A Radio Environment Map (REM) is pivotal for optimizing wireless communication systems, yet its accuracy is inherently tied to the complex interplay of electromagnetic propagation and landform heterogeneity. Existing REM construction methods often implicitly ignore land features, leading to inaccuracies in REM estimation. In this paper, we introduce a novel Radio Oriented Heterogeneous Multitask Gaussian Process (RO-HMTGP) to address this gap by jointly integrating heterogeneous inputs, including land features and Reference Signal Receiving Power (RSRP). The proposed RO-HMTGP model treats land features as auxiliary knowledge and captures spatially correlated propagation effects across varying landforms while preserving feature-specific attenuation characteristics. RO-HMTGP enhances the construction accuracy of REM while quantifying uncertainty. Empirical evaluations using real-world datasets demonstrate that the land feature-aware RO-HMTGP achieves superior predictive performance compared to existing methods without land feature awareness. RO-HMTGP advances the integration of geospatial analytics into wireless communications, providing a pathway toward land feature-aware cognitive radio systems.

Radio environment mapping in urban scenarios presents significant challenges due to the complex interplay of multipath propagation, shadowing effects, and heterogeneous urban morphology. We present RadioVAE, a novel probabilistic framework that generates high-fidelity radio maps with uncertainty quantification through a Variational Autoencoder (VAE). The model addresses the critical limitations of deterministic neural networks by learning a structured latent space that explicitly encodes the posterior distribution of propagation features conditioned on urban topology and transmitter characteristics. A UNet-based feature extractor enables simultaneous modeling of both fine-scale spatial variations and city-wide propagation patterns, while KL-divergence regularization ensures physically plausible predictions. The generative process incorporates urban morphological constraints and transmitter parameters to accurately reconstruct complex propagation fields. Experimental results demonstrate that RadioVAE significantly outperforms existing deterministic methods in both prediction accuracy and uncertainty calibration, particularly in challenging urban environments with complex spatial correlations.

Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions (LFs), all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively represent and learn the hierarchical latent interactions between its LFs. In this paper, we further investigate the interactions in LMC of MTGP and then propose a novel kernel representation of the hierarchical interactions, which ameliorates both the expressiveness and the interpretability of MTGP. Specifically, we express the interaction as a product of function interaction (FI) and coefficient interaction. The FI is modeled by using cross convolution of LFs. The coefficient interaction between the LMCs is described as a free-form coupling coregionalization term. We validate that considering the interactions can promote knowledge transferring in MTGP and compare our approach with some state-of-the-art MTGPs on both synthetic-and real-world datasets.

Abstract Long-term forecasting involves predicting a horizon that is far ahead of the last observation. It is a problem of high practical relevance, for instance for companies in order to decide upon expensive long-term investments. Despite the recent progress and success of Gaussian processes (GPs) based on spectral mixture kernels, long-term forecasting remains a challenging problem for these kernels because they decay exponentially at large horizons. This is mainly due to their use of a mixture of Gaussians to model spectral densities. Characteristics of the signal important for long-term forecasting can be unravelled by investigating the distribution of the Fourier coefficients of (the training part of) the signal, which is non-smooth, heavy-tailed, sparse, and skewed. The heavy tail and skewness characteristics of such distributions in the spectral domain allow to capture long-range covariance of the signal in the time domain. Motivated by these observations, we propose to model spectral densities using a skewed Laplace spectral mixture (SLSM) due to the skewness of its peaks, sparsity, non-smoothness, and heavy tail characteristics. By applying the inverse Fourier Transform to this spectral density we obtain a new GP kernel for long-term forecasting. In addition, we adapt the lottery ticket method, originally developed to prune weights of a neural network, to GPs in order to automatically select the number of kernel components. Results of extensive experiments, including a multivariate time series, show the beneficial effect of the proposed SLSM kernel for long-term extrapolation and robustness to the choice of the number of mixture components.

Multioutput Gaussian processes (MOGPs) are an extension of Gaussian processes (GPs) for predicting multiple output variables (also called channels/tasks) simultaneously. In this article, we use the convolution theorem to design a new kernel for MOGPs by modeling cross-channel dependencies through cross convolution of time-and phase-delayed components in the spectral domain. The resulting kernel is called multioutput convolution spectral mixture (MOCSM) kernel. The results of extensive experiments on synthetic and real-life data sets demonstrate the advantages of the proposed kernel and its state-of-the-art performance. MOCSM enjoys the desirable property to reduce to the well-known spectral mixture (SM) kernel when a single channel is considered. A comparison with the recently introduced multioutput SM kernel reveals that this is not the case for the latter kernel, which contains quadratic terms that generate undesirable scale effects when the spectral densities of different channels are either very close or very far from each other in the frequency domain.

Multitask Gaussian processes (MTGPs) are a powerful approach for modeling dependencies between multiple related tasks or functions for joint regression. Current kernels for MTGPs cannot fully model nonlinear task correlations and other types of dependencies. In this article, we address this limitation. We focus on spectral mixture (SM) kernels and propose an enhancement of this type of kernels, called multitask generalized convolution SM (MT-GCSM) kernel. The MT-GCSM kernel can model nonlinear task correlations and dependence between components, including time and phase delay dependence. Each task in MT-GCSM has its GCSM kernel with its number of convolution structures, and dependencies between all components from different tasks are considered. Another constraint of current kernels for MTGPs is that components from different tasks are aligned. Here, we lift this constraint by using inner and outer full cross convolution between a base component and the reversed complex conjugate of another base component. Extensive experiments on two synthetic and three real-life data sets illustrate the difference between MT-GCSM and previous SM kernels as well as the practical effectiveness of MT-GCSM.

Abstract Gaussian processes (GPs) are an elegant Bayesian approach to model an unknown function. The choice of the kernel characterizes one’s assumption on how the unknown function autocovaries. It is a core aspect of a GP design, since the posterior distribution can significantly vary for different kernels. The spectral mixture (SM) kernel is derived by modelling a spectral density - the Fourier transform of a kernel - with a linear mixture of Gaussian components. As such, the SM kernel cannot model dependencies between components. In this paper we use cross convolution to model dependencies between components and derive a new kernel called Generalized Convolution Spectral Mixture (GCSM). Experimental analysis of GCSM on synthetic and real-life datasets indicates the benefit of modeling dependencies between components for reducing uncertainty and for improving performance in extrapolation tasks.