Description
Statistical Foundations of Data Science
Chapman & Hall/CRC Data Science Series
Authors: Fan Jianqing, Li Runze, Zhang Cun-Hui, Zou Hui
Language: EnglishSubjects for Statistical Foundations of Data Science:
Keywords
High-dimensional statistics; machine learning; graphical models; covariance matrix estimation; factor model; deep learning; Quantile Regression; Clustering algorithm; Empirical Loss Function; Covariance learning; Multiple Linear Regression; Statistical theories; Ridge Regression Estimator; Statistical models; Sure; Data science; Deep Neural Network Models; CQR; Feature Screening Procedure; Sparse Principal Components; Regular PCA; Kernel Ridge Regression; ADMM Algorithm; Stochastic Block Model; Scad Penalty; Ultrahigh Dimensional; Sparse PCA; High Dimensional Sparse Regression; Sis Procedure; Bond Risk Premia; Check Loss Function; Precision Matrix; Ridge Regression; Cumulative Distribution Function; High Dimensional Covariance Matrix; Ultrahigh Dimensional Data
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Add to cart the book of Fan Jianqing, Li Runze, Zhang Cun-Hui, Zou Hui· 15.6x23.4 cm · Hardback
Description
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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.
1. Introduction. 2. Multiple and Nonparametric Regression. 3. Introduction to Penalized Least-Squares. 4. Penalized Least Squares: Properties. 5. Generalized Linear Models and Penalized Likelihood. 6. Penalized M-estimators. 7. High Dimensional Inference 8. Feature Screening. 9. Covariance Regularization and Graphical Models. 10. Covariance Learning and Factor Models. 11. Applications of Factor Models and PCA. 12. Supervised Learning. 13. Unsupervised Learning. 14. An Introduction to Deep Learning.
The authors are international authorities and leaders on the presented topics. All are fellows of the Institute of Mathematical Statistics and the American Statistical Association.
Jianqing Fan is Frederick L. Moore Professor, Princeton University. He is co-editing Journal of Business and Economics Statistics and was the co-editor of The Annals of Statistics, Probability Theory and Related Fields, and Journal of Econometrics and has been recognized by the 2000 COPSS Presidents' Award, AAAS Fellow, Guggenheim Fellow, Guy medal in silver, Noether Senior Scholar Award, and Academician of Academia Sinica.
Runze Li is Elberly family chair professor and AAAS fellow, Pennsylvania State University, and was co-editor of The Annals of Statistics.
Cun-Hui Zhang is distinguished professor, Rutgers University and was co-editor of Statistical Science.
Hui Zou is professor, University of Minnesota and was action editor of Journal of Machine Learning Research.