The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domain
In the univariate setting, using the kernel spectral representation is an appealing approach for generating stationary covariance functions. However, performing the same task for multiple-output Gaussian processes is substantially more challenging. We demonstrate that current approaches to modelling cross-covariances with a spectral mixture kernel possess a critical blind spot. For a given pair of processes, the cross-covariance is not reproducible across the full range of permitted correlations, aside from the special case where their spectral densities are of identical shape. We present a solution to this issue by replacing the conventional Gaussian components of a spectral mixture with block components of finite bandwidth (i.e. rectangular step functions). The proposed family of kernel represents the first multi-output generalisation of the spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesMinecraftSimilar Papers 제목 키워드 기반
Transformed Latent Variable Multi-Output Gaussian Processes
Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To main…
Computational EfficiencyGaussian ProcessesFunction-Space Distributions over Kernels
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,…
Gaussian ProcessesRepresentation LearningVariational zero-inflated Gaussian processes with sparse kernels
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 lead…
Gaussian ProcessesVariational InferenceGaussian Process Kernels for Pattern Discovery and Extrapolation
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 t…
Gaussian ProcessesGPatt: Fast Multidimensional Pattern Extrapolation with Gaussian Processes
Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on…
Gaussian Processes