{"product_id":"rankbased-methods-for-shrinkage-and-selection-9781119625391","title":"RankBased Methods for Shrinkage and Selection","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eRank-Based Methods for Shrinkage and Selection\u003c\/b\u003e \u003cp\u003e\u003cb\u003eA practical and hands-on guide to the theory and methodology of statistical estimation based on rank\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eRobust statistics is an important field in contemporary mathematics and applied statistical methods. \u003ci\u003eRank-Based Methods for Shrinkage and Selection: With Application to Machine Learning\u003c\/i\u003e describes techniques to produce higher quality data analysis in shrinkage and subset selection to obtain parsimonious models with outlier-free prediction. This book is intended for statisticians, economists, biostatisticians, data scientists and graduate students. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eRank-Based Methods for Shrinkage and Selection\u003c\/i\u003e elaborates on rank-based theory and application in machine learning to robustify the least squares methodology. It also includes: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eDevelopment of rank theory and application of shrinkage and selection\u003c\/li\u003e \u003cli\u003eMethodology for robust data science using penalized rank estimators\u003c\/li\u003e \u003cli\u003eTheory and methods of p\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e1 Introduction to Rank-based Regression \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Robustness of the Median 1\u003c\/p\u003e \u003cp\u003e1.2.1 Mean vs. Median 1\u003c\/p\u003e \u003cp\u003e1.2.2 Breakdown Point 4\u003c\/p\u003e \u003cp\u003e1.2.3 Order and Rank Statistics 5\u003c\/p\u003e \u003cp\u003e1.3 Simple Linear Regression 6\u003c\/p\u003e \u003cp\u003e1.3.1 Least Squares Estimator (LSE) 6\u003c\/p\u003e \u003cp\u003e1.3.2 Theil’s Estimator 7\u003c\/p\u003e \u003cp\u003e1.3.3 Belgium Telephone Data Set 7\u003c\/p\u003e \u003cp\u003e1.3.4 Estimation and Standard Error Comparison 9\u003c\/p\u003e \u003cp\u003e1.4 Outliers and their Detection 11\u003c\/p\u003e \u003cp\u003e1.4.1 Outlier Detection 12\u003c\/p\u003e \u003cp\u003e1.5 Motivation for Rank-based Methods 13\u003c\/p\u003e \u003cp\u003e1.5.1 Effect of a Single Outlier 13\u003c\/p\u003e \u003cp\u003e1.5.2 Using Rank for the Location Model 16\u003c\/p\u003e \u003cp\u003e1.5.3 Using Rank for the Slope 19\u003c\/p\u003e \u003cp\u003e1.6 The Rank Dispersion Function 20\u003c\/p\u003e \u003cp\u003e1.6.1 Ranking and Scoring Details 23\u003c\/p\u003e \u003cp\u003e1.6.2 Detailed Procedure for R-estimation 25\u003c\/p\u003e \u003cp\u003e1.7 Shrinkage Estimation and Subset Selection 30\u003c\/p\u003e \u003cp\u003e1.7.1 Multiple Linear Regression using Rank 30\u003c\/p\u003e \u003cp\u003e1.7.2 Penalty Functions 32\u003c\/p\u003e \u003cp\u003e1.7.3 Shrinkage Estimation 34\u003c\/p\u003e \u003cp\u003e1.7.4 Subset Selection 36\u003c\/p\u003e \u003cp\u003e1.7.5 Blended Approaches 39\u003c\/p\u003e \u003cp\u003e1.8 Summary 39\u003c\/p\u003e \u003cp\u003e1.9 Problems 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Characteristics of Rank-based Penalty Estimators \u003c\/b\u003e\u003cb\u003e47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 47\u003c\/p\u003e \u003cp\u003e2.2 Motivation for Penalty Estimators 47\u003c\/p\u003e \u003cp\u003e2.3 Multivariate Linear Regression 49\u003c\/p\u003e \u003cp\u003e2.3.1 Multivariate Least Squares Estimation 49\u003c\/p\u003e \u003cp\u003e2.3.2 Multivariate R-estimation 51\u003c\/p\u003e \u003cp\u003e2.3.3 Multicollinearity 51\u003c\/p\u003e \u003cp\u003e2.4 Ridge Regression 53\u003c\/p\u003e \u003cp\u003e2.4.1 Ridge Applied to Least Squares Estimation 53\u003c\/p\u003e \u003cp\u003e2.4.2 Ridge Applied to Rank Estimation 55\u003c\/p\u003e \u003cp\u003e2.5 Example: Swiss Fertility Data Set 56\u003c\/p\u003e \u003cp\u003e2.5.1 Estimation and Standard Errors 59\u003c\/p\u003e \u003cp\u003e2.5.2 Parameter Variance using Bootstrap 60\u003c\/p\u003e \u003cp\u003e2.5.3 Reducing Variance using Ridge 61\u003c\/p\u003e \u003cp\u003e2.5.4 Ridge Traces 62\u003c\/p\u003e \u003cp\u003e2.6 Selection of Ridge Parameter 𝜆2 65\u003c\/p\u003e \u003cp\u003e2.6.1 Quadratic Risk 