大规模深度核学习的理论与算法研究

核方法具有坚实的理论基础、完备的学习框架和优雅的凸优化形式，但受限于浅层核方法模型表征能力不强的问题，其在复杂任务上的学习性能相较于深度学习方法具有一定的差距，已成为制约核方法进一步发展的瓶颈问题。针对上述问题，本项目旨在将核方法与深度网络相融合，构建面向大规模学习任务的深度核学习理论与自动算法。首先，通过层次化构造，并融合样本局部性和时序性等特性，设计具有强表征能力的深度核函数结构；在此基础上，研究大规模深度核学习的近似性、泛化性和鲁棒性，构建大规模深度核学习理论；最后，以大规模深度核学习理论为指导，设计兼具学习理论保障和计算高效的深度核学习准则和自动学习算法。本项目所提的大规模深度核学习方法既保留核方法理论基础扎实、学习框架完备和优化形式优雅等优点，同时又兼具深度网络强表征能力，为解决当前核方法理论研究和实际应用面临的瓶颈问题提供一条可行路径。

Kernel methods have a solid theoretical foundation, a complete learning framework, and an elegant convex optimization form. However, due to the limitations of representational ability of kernel methods, its learning performance on complex tasks has a certain gap compared with the deep learning methods, which has become a bottleneck problem for the further development of the kernel methods. To address these issues, we propose to establish the large-scale deep kernel learning theory and give automatic learning algorithms for large-scale tasks. Specifically, through the hierarchical construction, and combining with the locality and timing of characteristics, we first design a novel structure of deep kernel function with strong representational ability. Then, we study the approximation, generalization and robustness of large-scale deep kernel learning, and further build a large-scale deep kernel learning theory. Finally, based on the deep kernel learning theory, we design the criteria and automatic algorithms of deep kernel learning with both theoretical guarantee and computational efficiency. The large-scale deep kernel learning methods proposed in this project can not only retain the solid theoretical foundation, complete learning framework and elegant optimization form, but also have strong representational ability, which provide a feasible path to solve the bottleneck of theoretical research and practical application for large-scale kernel methods.