The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational efficiency. To overcome these issues, we first introduce a new duality between the spectral density and the kernel function. By modeling the spectral density with a bivariate Gaussian mixture, we then derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. To address the inherent computational inefficiency of the NG-SM kernel, we propose a random Fourier feature approximation. Combined with a tailored reparameterization trick, this approximation enables scalable variational inference for both the model and the unified latent representations. Numerical evaluations across a diverse range of multi-view datasets demonstrate that our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.

Random feature latent variable models (RFLVMs) are state-of-the-art tools for uncovering structure in high-dimensional, non-Gaussian data. However, their reliance on Monte Carlo sampling significantly limits scalability, posing challenges for large-scale applications. To overcome these limitations, we develop a scalable RFLVM framework based on variational Bayesian inference (VBI), a deterministic and optimization-based alternative to sampling methods. Applying VBI to RFLVMs is nontrivial due to two key challenges: (i) the lack of an explicit probability density function (PDF) for Dirichlet process (DP) mixing weights, and (ii) the inefficiency of existing VBI approaches when handling the high-dimensional variational parameters of RFLVMs. To address these issues, we adopt the stick-breaking construction for the DP, which provides an explicit and tractable PDF over mixing weights, and propose a novel inference algorithm, block coordinate descent variational inference (BCD-VI), which partitions variational parameters into blocks and applies tailored solvers to optimize them efficiently. The resulting scalable model, referred to as SRFLVM, supports various likelihoods; we demonstrate its effectiveness under Gaussian and logistic settings. Extensive experiments on diverse benchmark datasets show that SRFLVM achieves superior scalability, computational efficiency, and performance in latent representation learning and missing data imputation, consistently outperforming state-of-the-art latent variable models, including deep generative approaches.

Accurate prediction of mmWave time-varying channels is essential for mitigating the issue ofchannel agingin highly dynamic scenarios. Existing channel prediction methods have limitations: classical model-based methods often struggle to track highly nonlinear channel dynamics due to limited expert knowledge, while emerging data-driven methods typically require substantial labeled data for effective training and often lack interpretability. To address these issues, this paper proposes a novel hybrid method that integrates a data-driven neural network into a conventional model-based workflow based on a state-space model (SSM), implicitly tracking complex channel dynamics from data without requiring precise expert knowledge. Additionally, a novel unsupervised learning strategy is developed to train the embedded neural network solely with unlabeled data. Theoretical analyses and ablation studies are conducted to interpret the enhanced benefits gained from the hybrid integration. Numerical simulations based on the 3GPP mmWave channel model corroborate the superior prediction accuracy of the proposed method, compared to state-of-the-art methods that are either purely model-based or data-driven. Furthermore, extensive experiments validate its robustness against various challenging factors, including among others severe channel variations.

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyperparameter optimization. This article presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyperparameters. The newly proposed grid spectral mixture product (GSMP) kernel is tailored for multidimensional data, effectively reducing the number of hyperparameters while maintaining good approximation capability. We further demonstrate that the associated hyperparameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity of the solutions, we introduce the sparse linear multiple kernel learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMMs) scheme for collaborative learning among multiple agents, where the local optimization problem is solved using a distributed successive convex approximation (DSCA) algorithm. SLIM-KL effectively manages large-scale hyperparameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. The theoretical analysis establishes convergence guarantees for the learning framework, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our proposed methods.

Deep state-space models (DSSMs) have gained popularity in recent years due to their potent modeling capacity for dynamic systems. However, existing DSSM works are limited to single-task modeling, which requires retraining with historical task data upon revisiting a forepassed task. To address this limitation, we propose continual learning DSSMs (CLDSSMs), which are capable of adapting to evolving tasks without catastrophic forgetting. Our proposed CLDSSMs integrate mainstream regularization-based continual learning (CL) methods, ensuring efficient updates with constant computational and memory costs for modeling multiple dynamic systems. We also conduct a comprehensive cost analysis of each CL method applied to the respective CLDSSMs, and demonstrate the efficacy of CLDSSMs through experiments on real-world datasets. The results corroborate that while various competing CL methods exhibit different merits, the proposed CLDSSMs consistently outperform traditional DSSMs in terms of effectively addressing catastrophic forgetting, enabling swift and accurate parameter transfer to new tasks.

