Big Data Analysis High Dimensional Probability, Statistics, Optimization, and Inference /
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 d...
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| Format: | Elektronski eKnjiga |
| Jezik: | angleščina |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Izdaja: | 1st ed. 2025. |
| Teme: | |
| Online dostop: | https://doi.org/10.1007/978-3-032-03161-7 |
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Kazalo:
- 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.