"Text-based data, collaborative filtering, covariance matrix estimation, and other statistical problems"

“基于文本的数据、协同过滤、协方差矩阵估计和其他统计问题”

• 批准号: 9133-2012
• 负责人: Feuerverger, Andrey
• 金额: $ 0.87万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568646
• 关键词: Text; based; data; collaborative; filtering

My research to date has been broadly based, with contributions to many areas of statistics; accordingly, this proposal ranges over a number of projects. (1) Statistical methods for text-based documents: (a) Automated computerized dating of documents, via nearest neighbours, maximum likelihood analogues, quantile regression, and other methods, and (b) Nonparametric temporal sequencing of document collections when none have been dated, by constructing noisy matrices of distances between documents pairs using singular value decomposition, and combinatorial optimization of objective functions that measure sequence correctness. (2) Nonlinear methods for collaborative filtering: (a) Predicting ratings users will give to products from large sparse matrices of user ratings via nonlinear SVD methods to improve prediction, and (b) Penalization problems related to the `large p small n' context. (3) Estimating large covariance matrices: (a) Allocating Fisher information for inference on the matrix structure given no prior information, (b) Shrinkage, empirical Bayes, penalization, regularization and sparseness methods to improve estimation, (c) Non-negative definiteness constraints, and (d) Choice of norms for assessing performance. Other problems include (a) Inference in certain exponential dispersion models generated by exponential tilting of extreme stable laws, (b) Inference in stable processes, (c) Deconvolution problems, and (d) Dependency structures in stationary point processes.

迄今为止，我的研究基础广泛，对统计的许多领域都有贡献;因此，这项建议涉及许多项目。 (1)基于文本的文档的统计方法：（a）通过最近邻、最大似然模拟、分位数回归和其他方法，自动计算机化确定文件日期，以及（B）在没有确定日期的情况下，通过使用奇异值分解构建文件对之间距离的噪声矩阵，对文件集合进行非参数时间排序，以及测量序列正确性的目标函数的组合优化。 (2)用于协同过滤的非线性方法：（a）通过非线性SVD方法预测用户将从用户评级的大型稀疏矩阵对产品给出的评级，以改进预测，以及（B）与“大p小n”上下文相关的惩罚问题。 (3)估计大的协方差矩阵：（a）在没有先验信息的情况下，分配Fisher信息用于矩阵结构的推断，（B）收缩、经验贝叶斯、惩罚、正则化和稀疏方法，以改进估计，（c）非负确定性约束，以及（d）选择评估性能的规范。 其他问题包括：（a）极端稳定律的指数倾斜所产生的某些指数分散模型中的推断，（B）稳定过程中的推断，（c）反卷积问题，以及（d）驻点过程中的依赖结构。