Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyper-parameters. The newly proposed grid spectral mixture (GSM) kernel is tailored for multi-dimensional data, effectively reducing the number of hyper-parameters while maintaining good approximation capabilities. We further demonstrate that the associated hyper-parameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity property of the solutions, we introduce the Sparse LInear Multiple Kernel Learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMM) 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 hyper-parameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. 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.

翻译：高斯过程（GPs）是机器学习和信号处理中的关键工具，其有效性依赖于核函数设计与超参数优化。本文提出了一种新型GP线性多核（LMK）及通用稀疏感知分布式学习框架用于超参数优化。新提出的网格谱混合（GSM）核专门针对多维数据设计，在保持良好逼近能力的同时有效减少超参数数量。我们进一步证明了该核所关联的超参数优化能产生稀疏解。为利用解固有的稀疏特性，我们引入稀疏线性多核学习（SLIM-KL）框架。该框架集成了量化交替方向乘子法（ADMM）方案以实现多智能体协同学习，其中局部优化问题通过分布式逐次凸逼近（DSCA）算法求解。SLIM-KL能有效处理所提出核的大规模超参数优化，同时确保数据隐私并最小化通信成本。理论分析确立了该学习框架的收敛性保证，而多数据集实验表明我们提出的方法具有优越的预测性能与效率。