Sparsity-Aware Distributed Learning for Gaussian Processes with Linear Multiple Kernel

TL;DR

This paper introduces a sparsity-aware distributed learning framework for Gaussian processes using a novel linear multiple kernel, improving hyper-parameter optimization efficiency and scalability for multi-dimensional data.

Contribution

It proposes a new GSMP kernel tailored for multi-dimensional data and a distributed learning framework that exploits sparsity for efficient hyper-parameter optimization.

Findings

The GSMP kernel reduces hyper-parameter complexity while maintaining approximation quality.

The SLIM-KL framework achieves efficient, privacy-preserving distributed hyper-parameter optimization.

Experimental results show superior prediction accuracy and computational efficiency.

Abstract

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 product (GSMP) kernel is tailored for multi-dimensional data, effectively reducing the number of hyper-parameters while maintaining good approximation capability. We further demonstrate that the associated hyper-parameter 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 (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.