含有潜在因子的大规模数据统计分析及应用

大规模数据的统计推断是当前统计学研究的前沿领域之一。现有的方法通常假设模型中的影响因子均是可观测的。然而实际模型中却可能隐藏有不可观测的潜在因子。本课题以高维统计推断方法的研究为基础，从潜在因子对可观测变量及因变量的影响入手，探索可以对可观测变量及潜在因子作用系数进行推断的统计方法，并寻求针对样本海量增长时含有潜在因子的大规模数据的新型统计分析框架。主要研究工作将从高维潜在因子的估计、高维可观测变量及潜在因子作用系数的统计推断、海量样本情形下的综合统计量三个方面展开。相关研究成果将应用于经济、金融、生物医疗以及机器学习等领域的大规模数据处理。

Statistical inference for large scale data sets is one of the frontier issues in the current studies on statistical science. Most of existing methods assume implicitly that all features in a model are observable. Yet some latent factors may potentially exist in the hidden structure of the original model. Based on the studies on high-dimensional statistical inference, the current project aims to explore statistical methods that can provide inference for the effects of both the observable covariates and latent factors from the impacts of latent features on the observable covariates and outcome. Moreover, we also want to establish new statistical frameworks for large scale data with latent factors when the sample sizes are extraordinarily large. Main research contents of the project include three aspects: estimation of high-dimensional latent factors, statistical inference for the effects of both observable covariates and latent features, and the overall statistics for extraordinarily large sample sizes. The research results will have broad applications in the areas of economics, finance, biomedical treatment and machine learning for large scale data analysis.