Proposes GPHMEs using Gaussian processes for hierarchical expert models.
problem Hierarchical mixtures of experts with complex gating functions.
method Gaussian process-gated hierarchical mixtures of experts (GPHMEs) with non-linear gating and expert functions.
result Outperforms tree-based HMEs and achieves good performance with reduced complexity.
Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
problem High nodal variance in BHMC trees, leading to weak separation between nodes at higher levels.
method Employing Posterior Regularization to impose max-margin constraints on nodes at every level.
result Improves cluster separation in BHMC models, enhancing overall model performance.
Improved outlier detection in hierarchical Gaussian Processes using Wasserstein-2 kernels.
problem Outlier detection limitations in stacked Gaussian Processes.
method Proposed a hybrid kernel combining Euclidean and Wasserstein-2 distances, emphasizing variance in Wasserstein-2 computations.
result Improved performance and enhanced out-of-distribution detection on various datasets.
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.
A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is minimized through the hierarchical design. The method is further extended to joint mod…
We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for effici…
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 estimators for causal inference using hierarchical Gaussian Processes.
problem Estimating causal effects in sharp and fuzzy RD/RK designs.
method Hierarchical Gaussian Process models for regression and classification.
result Hierarchical GP models improve precision and coverage of RD/RK estimations.
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 …
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…
BITS for GAPS uses Bayesian methods to improve surrogate model accuracy in complex systems.
problem Improving surrogate model accuracy in complex physical systems with uncertainty.
method Bayesian Information-Theoretic Sampling for hierarchical Gaussian Process Surrogates.
result Increased expected information gain and predictive accuracy by targeting high-uncertainty regions.
BOSH optimizes functions with stochastic evaluations more efficiently and precisely.
problem Optimizing functions with noisy evaluations can lead to suboptimal solutions.
method BOSH uses a hierarchical Gaussian process to generate a growing pool of realizations.
result BOSH provides more efficient and higher-precision optimization than standard BO.
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.
DeepICMGP surrogate models multiple outputs efficiently.
problem Challenges in modeling dependencies between multiple outputs using traditional multi-output GPs.
method Introduces hierarchical coregionalization structures across layers in DGPs.
result Demonstrates competitive performance and active learning strategies.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
This paper introduces hierarchical Gaussian process priors for neural networks to capture weight correlations and inductive biases.
problem Capturing weight correlations and inductive biases in neural networks.
method Hierarchical Gaussian process priors with unit embeddings and input-dependent kernels.
result Hierarchical Gaussian process priors provide competitive predictive performance and desirable uncertainty estimates.
Bayesian models forecast COVID-19 hospitalizations at single sites.
problem Forecasting daily COVID-19 hospitalizations at a single hospital.
method Hierarchical Bayesian models with generalized Poisson likelihood and autoregressive/Gaussian process latent processes.
result Demonstrated superior performance compared to baselines in public datasets.
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.
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian p…
The paper extends NSGPs with L1-regularization for sparsity and solves the resulting R-NSGP regression problem.
problem Sparsity in non-stationary temporal data.
method Developed an ADMM-based method for solving the regularized NSGP regression problem.
result The proposed methods induce sparsity in the parameters of NSGPs.
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approa…
Improves sampling efficiency for complex Bayesian models.
problem Inference challenges in hierarchical Gaussian-process models.
method Optimised Riemannian-manifold Hamiltonian Monte Carlo (RMHMC) with dynamic programming.
result Significant improvement in sampling efficiency and model evidence calculation.
In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed. It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients. We design an inference algorithm based on Expectation Propagation and evaluate the mode…
HIP-GP improves GP inference for inter-domain observations with millions of inducing points.
problem Inference for Gaussian Processes across different domains.
method Hierarchical inducing point Gaussian process with grid structure and stationary kernel assumption.
result Improved approximation accuracy through increased number of inducing points.
GPflux simplifies deep Gaussian processes for Python.
problem Challenges in implementing deep Gaussian processes.
method Python library for Bayesian deep learning with DGPs.
result Efficient, modular, and extensible library for DGPs.
