我院博士生丁飞（第一作者）与导师贺诗源在《Technometrics》期刊发表论文"Functional PCA With Covariate-Dependent Mean and Covariance Structure"。该论文考虑受协变量影响的函数数据的均值、协方差和主成分函数的估计问题。既有研究有极大的计算开销或者模型假设过于简单，从而难以应用于实际场景。丁飞的文章巧妙构造从欧几里得空间到半正定矩阵的映射，从而保证协方差函数的正定性和计算的高效性。该方法被应用于天文的双星系统，能从大规模数据中快速计算结果，且能够精确刻画和预测各类双星系统的明暗涨落。

论文概述

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not make use of covariates, and those that do often have high computational cost or make overly simplistic assumptions that are violated in practice. In this article, we propose a new framework, called covariate-dependent functional principal component analysis (CD-FPCA), in which both the mean and covariance structure depend on covariates. We propose a corresponding estimation algorithm, which makes use of spline basis representations and roughness penalties, and is substantially more computationally efficient than competing approaches of adequate estimation and prediction accuracy. A key aspect of our work is our novel approach for modeling the covariance function and ensuring that it is symmetric positive semidefinite. We demonstrate the advantages of our methodology through a simulation study and an astronomical data analysis.

发表页面

作者简介

丁飞，中国人民大学统计与大数据研究院2021届博士毕业生，2021年5月曾获 Texas A&M University 博士学位，曾参加2020 Joint Statistical Meetings会议做报告。曾获优秀研究生，Grad Enhancement Fellowship, Statistics Industrial Affiliate等奖学金。入选腾讯“大咖计划”，现就职于腾讯PCG公共数据科学部。

贺诗源，中国人民大学统计与大数据研究院助理教授，博士生导师。贺诗源的研究领域包括统计函数数据分析、贝叶斯计算等，并将统计学方法与天文相结合，研究超新星、Mira变星等光谱和光面曲线拟合，进而测量宇宙尺度。已在Journal of the American Statistical Association、The Annals of Applied Statistics、The Astrophysical Journal等统计学、天文学一流期刊发表多篇论文。

David E. Jones, Department of Statistics, Texas A&M University, College Station, TX;

Jianhua Z. Huang. School of Data Science, The Chinese University of Hong Kong, Shenzhen, China.