arXiv research

This work explores variably scaled kernels to improve non-stationary Gaussian processes.

Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian Processes, this method may not be adapted for non-stationary functions involved in the op…

Inter-domain Deep Gaussian Processes improve inference for non-stationary data.

Model separates overall uncertainty into aleatoric and epistemic components for active learning.

ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.

Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.

Advanced kernels improve Gaussian process accuracy by incorporating domain knowledge.

This paper proposes a novel Gaussian process approach to fault removal in time-series data. Fault removal does not delete the faulty signal data but, instead, massages the fault from the data. We assume that only one fault occurs at any one time and model the signal by two separate non-parametric Gaussian process model…

Flexible GP model improves wind power prediction accuracy.

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-…

The paper extends NSGPs with $L^1$-regularization for sparsity and solves the resulting R-NSGP regression problem.

The paper examines Nash equilibrium in GANs for stationary Gaussian processes.

This work improves Gaussian process regression for large, non-stationary data.

A new kernel improves Gaussian process performance for non-stationary data.

Develops Gaussian processes on non-Euclidean spaces with symmetries.

Develops Gaussian processes on non-compact Lie groups.

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in $\mathcal{O}(n\log_2 n)$ operations, where…

New analysis explains pathology of deep Gaussian processes.

This work improves Gaussian process inference using mixtures of experts and nested SMC samplers.

Develops nonstationary MOGP kernels for better performance.

ETGP improves multi-class classification efficiency.

Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training …

Bayesian optimization with Gaussian processes speeds up searches for stationary points.

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with non-stationary process…

We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based inference methods to learn the unknown function and the non-stationary model param…

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting …

Adaptive sparse GP model for non-stationary data.

New kernel models multi-output Gaussian processes accurately.

A new method optimizes in nonstationary environments with many arms efficiently.

This work develops discrete Gaussian models for vector-valued data on triangular meshes.

New Hida-Matérn kernels enable flexible process priors and efficient GP inference.

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the latter suffers from intractable computation and can lead to overfitting. Taking the i…

Standard kernels such as Matérn or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more complicated patterns in the data. Spectral mixture kernels have recently been generalized in…

Maximum likelihood estimation fails to be well-posed in Gaussian process regression.

A new method for nonstationary Gaussian processes using Fourier features.

The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where $n$ is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS …

ConvGNP improves sensor placement for climate monitoring.

A novel GPDA method for high-dimensional functional data.

A new learning strategy using two GP layers for inhomogeneous data.

Gaussian processes improved for ocean current reconstruction and divergence identification.

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzi…

A new method warps inputs to learn nonstationary kernels efficiently.

Exact Gaussian Processes for massive datasets using non-stationary sparsity-discovering kernels.

The study recovers airflow from thoracic and abdominal movements using advanced signal processing.

We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of the article is to establish a diffusion approximation …

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral dens…

ConvNets improve nonstationary covariance estimation for large-scale spatial data.