Gaussian Processes (GPs), as a nonparametric learning method, offer flexible modeling capabilities and calibrated uncertainty quantification for function approximations. Additionally, GPs support online learning by efficiently incorporating new data with polynomial-time computation, making them well-suited for safety-critical dynamical systems that require rapid adaptation. However, the inference and online updates of exact GPs, when processing streaming data, incur cubic computation time and quadratic storage memory complexity, limiting their scalability to large datasets in real-time settings. In this paper, we propose a streaming kernel-induced progressively generated expert framework of Gaussian processes (SkyGP) that addresses both computational and memory constraints by maintaining a bounded set of experts, while inheriting the learning performance guarantees from exact Gaussian processes. Furthermore, two SkyGP variants are introduced, each tailored to a specific objective, either maximizing prediction accuracy (SkyGP-Dense) or improving computational efficiency (SkyGP-Fast). The effectiveness of SkyGP is validated through extensive benchmarks and real-time control experiments demonstrating its superior performance compared to state-of-the-art approaches.

翻译：高斯过程作为一种非参数学习方法，为函数逼近提供了灵活的建模能力和经过校准的不确定性量化。此外，高斯过程通过多项式时间计算高效整合新数据，支持在线学习，使其非常适合需要快速适应的安全关键动态系统。然而，在处理流式数据时，精确高斯过程的推断和在线更新会产生立方级计算时间和二次存储内存复杂度，限制了其在实时场景下对大规模数据集的可扩展性。本文提出一种流式核诱导的渐进生成高斯过程专家框架，通过维护一个有界专家集合，在继承精确高斯过程学习性能保证的同时，解决了计算和内存约束问题。此外，本文引入了两种SkyGP变体，分别针对特定目标进行优化：一种旨在最大化预测精度，另一种则专注于提升计算效率。通过广泛的基准测试和实时控制实验，验证了SkyGP的有效性，其性能优于现有先进方法。