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…
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48 results for “Stationary Kernel Functions”
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.
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-…
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.
Algorithm adapts to non-stationary rewards without prior knowledge.
problem Optimizing decisions in non-stationary environments without prior knowledge of changes.
method Optimization-based algorithm that restarts when non-stationarity is detected.
result Achieves tighter dynamic regret bound and is nearly minimax optimal.
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.
Develops a deep non-stationary kernel for non-stationary spatio-temporal point processes.
problem Capturing non-stationary dependencies in point process data.
method Approximates the influence kernel with a novel low-rank decomposition and introduces a log-barrier penalty to maintain non-negativity.
result Demonstrates superior performance and computational efficiency compared to state-of-the-art methods.
New GP kernels avoid mean reversion without losing smoothness.
problem Pathological behavior in stationary GP regression.
method Improper Gaussian processes with non-positive kernels.
result Stationary, non-reverting covariance functions.
Paper establishes lower bounds for non-stationary kernelized bandits.
problem Optimizing functions with noisy observations in non-stationary scenarios.
method Develops algorithm-independent lower bounds for time-varying functions under total variation constraints.
result First algorithm-independent lower bounds for time-varying kernelized bandits.
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.
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.
Paper tackles non-stationary kernelized bandits with near-optimal algorithm.
problem Minimizing regret in a time-varying reward function.
method Near-optimal algorithm with a novel restarting phased elimination with random permutation (R-PERP).
result Regret upper bound matches the lower bound, making the algorithm near-optimal.
A new method warps inputs to learn nonstationary kernels efficiently.
problem Learning nonstationary patterns in data with varying smoothness.
method Sparse spectrum Gaussian processes with input warping as conditional Gaussian measures.
result Efficient learning of nonstationary patterns with fewer parameters.
Bayesian convolutional deep sets improve ambiguity in stationary process modeling.
problem Ambiguity in translation equivariant functional representations due to insufficient data points.
method Introduce Bayesian convolutional deep sets with task-dependent stationary prior.
result Improves representation quality compared to kernel smoother and non-parametric models.
New method reduces variance and bias in approximating indefinite kernels.
problem Approximating non-stationary indefinite kernels with low variance and bias.
method Generalized orthogonal random features (GORF)
result GORF achieves lower variance and approximation error compared to existing methods.
New kernel models multi-output Gaussian processes accurately.
problem Challenges in modelling cross-covariances for multiple-output Gaussian processes.
method Replaced Gaussian components with block components of finite bandwidth in spectral mixture kernel.
result First multi-output generalization of spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
Hida-Matérn Kernelstat.ML
New Hida-Matérn kernels enable flexible process priors and efficient GP inference.
problem Flexible modeling of stationary processes with oscillatory components.
method Introducing a new class of covariance functions (Hida-Matérn kernels) and their state space representations.
result Efficient Gaussian Process inference and improved numerical stability.
We present a novel variation of online kernel machines in which we exploit a consensus based optimization mechanism to guide the evolution of decision functions drawn from a reproducing kernel Hilbert space, which efficiently models the observed stationary process.
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…
We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present a principled framework to interpret CSK, as well as other deep probabilistic mo…
Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernelsstat.ML
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.
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…
New algorithm optimizes resource allocation in non-stationary networks.
problem Optimal resource allocation in non-stationary RMABs is computationally hard.
method Sliding-Window Online Whittle (SW-Whittle) policy for non-stationary transition kernels.
result Sub-linear dynamic regret achieved with unknown variation budget.
Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.
problem Sparse learning for high-dimensional heavy-tailed locally stationary time series.
method Additive modeling with kernel smoothing, sparsity-inducing penalized estimation.
result Prediction-error bounds and convergence rates for different sparsity structures.
PROPO tackles non-stationary MDPs with efficient policy optimization.
problem Non-stationary MDPs with varying reward and transition kernels.
method PROPO, a periodic restarted optimistic policy optimization algorithm with sliding-window-based policy evaluation and improvement.
result PROPO achieves near-optimal performance in non-stationary MDPs.
New analysis explains pathology of deep Gaussian processes.
problem Pathology of deep Gaussian processes reduces learning capacities with increased layers.
method Study nonlinear dynamic systems corresponding to DGPs, derive recurrence relations.
result Provide tighter bounds and rate of convergence for dynamic systems.
