arXiv research

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

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

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

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

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

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…

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

Proposes a new Bayesian mixture of student-t processes for modeling non-stationary data.

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

A new method for nonstationary Gaussian processes using Fourier features.

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.

The paper develops a stationary-distribution theory for Random Forest ensemble size selection.

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.

Automated denoising score matching handles nonlinear diffusion processes.

Advanced kernels improve Gaussian process accuracy by incorporating domain knowledge.

The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatmen…

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.

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.

Proposes LSGP for better graph signal representation.

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.

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and non-uniformly smooth spatial boundaries. A Gaussian process regression using a non-stat…

Bayesian optimization has shown to be a fundamental global optimization algorithm in many applications: ranging from automatic machine learning, robotics, reinforcement learning, experimental design, simulations, etc. The most popular and effective Bayesian optimization relies on a surrogate model in the form of a Gaus…

The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and thus invariant to the translations in the input space. The optimization of the hyp…

Develops nonstationary MOGP kernels for better performance.

ETGP improves multi-class classification efficiency.

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 …

Distributed Quantum Gaussian Processes improve modeling in multi-agent systems.

Paper proposes no-regret algorithms for private GP bandit optimization.

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 …

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a novel construction of Gaussian process as a projection from fixed discrete frequen…

Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over composition functions. We propose interpretable DGP based on approximating DGP …

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…