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.
The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.
problem Analyzing uncertainty in sparse Gaussian process regression with a Brownian motion prior.
method Theoretical guarantees and limitations for pointwise credible sets are derived for a rescaled Brownian motion prior with a sparse variational Gaussian process method.
result Theoretical characterization of asymptotic frequentist coverage for credible sets, distinguishing conservative and overconfident cases.
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). 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.
Zero-inflated datasets, which have an excess of zero outputs, are commonly encountered in problems such as climate or rare event modelling. Conventional machine learning approaches tend to overestimate the non-zeros leading to poor performance. We propose a novel model family of zero-inflated Gaussian processes (ZiGP) …
Sparse Gaussian processes with compact kernels for faster inference.
problem Efficient Gaussian process inference with high computational complexity.
method Parametric families of compactly-supported kernels for sparse matrix representations.
result Sub-quadratic inference complexity and improved performance on real-world tasks.
Sparse Markovian Gaussian processes improve probabilistic model inference for large datasets.
problem Efficient inference for large-scale time series data.
method Combining inducing variables with Kalman filter-like recursions for linear scaling.
result General site-based approach for approximating non-Gaussian likelihoods.
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems, so called recurrent models are frequently used. In this paper we introduce several new Deep recurrent Gaussian process (DRGP) models based on…
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…
A new knot selection method speeds up sparse Gaussian process approximations.
problem Efficiently selecting knots for sparse Gaussian processes.
method One-at-a-time Bayesian optimization for knot selection.
result Competitive performance with reduced computational cost.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
A new method for efficient Gaussian process inference using sparse approximations.
problem Scalable and accurate inference for latent Gaussian processes.
method Variational approximation with sparse inverse Cholesky factors and double Kullback-Leibler minimization.
result The proposed method can achieve highly accurate approximations with polylogarithmic time complexity.
SGPA calibrates transformer uncertainty for safety-critical tasks.
problem Uncertainty estimation in transformer models for safety-critical domains.
method Bayesian inference in transformer's output space using sparse Gaussian processes.
result SGPA-based Transformers improve in-distribution calibration and out-of-distribution robustness.
Develops SGP-VAE for efficient sparse GP inference in multi-dimensional datasets.
problem Sparse GP approximations and missing data in multi-dimensional spatio-temporal datasets.
method Leverages partial inference networks for sparse GP approximations and amortized variational inference.
result Outperforms multi-output GPs and structured VAEs in various experiments.
Improved sample complexity for Gaussian process approximations.
problem Efficiently approximating Gaussian processes with sparse spectrum.
method Improved sample complexity analysis and auto-encoding algorithm.
result Gaussian process predictions and model evidence can be well-approximated with low sample complexity.
Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.
problem Generating high-dimensional Gaussian random vectors for GP sampling is computationally challenging.
method Proposes a scalable algorithm using inducing points approximation with sparse grids and additive Schwarz preconditioners.
result Demonstrates the efficacy and accuracy of the proposed method through experiments and comparisons.
SigGPDE scales sparse Gaussian processes for sequential data.
problem Predicting and quantifying uncertainty in sequential data.
method Sparse variational inference framework for Gaussian Processes, leveraging GP signature kernel gradients as PDE solutions.
result Significant computational gains and state-of-the-art performance on large sequential datasets.
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.
Sparse Gaussian process hyperparameters optimized using MCMC.
problem Hyperparameter uncertainty leads to biased estimates and underestimation of predictive uncertainty.
method Proposes an MCMC algorithm to sample from the hyperparameter posterior in sparse Gaussian process regression.
result Significantly improves sampling efficiency in the Gaussian likelihood case.
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.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
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.
Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.
problem Scaling Gaussian processes for large datasets.
method Structured diagonal scaling matrix and Power-EP framework.
result Structured approximations improve performance without increasing computational cost.
Improves SVGP methods for faster and more accurate Gaussian process inference.
problem Efficient non-conjugate Gaussian process inference.
method Dual parameterization of SVGP methods using site parameters.
result Faster and more accurate inference with tighter evidence lower bound.
