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: | Electronic eBook |
| Language: | English |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Edition: | 1st ed. 2025. |
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| Online Access: | https://doi.org/10.1007/978-3-032-03161-7 |
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| 100 | 1 | |a Lu, Junwei. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Big Data Analysis |h [electronic resource] : |b High Dimensional Probability, Statistics, Optimization, and Inference / |c by Junwei Lu. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XIII, 170 p. 1 illus.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 341 | 0 | |b Single logical reading order |2 onix | |
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| 341 | 0 | |b Use of high contrast between text and background color |2 onix | |
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| 341 | 0 | |b All non-decorative content supports reading without sight |2 onix | |
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| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Big data. | |
| 650 | 0 | |a Statistics . | |
| 650 | 0 | |a Probabilities. | |
| 650 | 1 | 4 | |a Big Data. |
| 650 | 2 | 4 | |a Statistics. |
| 650 | 2 | 4 | |a Applied Probability. |
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| 950 | |a Focus Bundle Business (SpringerNature-85394) | ||