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for reconstructing the time-frequency information is that when a nonparame…
The paper studies convergence of kernel autocovariance operators for stationary processes.
problem Estimating autocovariance operators of stationary processes on Polish spaces.
method Investigates convergence of empirical estimates of autocovariance operators under various conditions.
result Provides consistency results for kernel PCA and spectral analysis methods.
Study on fake stationary Volterra Heston model for non-stationary processes.
problem Non-stationary nature of true Volterra equations.
method Weak notion of stationarity (fake stationary regime) for inhomogeneous affine Stochastic Volterra equations.
result Existence of limiting distributions in the long run, which may depend on initial state.
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop functional kernel learning (FKL) to directly infer functional posteriors over kernels. I…
A new convolutional spectral kernel network learns hierarchical and local features.
problem Lack of deep learning in non-stationary spectral kernels.
method Introduces convolutional filters and deep architectures into non-stationary spectral kernels, derives generalization error bounds, and introduces regularizers.
result Validated the effectiveness of the convolutional spectral kernel network on real-world datasets.
Develops nonstationary MOGP kernels for better performance.
problem Limited applicability of existing MOGP kernels for nonstationary data.
method Harmonizable spectral mixture kernels for nonstationary MOGP.
result Automatic identification of nonstationary behavior in data.
Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Seriesstat.ME
Kernel-based tests detect dependencies in multivariate time series, including stationary and non-stationary data.
problem Detecting dependencies in multivariate time series data, especially non-stationary data.
method Kernel-based statistical tests of joint independence, extending dHSIC to handle both stationary and non-stationary processes.
result Robustly uncovers significant higher-order dependencies in synthetic and real-world data.
Generalized Spectral Kernelsstat.ML
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…
The Human Kernelcs.LG
Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating human expertise remains elusive; for example, Gaussian processes with standard kerne…
New method reduces computational cost for learning stationary diffusions.
problem Learning parameters of stationary diffusions efficiently.
method Stein-type discrepancy (SKDS) for estimating generator expectations.
result SKDS guarantees alignment with target stationary distribution.
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…
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.
Identifies a gradient flow to solve kernel learning problems with noise reduction.
problem Kernel learning problem with Gaussian noise.
method Riemannian gradient flow with continuous Lyapunov functionals.
result Flow reduces noise and finds stationary points.
Paper introduces a neural network-based non-stationary influence kernel for complex event data.
problem Modeling complex, non-stationary, and dependent discrete event data.
method Neural Spectral Marked Point Processes (NSMPP) with a versatile non-stationary influence kernel.
result NSMPP outperforms state-of-the-art models on synthetic and real data.
Efficiently approximates statistical leverage scores for faster KRR.
problem Accurately estimating statistical leverage scores for fast KRR.
method Analytic formula for statistical leverage scores, leveraging kernel spectral density.
result Linear time approximation with theoretical guarantees, significantly faster than existing methods.
KeRNS tackles non-stationary reinforcement learning in metric spaces.
problem Non-stationary reinforcement learning in metric spaces.
method KeRNS uses time-dependent kernels to model non-stationary Markov Decision Processes (MDPs).
result KeRNS achieves a regret bound that scales with the covering dimension and total variation of the MDP.
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limi…
The thesis presents a new perspective on high-dimensional optimization.
problem The failure point of classical optimization methods in high dimensions.
method A distributional view of optimization, focusing on random objective functions and Bayesian Optimization.
result The distributional view explains predictable progress in high-dimensional optimization and provides insights into optimal step size control.
Kernel-based methods improve policy evaluation in MRP models.
problem Estimating value functions in infinite-horizon discounted MRP models.
method Kernel-based temporal difference methods using reproducing kernel Hilbert spaces.
result Optimal error bounds derived for the kernel-based LSTD estimate.
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…
Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.
problem Inefficient marginalization over Gaussian Process kernels for large datasets.
method Bayesian Quadrature scheme with maximum mean discrepancies and invariances between Spectral Mixture kernels.
result Achieves more accurate predictions and better calibrated uncertainty than state-of-the-art baselines.