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.
