报告题目：Shape-on-Scalar Regression Models: Going Beyond Prealigned Non-Euclidean Responses
报告人：黄超 博士
报告时间：2023年6月20日（周二）上午 11:00-12:00
报告地点：藕舫楼629
主持人：曹春正 教授
报告人简介：
黄超，现任佛罗里达州立大学统计系助理教授，于2008年，2014年在东南大学分别获得应用数学学士和博士学位，2019年在美国北卡罗来纳大学教堂山分校获得生物统计博士学位，研究方向包括生物统计，医学图像分析，函数数据分析，形状数据分析等。在高水平国际统计医学期刊以及图像模式识别顶会上发表学术论文40多篇，包括《Journal of the American Statistical Association》《Biometrika》《IEEE Transactions on Neural Networks and Learning Systems》《IEEE Transactions on Medical Image》《NeuroImage》《Medical Image Analysis》等。
报告简介：
The problem of using covariates to predict shapes of objects in a regression setting is important in many fields. A formal statistical approach, termed geodesic regression model, is commonly used for modeling and analyzing relationships between Euclidean predictors and shape responses. Despite its popularity, this model faces several key challenges, including (i) misalignment of shapes due to pre-processing steps, (ii) difficulties in shape alignment due to imaging heterogeneity, and (iii) lack of spatial correlation in shape structures. We propose a comprehensive geodesic factor regression model that addresses all these challenges. Instead of using shapes as extracted from pre-registered data, it takes a more fundamental approach, incorporating alignment step within the proposed regression model and learns them using both pre-shape and covariate data. Additionally, it specifies spatial correlation structures using low-dimensional representations, including latent factors on the tangent space and isotropic error terms. Furthermore, the geodesic factor regression model is extended to a mixture of geodesic factor regression model, which can cluster objects and recover the underlying sub-group structure according to their shapes and covariates in Euclidean space. Both simulation studies and real data analysis are conducted to compare the performance of our proposed method with other existing methods.
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数学与统计学院
2023年6月19日