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension, leading to escalating computational complexity and parameter proliferation, thus posing challenges for modeling dynamical systems with high-dimensional latent states. To surmount this obstacle, we propose to integrate the efficient transformed Gaussian process (ETGP) into the GPSSM, which involves pushing a shared GP through multiple normalizing flows to efficiently model the transition function in high-dimensional latent state space. Additionally, we develop a corresponding variational inference algorithm that surpasses existing methods in terms of parameter count and computational complexity. Experimental results on diverse synthetic and real-world datasets corroborate the efficiency of the proposed method, while also demonstrating its ability to achieve similar inference performance compared to existing methods. Code is available at https://github.com/zhidilin/gpssmProj.

Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel flexibility and improper selection of the projection noise, leading to a type of model collapse characterized by vague latent representations that do not reflect the underlying data structure. This paper addresses these issues by, first, theoretically examining the impact of projection variance on model collapse through the lens of a linear GPLVM. Second, we tackle model collapse due to inadequate kernel flexibility by integrating the spectral mixture (SM) kernel and a differentiable random Fourier feature (RFF) kernel approximation, which ensures computational scalability and efficiency through off-the-shelf automatic differentiation tools for learning the kernel hyperparameters, projection variance, and latent representations within the variational inference framework. The proposed GPLVM, named advisedRFLVM, is evaluated across diverse datasets and consistently outperforms various salient competing models, including state-of-the-art variational autoencoders (VAEs) and other GPLVM variants, in terms of informative latent representations and missing data imputation.

Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be independent, meaning that the GPSSMs cannot exploit the inductive biases between different outputs and lose certain model capacities. To address this issue, this paper proposes an output-dependent and more realistic GPSSM by utilizing the well-known, simple yet practical linear model of coregionalization (LMC) framework to represent the output dependency. To jointly learn the output-dependent GPSSM and infer the latent states, we propose a variational sparse GP-based learning method that only gently increases the computational complexity. Experiments on both synthetic and real datasets demonstrate the superiority of the output-dependent GPSSM in terms of learning and inference performance.

Graph neural networks (GNNs) are popular to use for classifying structured data in the context of machine learning. But surprisingly, they are rarely applied to regression problems. In this work, we adopt GNN for a classic but challenging nonlinear regression problem, namely the network localization. Our main findings are in order. First, GNN is potentially the best solution to large-scale network localization in terms of accuracy, robustness and computational time. Second, proper thresholding of the communication range is essential to its superior performance. Simulation results corroborate that the proposed GNN based method outperforms all state-of-the-art benchmarks by far. Such inspiring results are theoretically justified in terms of data aggregation, non-line-of-sight (NLOS) noise removal and low-pass filtering effect, all affected by the threshold for neighbor selection. Code is available at https://github.com/Yanzongzi/GNN-For-localization.

We propose a novel Gaussian process kernel that takes advantage of a deep neural network (DNN) structure but retains good interpretability. The resulting kernel is capable of addressing four major issues of the previous works of similar art, i.e., the optimality, explainability, model complexity, and sample efficiency. Our kernel design procedure comprises three steps: (1) Derivation of an optimal kernel with a non-stationary dot product structure that minimizes the prediction/test mean-squared-error (MSE); (2) Decomposition of this optimal kernel as a linear combination of shallow DNN subnetworks with the aid of multi-way feature interaction detection; (3) Updating the hyper-parameters of the subnetworks via an alternating rationale until convergence. The designed kernel does not sacrifice interpretability for optimality. On the contrary, each subnetwork explicitly demonstrates the interaction of a set of features in a transformation function, leading to a solid path toward explainable kernel learning. We test the proposed kernel with both synthesized and real-world data sets, and the proposed kernel is superior to its competitors in terms of prediction performance in most cases. Moreover, it tends to maintain the prediction performance and be robust to data over-fitting issue, when reducing the number of samples.