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
The paper improves Gaussian process regression by optimizing hyperparameters.
problem Hyperparameter tuning for Gaussian process regression models.
method Adaptive sparse variational approximations using variational Bayes.
result Minimax optimal rates of convergence for variational posterior.
Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions, all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively…
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…
HierGP improves emulator efficiency for sparse, structured data.
problem Sparse, structured data in expensive simulations.
method Hierarchical shrinkage GP framework with cumulative shrinkage priors.
result HierGP identifies structured sparse features from limited data.
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
HyperBO+ pre-trains a universal prior for Bayesian optimization across different domains.
problem Bayesian optimization requires domain-specific priors, limiting its applicability.
method Two-step pre-training method for hierarchical Gaussian processes.
result HyperBO+ achieves lower regrets on unseen search spaces.
Combines physics-based ML with hierarchical Bayesian techniques for better model performance.
problem Lack of physical knowledge in black-box machine learning models.
method Embeds physics-based models into Gaussian Process mean function and uses kernel machines to characterize discrepancies.
result Improved model performance under blind conditions through integration of physics-based knowledge.
Unified view on GP transfer learning for Bayesian optimization.
problem Improving data efficiency in Bayesian optimization with scarce data.
method Unified hierarchical GP models for transfer learning, including a novel boosted GP transfer model.
result Unified analysis and comparison of transfer learning methods for GP models.
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.
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called \textit{Type II maximum likelihood} or ML-II). An alternative learning proced…
Wide neural networks can degrade performance, contrary to conventional wisdom.
problem Understanding the limitations of increasing network width in neural networks.
method Using Deep Gaussian Processes to decouple capacity and width, analyzing their effects on representational power and non-Gaussianity.
result Wide neural networks can become less adaptable and more Gaussian, leading to performance degradation.
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. W…
This paper reviews recent advances in Gaussian process regression methods.
problem Handling uncertainties and scalability in large-scale systems with sparse data.
method Factorised Gaussian process methods, including hierarchical off-diagonal low-rank approximation and GP with Kronecker structures.
result These methods provide scalable solutions with inherent uncertainty assessment.
HPPCA improves imputation of longitudinal data with missing values.
problem Handling incomplete, high-dimensional longitudinal data with nested sources of variation and temporal dependency.
method Hierarchical probabilistic principal component analysis (HPPCA) with a two-level latent factor model and Gaussian process.
result HPPCA outperforms standard PPCA and multivariate functional PCA in imputation accuracy, even under heavy missingness and model misspecification.
Study uses SABR model to create implied volatilities from sparse quotes.
problem Creating accurate implied volatility surfaces from limited market data.
method Multitask Gaussian process with SABR model embeddings and hierarchical regularization.
result Model produces more accurate volatilities than single-task methods.
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that exact inference is intractable. The current state-of-the-art inference method, …
Develops scalable model for learning velocity fields in complex traffic scenarios.
problem Learning heterogeneous and dynamic velocity fields in complex traffic scenarios.
method Nonparametric Bayesian modeling with hierarchical Dirichlet process and infinite hidden Markov model, Gaussian process prior, and scalable approximate inference.
result Demonstrates effective scalability and applicability to real-world traffic data.
Enhances topic models to better handle polysemous words.
problem Lack of polysemy handling in Gaussian latent Dirichlet allocation.
method Introduces a hierarchical structure to capture polysemy in Gaussian latent Dirichlet allocation.
result Significantly improves polysemy detection and provides more parsimonious topic representations.
We consider the problem of aggregating models learned from sequestered, possibly heterogeneous datasets. Exploiting tools from Bayesian nonparametrics, we develop a general meta-modeling framework that learns shared global latent structures by identifying correspondences among local model parameterizations. Our propose…
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the great flexibility of multilayer models. In DGPs, given the inputs, the outputs …
Bayesian approach for learning spatiotemporal systems from noisy data.
problem Efficiently modeling and learning from spatiotemporal dynamical systems with noisy data.
method Hierarchical state-space models with Gaussian process regression for efficient interpolation and training.
result Efficient modeling and learning of spatiotemporal dynamics using Bayesian methods.
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process based c…