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010   $a9783032031617$b(electronic bk.)
010   $z9783032031600
024 7 $a10.1007/978-3-032-03161-7
035   $a(MiAaPQ)EBC32394213
035   $a(Au-PeEL)EBL32394213
035   $a(CKB)42027259700041
035   $a(DE-He213)978-3-032-03161-7
035   $a(EXLCZ)9942027259700041
100   $a20251106d2025      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aBig Data Analysis $eHigh Dimensional Probability, Statistics, Optimization, and Inference /$fby Junwei Lu
205   $a1st ed. 2025.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025.
215   $a1 online resource (266 pages)
225 1 $aMathematics and Statistics Series
311 08$aPrint version: Lu, Junwei Big Data Analysis Cham : Springer,c2025 9783032031600 
327   $aPart 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.
330   $aThis book covers the methods and theory of high dimensional probability, statistics, large-scale optimization, and inference. We aim to quickly bring readers to the frontier and interdisciplinary areas of statistics, optimization, probability, and machine learning. This book covers topics in: High dimensional probability, Concentration inequality, Sub-Gaussian random variables, Chernoff bounds, Hoeffding's inequality, Maximal inequalities, High dimensional linear regression, Ordinary least square, Compressed sensing, Lasso, Variations of Lasso including group lasso, fused lasso, adaptive lasso, etc., General high dimensional M- estimators, Variable selection consistency, High dimensional Optimization, Convex geometry, Lagrange duality, Gradient descent, Proximal gradient descent, LARS, ADMM, Mirror descent, Stochastic optimization, Large-Scale Inference, Linear model hypothesis testing, high dimensional inference, Chi-square test, maximal test, and Higher criticism, False discovery rate control.
410  0$aMathematics and Statistics Series
606   $aBig data
606   $aStatistics
606   $aProbabilities
606   $aBig Data
606   $aStatistics
606   $aApplied Probability
615  0$aBig data.
615  0$aStatistics.
615  0$aProbabilities.
615 14$aBig Data.
615 24$aStatistics.
615 24$aApplied Probability.
676   $a005.7
700   $aLu$b Junwei$01697233
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9911039317303321
996   $aBig Data Analysis$94454494
997   $aUNINA