Big Data Analysis : High Dimensional Probability, Statistics, Optimization, and Inference / by Junwei Lu.

Format:

Book

Author/Creator:

Lu, Junwei.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Big data.

Statistics.

Probabilities.

Big Data.

Applied Probability.

Local Subjects:

Big Data.

Statistics.

Applied Probability.

Physical Description:

1 online resource (266 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

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.

Contents:

Part I Foundations of Big Data Analysis

Chapter 1 Introduction

Chapter 2 Preliminaries in Probability

Chapter 3 Preliminaries in Linear Algebra

Part II High-Dimensional Probability

Chapter 4 Concentration Inequalities

Chapter 5 Sub-Exponential Random Variables

Chapter 6 Maximal Inequality

Part III High-Dimensional Statistics

Chapter 7 Ordinary Least Squares

Chapter 8 Compressive Sensing

Chapter 9 Restricted Isometry Property

Chapter 10 Statistical Properties of Lasso

Chapter 11 Variations of Lasso

Part IV High-Dimensional Optimization

Chapter 12 Convexity and Subgradient

Chapter 13 Gradient Descent

Chapter 14 Proximal Gradient Descent

Chapter 15 Mirror Descent and Nesterov’s Smoothing

Chapter 16 Duality and ADMM

Part V High-Dimensional Inference

Chapter 17 High Dimensional Inference

Chapter 18 Debiased Lasso

Chapter 19 Multiple Hypotheses

Chapter 20 False Discovery Rate

Chapter 21 Knock-Off

References.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Lu, Junwei Big Data Analysis

ISBN:

9783032031617

OCLC:

1572213843