Forward Variable Selection For Ultra High Dimensional Quantile Regression Models
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Statistical Foundations of Data Science
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
超高维数据统计模型变量筛选方法
隨著現代科技的高速發展，海量數據隨處可見，特別是生物工程、航空航天、人工智能以及電子商務等方面。海量數據的特點是維數較大，數據的維數以樣本的指數階增加即所謂的超高維數據。本書研究內容包括：(1)對於超高維數據分位數回歸變係數模型，利用樣條近似方法提出了排列邊際回歸係數的變量篩選方法；(2)使用經驗似然方法研究了可加模型的變量篩選問題；(3)利用核回歸方法估計條件期望損失研究了非參回歸模型的變量篩選問題，提出一般模型的變量選擇方法；(4)在廣義線性模型框架下，探討了順序Lasso變量選擇問題，提出了順序Lasso迭代選擇方法；(5)對於超高維數據， 首次研究了GINI相關係數變量選擇問題，所提到方法不受異常值點的影響，具有很好的穩健性，為超高維數據提供了一個簡單、穩健和有效的變量選擇方法。