Linear Multiple Low-Rank Kernel Based Stationary Gaussian Processes Regression for Time Series

Recent advances in data-driven wireless communication using Gaussian processes: A comprehensive survey

“…Generally, for kernel function designation, there are broadly four categories of covariance design in the existing works for GP, including (1) compositional kernel design [22], [23], where kernels are constructed compositionally from several existing base kernels; (2) spectral kernel learning, where kernels are derived by modeling the kernel spectral density as a mixture of distributions [24], [25], [26], [27]; (3) deep kernel representation [28], [29], where DNN plays a role in nonlinear mapping between input space and feature space; and (4) multitask kernel [30], [31], where adjacent devices (tasks) share knowledge and interact with each other to obtain collective intelligence. In the next sections, we review related works in detail.…”

“…To overcome the computational complexity issue of GP [16], [32], scalable inference can be achieved by exploring (1) low-rank covariance matrix approximation [33], [34], (2) special structures of the kernel matrix [35], [36], (3) Bayesian committee machine (BCM), which distributes computations to a big number of computing units [37], [38], (4) variational Bayesian inference [39], [40], and (5) special optimization [41], [27]. Notably, these scalable methods are not exclusive, and we can combine some of them to get a better method, for instance, stochastic variational inference (SVI) [39], [40] combines the strength of inducing points for low-rank approximation and variational inference.…”

Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling

“…From (7), Bayesian prediction can be interpreted as the weighted average of the predicted probability p M (D new |θ) among all possible model configurations, each of which is specified by different model parameters, θ, and weighted by the respective posterior p M (θ|D; η). 2 In other words, prediction does not depend on a specific point estimate of the unknown parameters, which equips Bayesian methods with great potential for more robust predictions against the estimation error of θ, see, e.g., [1], [19].…”

“…In a similar vein, in [7]- [9], sparsity-promoting priors have been used in the context of the GPs that give rise to optimal and interpretable kernels that are capable of identifying a sparse subset of effective frequency components automatically. In the unsupervised learning front, some advanced works on tensor decomposition, e.g., [10]- [15], have shown that sparsity-promoting priors are able to unravel the few underlying interpretable components in a completely tuning-free fashion.…”

“…In the unsupervised learning front, some advanced works on tensor decomposition, e.g., [10]- [15], have shown that sparsity-promoting priors are able to unravel the few underlying interpretable components in a completely tuning-free fashion. Such techniques have found various signal processing applications, including data classification [2], [5], [6], adversarial learning [3], [4], time-series prediction [7]- [9], [16], blind source separation [10], [13], [17], image completion [12], [14], [15], and wireless communications [18].…”