New method speeds up sparse Gaussian processes for large datasets.
problem Efficiently modeling large datasets with many inducing variables.
method Projecting a GP onto B-spline basis functions for sparse linear algebra.
result Efficiently models fast-varying spatial phenomena with tens of thousands of inducing variables.
New method improves stability of Gaussian process approximations.
problem Numerical instability in Gaussian process computations.
method Cover tree modification for inducing points, alternative sparse approximation.
result Improved stability and predictive performance in spatial tasks.
DistGP models multi-robot mapping with distributed Gaussian process learning.
problem Collaborative mapping by multiple robots with limited local data.
method Sparse Gaussian process with factorisation and distributed training via GBP.
result DistGP achieves superior accuracy and robustness compared to DiNNO.
New method optimizes Gaussian process allocation for BO.
problem Existing methods for inducing point allocation in BO hinder performance.
method Proposes a new allocation strategy using quality-diversity decomposition.
result Demonstrates improved BO performance through local high-fidelity modeling.
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 propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…
The class of Gaussian Process (GP) methods for Temporal Difference learning has shown promise for data-efficient model-free Reinforcement Learning. In this paper, we consider a recent variant of the GP-SARSA algorithm, called Sparse Pseudo-input Gaussian Process SARSA (SPGP-SARSA), and derive recursive formulas for its…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of two independent processes: one spanned by a finite basis of inducing points and…
Paper proposes a fast data-driven AC-OPF method using sparse hybrid Gaussian processes.
problem Optimizing electricity generation and delivery under generation uncertainty in modern power grids.
method Data-driven approach using sparse hybrid Gaussian processes to model power flow equations.
result Shows up to two times faster and more accurate solutions compared to state-of-the-art methods.
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.
Online anomaly detection of time-series data is an important and challenging task in machine learning. Gaussian processes (GPs) are powerful and flexible models for modeling time-series data. However, the high time complexity of GPs limits their applications in online anomaly detection. Attributed to some internal or e…
Sparse GPs improved with nearest neighbor inducing variables.
problem Sparse GPs struggle with large numbers of inducing variables.
method Introduced a hierarchical prior for inducing variables and used nearest neighbor information for sparsity.
result Significant computational gains compared to standard sparse GPs.
SVGP KAN integrates uncertainty quantification into Kolmogorov-Arnold networks.
problem Uncertainty quantification in scientific machine learning models.
method Sparse variational Gaussian process inference with Kolmogorov-Arnold topology.
result Demonstrated ability to distinguish aleatoric and epistemic uncertainty in various scientific applications.
Proposes a robust similarity measure for sparse time series data.
problem Sparse time course data in biological settings.
method Gaussian processes (GP) similarity measure based on log-likelihood ratio.
result Enhanced robustness to noise compared to Euclidean distance.
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.
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and estimates are calculated directly from dense data sets using Gaussian process r…
Kernel Multigrid accelerates Back-fitting for additive Gaussian Processes.
problem Slow convergence of Back-fitting in training additive Gaussian Processes.
method Kernel Packets (KP) and Sparse Gaussian Process Regression (GPR) to enhance Back-fitting.
result Kernel Multigrid reduces the required iterations to O(logn). New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.
problem Inference and simulation of GMRFs are computationally prohibitive with many constraints.
method Proposes a basis transformation into blocks of constrained and non-constrained subspaces.
result Significantly outperforms existing alternatives in computational cost.
New method trains sparse Gaussian processes without matrix inversion.
problem Costly training of Gaussian processes at scale.
method Inverse-free approach using matmul-only natural-gradient updates.
result Significantly improved stability and convergence in training.
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we introduce two new Deep Recurrent Gaussian Process (DRGP) models based on the Sparse Sp…
Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated Bayesian treatment of GAMs using Gaussian processes (GPs) and leveraging recent adv…
The paper improves sparse Gaussian processes by optimizing predictive loss.
problem Optimizing predictive loss in sparse Gaussian processes.
method Direct loss minimization (DLM) for log-loss and square loss, with product sampling (uPS) and biased Monte Carlo (bMC) for non-conjugate cases.
result DLM shows significant performance improvement in both log-loss and square loss cases.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
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 …