural networks with unbounded weights.
method Conditionally Gaussian representation for efficient posterior inference.
result Interpretable and computationally efficient procedure for posterior inference.
A fast Bayesian optimization method using threshold-guided marginal likelihood maximization.
problem Efficiently optimizing models with Gaussian process regression.
method Guided marginal likelihood maximization with a pre-defined threshold to reduce model selection steps.
result Significantly reduces execution time without compromising optimization quality.
Bayesian approach for inhomogeneous Poisson process intensity estimation.
problem Intractable integral in likelihood of Gaussian Cox process.
method Joint modeling of intensity and cumulative intensity as transformed Gaussian process; exact MCMC sampler.
result Exact posterior inference without approximations.
Bayesian Gaussian Processes layer detects out-of-distribution data in medical imaging.
problem Detecting out-of-distribution data in medical imaging tasks.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates enable superior out-of-distribution detection compared to previous methods.
Combines Gaussian process and Geometric Harmonics for better uncertainty estimation.
problem Uncertainty estimation in kernel-based methods.
method Combines Gaussian process and Geometric Harmonics.
result Alternative interpretations of uncertainty and accelerated Bayesian Optimization.
Deep Gaussian Processes improve likelihood-free inference for complex distributions.
problem Limited flexibility of Bayesian Optimization with GPs for multimodal distributions.
method Proposes Deep Gaussian Processes (DGPs) as a surrogate model for likelihood-free inference.
result DGPs outperform GPs on multimodal distributions while maintaining comparable performance on unimodal cases.
Student's-T processes improve on Gaussian processes by handling outliers and variance more flexibly.
problem Outliers and variance limitations in Gaussian processes.
method Generalization of Gaussian processes using Student's-T distribution, with new kernel function and update rule.
result Student's-T processes provide better performance in Bayesian optimization, especially with outliers.
Enhanced Gaussian process models accelerate optimization and posterior approximation.
problem Improving the accuracy and speed of Gaussian process models for optimization and inference.
method Introduces a random exploration step to classical GP-UCB algorithms, facilitating faster convergence.
result New algorithms achieve nearly optimal convergence rates and provide bounds for Hellinger distance.
Scalable GAMs using sparse variational Gaussian processes.
problem Flexible modeling of data beyond linear models.
method Bayesian treatment of GAMs using Gaussian processes (GPs) with sparse representation and additive structure.
result Efficient and well-calibrated Bayesian treatment of GAMs.
New method learns Gaussian Processes with better generalization guarantees.
problem Lack of good performance guarantees for Gaussian Processes in safety-critical applications.
method Optimizes a PAC-Bayesian bound on generalization performance.
result Significantly better generalization guarantees on benchmark datasets.
Study how depth affects inference in deep Bayesian neural networks.
problem Understanding how depth impacts inference in overparameterized linear Bayesian neural networks.
method Interpreting finite deep linear Bayesian neural networks as scale mixtures of Gaussian process predictors.
result Advances analytical understanding of how depth affects inference in a simple class of Bayesian neural networks.