Ruiyi Yang, Doctor

Junjie Ma, Associate Professor

Gaussian Processes on Manifolds: Graph-based Approximation and Applications

10:30-11:30 December 17(Wednesday), S723

Gaussian processes (GPs) are important random function models with desirable analytic properties that have found wide applications in inverse problems, spatial statistics, and machine learning. In this talk, we shall investigate a generalization of the popular Matérn GP to the manifold setting. In the first part, we formalize its definition and introduce a graph-based approximation that is computable given only a point cloud of samples from the manifold. The resulting graph Matérn GP enjoys a sparsity structure that facilitates computation and is widely applicable in many aspects of Bayesian methodologies. In the second part, we discuss in detail its application in a manifold optimization problem where gradients are intractable to obtain. Exploiting tools from Bayesian optimization, we propose an efficient algorithm with provable guarantees, whose effectiveness is further demonstrated by numerical examples.

报告人简介：杨睿逸即将入职上海交通大学自然科学研究院担任长聘教轨副教授。2022 年博士毕业于芝加哥大学，之后在普林斯顿大学从事博士后研究。主要研究方向包括非欧几何场景下的贝叶斯计算方法和非参数统计理论，以及反问题和数据科学的数学基础。