Study evaluates DGMs' ability to recover non-stationary Gaussian fields.
problem Assessing DGMs' learning of non-stationary Gaussian random fields.
method Comprehensive evaluation of four DGMs (FM, DDPM, score-SDE, VAE) on a known non-stationary Gaussian random field.
result DDPM and score-SDE recover covariance structure reasonably well, while FM and VAE struggle.
Deep models struggle with non-stationary Gaussian fields, but DDPM and score-SDE perform best.
problem Evaluating deep generative models on non-stationary Gaussian random fields.
method Comprehensive evaluation of four DGMs (FM, DDPM, score-SDE, VAE) on a known non-stationary Gaussian random field.
result DDPM and score-SDE recover the covariance structure reasonably well, while FM and VAE have difficulties.
This work develops discrete Gaussian models for vector-valued data on triangular meshes.
problem Discrete representation of continuous vector-valued environmental data.
method Develops discrete intrinsic Gaussian processes for vector-valued data on triangular meshes using discrete differential operators.
result Models can capture harmonic flows, incorporate boundary conditions, and model non-stationary data.
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
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-…
Develops large-sample theory for non-stationary source separation.
problem Lack of large-sample results for non-stationary source separation methods.
method Large-sample theory for NSS-JD method under specific assumptions.
result Consistency of unmixing estimator and its convergence to Gaussian distribution.
Model separates overall uncertainty into aleatoric and epistemic components for active learning.
problem Active learning with uncertainty quantification.
method Non-stationary Heteroscedastic Gaussian process model.
result Model separates overall uncertainty into aleatoric and epistemic components.
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.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
Efficient GP framework for scalable non-stationary processes.
problem Heavy memory and computational requirements in Gaussian process regression for large data sets.
method Exploits structure in the kernel matrix, uses multiple sets of non-equidistant inducing points, and employs Toeplitz and Kronecker structure for efficient inference.
result Demonstrated scalability on numerical examples and large biomedical datasets.
Flexible GP model improves wind power prediction accuracy.
problem Accurate probabilistic prediction of wind power for grid stability.
method Heteroscedastic non-stationary Gaussian process with generalised spectral mixture kernel.
result The proposed model outperforms conventional GP models in wind power prediction.
New method learns time-varying home field advantage in football.
problem Discovering causal factors behind home field advantage in sports.
method DYNAMO: a novel causal discovery method for non-stationary processes.
result Time-varying home field advantages influenced by referee bias.
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
problem Prohibitive computational and parametric complexity in high-dimensional, non-stationary dynamical systems.
method ETGPSSM integrates a single shared GP with input-dependent normalizing flows for scalable and flexible modeling.
result ETGPSSM outperforms existing models in computational efficiency and accuracy.
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.
Image-to-image networks speed up SAR model parameter estimation.
problem Computational infeasibility of MLE for large, non-stationary spatial fields.
method Used image-to-image networks to estimate SAR model parameters.
result Image-to-image networks enable faster and more accurate parameter estimation.
Inter-domain Deep Gaussian Processes improve inference for non-stationary data.
problem Inference limitations in Gaussian processes for non-stationary data.
method Combines inter-domain and deep Gaussian processes for scalable approximate inference.
result Outperforms inter-domain shallow GPs and conventional DGPs on non-stationary data.
This work improves Gaussian process regression for large, non-stationary data.
problem Scalability issues and performance degradation for non-stationary data.
method Combines variational free energy approximations with online expectation propagation and local splitting steps.
result Incremental adaptation to locality, heterogeneity, and non-stationarity in training data.
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…
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
Novel CSK kernel improves GP model generalization for non-stationary patterns.
problem Improving generalization of Gaussian process models for non-stationary data.
method Introduced convolutional spectral kernel (CSK) derived from convolution of imaginary radial basis functions, using Fourier transform for interpretation.
result CSK improves GP model generalization on spatiotemporal datasets.
Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.
problem Uncertainty in precipitation patterns in the Upper Indus Basin, Himalayas.
method Proposes Gaussian processes with structured non-stationary kernels to model precipitation patterns, accounting for spatial variation with a latent Gaussian process.
result The proposed model adapts to varying precipitation patterns across distinct topography and outperforms stationary models in ablation experiments.
Adaptive sparse GP model for non-stationary data.
problem Non-stationary environments require efficient model updates.
method Reformulated variational sparse GP with adaptive forgetting factor and single inducing point update.
result Fast convergence and efficient model update in non-stationary environments.
DS-TS adapts to abrupt and smooth changes in bandit problems.
problem Non-stationary multi-armed bandit problems with abrupt and smooth changes.
method Discounted Thompson Sampling with Gaussian priors.
result Achieves nearly optimal regret bound for both abrupt and smooth changes.
