报告题目: Intrinsic Gaussian Process on point cloud with probablistic geometry

报告人：牛牧（英国格拉斯哥大学）

报告时间：2023年4月14日17:00-17:45

报告地点：文波楼201

摘要: This article presents a novel approach to construct Intrinsic Gauss ian Processes for regres- sion on unknown manifolds with probabilistic me trics (GPUM ) in point clouds. In many real world applications, one often encounters high dimensional data (e.g.‘point cloud data’) centered aro und some lower dimensional unknown manifolds. The geometry of manifold is in general different from the usual Euclidean geometry. Naively applying traditional smoothing methods such as Euclidean Gaussian Processes (GPs) to manifold-valued data and so ignoring the geometry of the space can po tentially lead to highly misleading pre- dictions and inferences. A manif old embedded in a high dimensional Euclidean space can be well described by a probabilistic mapping function and the corresponding latent space. W e investigate the geometrical structure of the unknown manifolds using th e Bayesian Gaussian Processes latent variable models(B-GPLVM) and Riemann ian geometry.The heat kernel is estimated as the transition density of Br ownian Motion and used as the covariance functions of GPUM . The applicat ions of GPUM are illustrated in the simulation studies on the Swiss roll, high dimensional real datasets of WiFi signals and image data examples.

报告人简介：牛牧，英国格拉斯哥大学数学与统计学院的讲师。主要研究方向：统计机器学习和贝叶斯统计学，在生态学、环境科学和图像处理中的应用。在《皇家统计学会杂志：B系列》和《机器学习研究杂志》发表文章多篇。