Multivariate Statistics
About Multivariate Statistics
This book explores multivariate statistics from both traditional and modern perspectives. The first section covers core topics like multivariate normality, MANOVA, discrimination, PCA, and canonical correlation analysis. The second section includes modern concepts such as gradient boosting, random forests, variable importance, and causal inference.A key theme is leveraging classical multivariate statistics to explain advanced topics and prepare for contemporary methods. For example, linear models provide a foundation for understanding regu-larization with AIC and BIC, leading to a deeper analysis of regularization through generalization error and the VC theorem. Discriminant analysis introduces the weighted Bayes rule, which leads into modern classification techniques for class-imbalanced machine learning problems. Steepest descent serves as a precursor to matching pursuit and gradient boosting. Axis-aligned trees like CART, a classical tool, set the stage for more recent methods like...
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