A new kernel improves Gaussian process performance for non-stationary data.
problem Poor prediction and uncertainty quantification with standard GPs.
method Study and comparison of non-stationary kernels, propose a new combined kernel.
result A new kernel outperforms existing stationary and non-stationary kernels.
Adaptive tuning of portfolio selection parameters improves performance in volatile markets.
problem Improving online portfolio selection in volatile financial markets.
method Modeling parameter space with Gaussian process prior and using adaptive Bayesian optimization for automatic configuration.
result Oracle-based adaptive configuration enhances performance of online portfolio selection algorithms.
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 …
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…
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 …
Incremental learning from non-stationary data poses special challenges to the field of machine learning. Although new algorithms have been developed for this, assessment of results and comparison of behaviors are still open problems, mainly because evaluation metrics, adapted from more traditional tasks, can be ineffec…
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 …
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…
ETGP improves multi-class classification efficiency.
problem Efficiently handling non-stationary, dependent multi-class classification problems.
method ETGP uses transformed Gaussian processes with efficient sparse variational inference.
result ETGPs outperform state-of-the-art methods in multi-class classification tasks.
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…
STACI uses neural nets to estimate spatio-temporal fields with valid uncertainty quantification.
problem Scalable spatio-temporal deep learning models fail to capture underlying correlation structure.
method Variational Bayesian neural network approximation of non-stationary spatio-temporal Gaussian Process (GP) with conformal inference.
result STACI provides accurate prediction intervals for spatio-temporal processes, outperforming competing methods.
A new method uses SPDEs to efficiently model random fields on complex domains.
problem Efficient representation of random fields on complex domains for engineering and machine learning.
method Uses SPDEs to develop a scalable framework for statFEM and GP regression.
result Can model anisotropic, non-stationary random fields with arbitrary smoothness.
ConvGNP improves sensor placement for climate monitoring.
problem Maximizing informativeness of environmental sensor placements in remote regions.
method Convolutional Gaussian neural processes (ConvGNP) for non-stationary spatial predictions.
result ConvGNP outperforms traditional GP models in predicting sensor performance and reducing uncertainty.
A novel GPDA method for high-dimensional functional data.
problem Classification and feature selection challenges in high-dimensional, non-stationary functional data.
method Unified two-layer non-stationary Gaussian process with Ising prior for variable selection and classification.
result Demonstrated superior performance on simulated and proteomics datasets.
A new learning strategy using two GP layers for inhomogeneous data.
problem Addressing inhomogeneous empirical correlation structures in data.
method Modeling the function as a sample function of a non-stationary Gaussian Process (GP) nested within multiple stationary GPs, with hyperparameters dependent on the outer GP.
result The approach is sufficient with two GP layers, and the model can be implemented using MCMC.
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model…
Warped Gaussian process model for non-stationary time series forecasting.
problem Non-stationary time series with gradually varying volatility, change points, or both.
method Non-parametric warping of input distances with Gaussian process, gradient optimization for training.
result State-of-the-art forecasting performance at lower implementation and computation cost.
Exact Gaussian Processes for massive datasets using non-stationary sparsity-discovering kernels.
problem High computational and storage costs for exact GPs in large datasets.
method Develop non-stationary kernels that allow the GP to discover sparse structure naturally.
result Exact Gaussian Processes scalable to over 5 million data points.
Adaptive tuning of latent space for non-stationary data.
problem Learning from large, non-stationary systems with quick characteristic changes.
method Adaptive tuning of low-dimensional latent space based on real-time feedback.
result Improved prediction of time-varying charged particle beam properties.
Advanced kernels improve Gaussian process accuracy by incorporating domain knowledge.
problem Improving function approximation accuracy in Gaussian processes.
method Advanced kernel designs that enforce specific function properties (symmetry, periodicity) and non-stationarity.
result Advanced kernels significantly enhance function approximation accuracy and relevance.
The study analyzes online predictions for non-stationary time series under model misspecification.
problem Analyzing predictive properties of statistical methods in non-stationary time series under model misspecification.
method Defining Kullback-Leibler risk, proving minimax predictive densities for dynamic models, extending results to multiple predictive densities.
result Dynamic random walk models produce exact minimax predictive densities under Gaussian assumptions and semi-martingale processes.
We use diffusion models to sample from complex GP priors in climate data.
problem Sampling from non-stationary Gaussian process priors is computationally hard.
method Replace GP prior with a diffusion model surrogate and use training-free guidance algorithms.
result Generated distributions are close to GP priors and can be fine-tuned.
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…
CNNs predict spatial fields from sparse data.
problem Predicting complete spatial fields from limited observations.
method Convolutional Neural Networks (CNNs) trained on a single partially observed field.
result CNNs can flexibly capture local spatial patterns without explicit covariance modeling.
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of …