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.
Kernel design for Gaussian processes (GPs) along with the associated hyper-parameter optimization is a challenging problem. In this paper, we propose a novel grid spectral mixture (GSM) kernel design for GPs that can automatically fit multidimensional data with affordable model complexity and superior modeling capability. To alleviate the computational complexity due to the curse of dimensionality, we leverage a multicore computing environment to optimize the kernel hyper-parameters in a distributed manner. We further propose a doubly distributed learning algorithm based on the alternating direction method of multipliers (ADMM) which enables multiple agents to learn the kernel hyper-parameters collaboratively. The doubly distributed learning algorithm is shown to be effective in reducing the overall computational complexity while preserving data privacy during the learning process. Experiments on various one-dimensional and multidimensional data sets demonstrate that the proposed kernel design yields superior training and prediction performance compared to its competitors.