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CIF: Small: Efficient Discriminant Analysis Through Parsimonious Probabilistic Models

CIF：小型：通过简约概率模型进行高效判别分析

基本信息

批准号：
1617691
负责人：
Xin Zhang
金额：
$ 41.42万
依托单位：
Florida State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-07-01 至 2020-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1617691&HistoricalAwards=false
关键词：
CIF Small Efficient Discriminant Analysis

项目摘要

In the Big-Data era, there is a pressing need to develop more efficient and easy-to-interpret data analysis methods to face the new challenges rising from real life applications, such as cancer diagnosis, brain connectivity network and neuroimaging studies. Besides their intimidating sizes, data sets in such applications demand researchers to understand the intrinsic and complex structure behind them. This research involves new directions in discriminant analysis and classification by exploring state-of-art statistical methods and contemporary computation techniques. The investigators will develop new statistical methods and computational tools to utilize the intrinsic structure of the data, such as high correlation, network structure and tensor/array data structure. The research results will advance the research in statistics, machine learning, text mining, bio-medical research, finance, neuroimaging analysis, among other fields. The research will also be integrated with substantial educational and outreach activities.In this research, the investigators aim to develop parsimonious probabilistic discriminant analysis models for efficiently analyzing data with intrinsically complicated structures, and for improved estimation of parameters and accuracy in predictions. Three sets of problems will be investigated: (1) parsimonious linear discriminant analysis with envelope, aiming to integrate a nascent technique of envelope modeling with the classical linear discriminant analysis model; (2) simultaneous discriminant analysis and differential network estimation, aiming to develop a novel and unified framework for simultaneously studying differential networks, estimating multiple covariance matrices, and training quadratic discriminant analysis classifier; and (3) sparse tensor discriminant analysis with feature selection, aiming to develop a sparse discriminant analysis method for tensor-valued data that directly uses the tensor-valued features for discriminant analysis, while simultaneously achieving feature selection and preserving interpretable tensor structure.

在大数据时代，迫切需要开发更高效、更易于解释的数据分析方法，以应对癌症诊断、脑连接网络和神经影像学研究等真实的生活应用带来的新挑战。除了它们令人生畏的大小之外，这些应用中的数据集还要求研究人员了解它们背后的内在和复杂结构。本研究通过探索最先进的统计方法和当代计算技术，涉及判别分析和分类的新方向。研究人员将开发新的统计方法和计算工具，以利用数据的内在结构，如高相关性，网络结构和张量/数组数据结构。研究成果将推动统计学、机器学习、文本挖掘、生物医学研究、金融、神经影像分析等领域的研究。在本研究中，研究人员的目标是开发简约的概率判别分析模型，以有效地分析具有内在复杂结构的数据，并提高参数估计和预测精度。将研究三组问题：（1）具有包络的简约线性判别分析，旨在将新兴的包络建模技术与经典的线性判别分析模型相结合;（2）同时判别分析和差分网络估计，旨在开发一种新颖的统一框架，用于同时研究差分网络，估计多个协方差矩阵，和训练二次判别分析分类器;（3）稀疏张量判别分析与特征选择，旨在开发一种用于张量值数据的稀疏判别分析方法，该方法直接使用张量值特征进行判别分析，同时实现特征选择并保留可解释的张量结构。