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

到目前为止，我的研究基础广泛，对许多统计领域都有贡献；因此，这项建议涉及许多项目。 (1)基于文本的文件的统计方法：(A)通过最近邻法、最大似然法、分位数回归法和其他方法对文件进行自动计算机测年，以及(B)通过使用奇异值分解构造文件对之间距离的噪声矩阵以及对衡量序列正确性的目标函数进行组合优化，在没有确定日期的情况下对文件集合进行非参数时间排序。 (2)协作过滤的非线性方法：(A)通过非线性奇异值分解(SVD)方法从用户评级的大型稀疏矩阵中预测用户将给予产品的评级，以改进预测；以及(B)与“大p小n”上下文相关的惩罚问题。 (3)估计大型协方差矩阵：(A)在没有先验信息的情况下分配Fisher信息用于关于矩阵结构的推断，(B)收缩、经验贝叶斯、惩罚、正则化和稀疏方法来改进估计，(C)非负确定性约束，以及(D)用于评估性能的规范的选择。 其他问题包括(A)由极稳定律的指数倾斜产生的某些指数离散模型中的推断，(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。

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.