Big Data Analysis: High Dimensional Probability, Statistics, Optimization, and Inference - Hardcover

Lu, Junwei

Hardcover

ISBN 10: 3032031605 ISBN 13: 9783032031600

Publisher: Springer, 2025

Synopsis

This book covers the methods and theory of high dimensional probability, statistics, large-scale optimization, and inference. We aim to quickly bring readers to the frontier and interdisciplinary areas of statistics, optimization, probability, and machine learning. This book covers topics in:

High dimensional probability, Concentration inequality, Sub-Gaussian random variables, Chernoff bounds, Hoeffding's inequality, Maximal inequalities, High dimensional linear regression, Ordinary least square, Compressed sensing, Lasso, Variations of Lasso including group lasso, fused lasso, adaptive lasso, etc., General high dimensional M- estimators, Variable selection consistency, High dimensional Optimization, Convex geometry, Lagrange duality, Gradient descent, Proximal gradient descent, LARS, ADMM, Mirror descent, Stochastic optimization, Large-Scale Inference, Linear model hypothesis testing, high dimensional inference, Chi-square test, maximal test, and Higher criticism, False discovery rate control.

About this title

About the Author

Junwei Lu is an Assistant Professor in Harvard T.H. Chan School of Public Health. His research focuses on the intersection of statistical machine learning and clinical studies, revealing scientific associations among clinical treatment strategies and patient phenotyping, especially focusing on precision medicine leveraging real-world clinical data such as electronic health records data for risk prediction and clinical optimization.

From the Back Cover

This book covers the methods and theory of high dimensional probability, statistics, large-scale optimization, and inference. We aim to quickly bring readers to the frontier and interdisciplinary areas of statistics, optimization, probability, and machine learning. This book covers topics in:

High dimensional probability, Concentration inequality, Sub-Gaussian random variables, Chernoff bounds, Hoeffding's inequality, Maximal inequalities, High dimensional linear regression, Ordinary least square, Compressed sensing, Lasso, Variations of Lasso including group lasso, fused lasso, adaptive lasso, etc., General high dimensional M- estimators, Variable selection consistency, High dimensional Optimization, Convex geometry, Lagrange duality, Gradient descent, Proximal gradient descent, LARS, ADMM, Mirror descent, Stochastic optimization, Large-Scale Inference, Linear model hypothesis testing, high dimensional inference, Chi-square test, maximal test, and Higher criticism, False discovery rate control.

Edition details

• Publisher: Springer
• Publication date: 2025
• Language: English
• ISBN 10: 3032031605
• ISBN 13: 9783032031600
• Binding: Hardcover
• Number of pages: 183