65\u003c\/p\u003e \u003cp\u003e2.6.2 K-fold Cross-validation Scheme 68\u003c\/p\u003e \u003cp\u003e2.7 LASSO and aLASSO 71\u003c\/p\u003e \u003cp\u003e2.7.1 Subset Selection 71\u003c\/p\u003e \u003cp\u003e2.7.2 Least Squares with LASSO 71\u003c\/p\u003e \u003cp\u003e2.7.3 The Adaptive LASSO and its Geometric Interpretation 73\u003c\/p\u003e \u003cp\u003e2.7.4 R-estimation with LASSO and aLASSO 77\u003c\/p\u003e \u003cp\u003e2.7.5 Oracle Properties 78\u003c\/p\u003e \u003cp\u003e2.8 Elastic Net (Enet) 82\u003c\/p\u003e \u003cp\u003e2.8.1 Naive Enet 82\u003c\/p\u003e \u003cp\u003e2.8.2 Standard Enet 83\u003c\/p\u003e \u003cp\u003e2.8.3 Enet in Machine Learning 84\u003c\/p\u003e \u003cp\u003e2.9 Example: Diabetes Data Set 85\u003c\/p\u003e \u003cp\u003e2.9.1 Model Building with R-aEnet 85\u003c\/p\u003e \u003cp\u003e2.9.2 MSE vs. MAE 88\u003c\/p\u003e \u003cp\u003e2.9.3 Model Building with LS-Enet 91\u003c\/p\u003e \u003cp\u003e2.10 Summary 94\u003c\/p\u003e \u003cp\u003e2.11 Problems 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Location and Simple Linear Models \u003c\/b\u003e\u003cb\u003e101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 101\u003c\/p\u003e \u003cp\u003e3.2 Location Estimators and Testing 104\u003c\/p\u003e \u003cp\u003e3.2.1 Unrestricted R-estimator of 𝜃 104\u003c\/p\u003e \u003cp\u003e3.2.2 Restricted R-estimator of 𝜃 107\u003c\/p\u003e \u003cp\u003e3.3 Shrinkage R-estimators of Location 108\u003c\/p\u003e \u003cp\u003e3.3.1 Overview of Shrinkage R-estimators of 𝜃 108\u003c\/p\u003e \u003cp\u003e3.3.2 Derivation of the Ridge-type R-estimator 113\u003c\/p\u003e \u003cp\u003e3.3.3 Derivation of the LASSO-type R-estimator 114\u003c\/p\u003e \u003cp\u003e3.3.4 General Shrinkage R-estimators of 𝜃 114\u003c\/p\u003e \u003cp\u003e3.4 Ridge-type R-estimator of 𝜃 117\u003c\/p\u003e \u003cp\u003e3.5 Preliminary Test R-estimator of 𝜃 118\u003c\/p\u003e \u003cp\u003e3.5.1 Optimum Level of Significance of PTRE 121\u003c\/p\u003e \u003cp\u003e3.6 Saleh-type R-estimators 122\u003c\/p\u003e \u003cp\u003e3.6.1 Hard-Threshold R-estimator of 𝜃 122\u003c\/p\u003e \u003cp\u003e3.6.2 Saleh-type R-estimator of 𝜃 123\u003c\/p\u003e \u003cp\u003e3.6.3 Positive-rule Saleh-type (LASSO-type) R-estimator of 𝜃 125\u003c\/p\u003e \u003cp\u003e3.6.4 Elastic Net-type R-estimator of 𝜃 127\u003c\/p\u003e \u003cp\u003e3.7 Comparative Study of the R-estimators of Location 129\u003c\/p\u003e \u003cp\u003e3.8 Simple Linear Model 132\u003c\/p\u003e \u003cp\u003e3.8.1 Restricted R-estimator of Slope 134\u003c\/p\u003e \u003cp\u003e3.8.2 Shrinkage R-estimator of Slope 135\u003c\/p\u003e \u003cp\u003e3.8.3 Ridge-type R-estimation of Slope 135\u003c\/p\u003e \u003cp\u003e3.8.4 Hard-Threshold R-estimator of Slope 136\u003c\/p\u003e \u003cp\u003e3.8.5 Saleh-type R-estimator of Slope 137\u003c\/p\u003e \u003cp\u003e3.8.6 Positive-rule Saleh-type (LASSO-type) R-estimator of Slope 138\u003c\/p\u003e \u003cp\u003e3.8.7 The Adaptive LASSO (aLASSO-type) R-estimator 138\u003c\/p\u003e \u003cp\u003e3.8.8 nEnet-type R-estimator of Slope 139\u003c\/p\u003e \u003cp\u003e3.8.9 Comparative Study of R-estimators of Slope 140\u003c\/p\u003e \u003cp\u003e3.9 Summary 141\u003c\/p\u003e \u003cp\u003e3.10 Problems 142\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Analysis of Variance (ANOVA) \u003c\/b\u003e\u003cb\u003e149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 149\u003c\/p\u003e \u003cp\u003e4.2 Model, Estimation and Tests 149\u003c\/p\u003e \u003cp\u003e4.3 Overview of Multiple Location Models 150\u003c\/p\u003e \u003cp\u003e4.3.1 Example: Corn Fertilizers 151\u003c\/p\u003e \u003cp\u003e4.3.2 One-way ANOVA 151\u003c\/p\u003e \u003cp\u003e4.3.3 Effect of Variance on Shrinkage Estimators 153\u003c\/p\u003e \u003cp\u003e4.3.4 Shrinkage Estimators for Multiple Location 156\u003c\/p\u003e \u003cp\u003e4.4 Unrestricted R-estimator 158\u003c\/p\u003e \u003cp\u003e4.5 Test of Significance 161\u003c\/p\u003e \u003cp\u003e4.6 Restricted R-estimator 162\u003c\/p\u003e \u003cp\u003e4.7 Shrinkage Estimators 163\u003c\/p\u003e \u003cp\u003e4.7.1 Preliminary Test R-estimator 163\u003c\/p\u003e \u003cp\u003e4.7.2 The Stein–Saleh-type R-estimator 164\u003c\/p\u003e \u003cp\u003e4.7.3 The Positive-rule Stein–Saleh-type R-estimator 165\u003c\/p\u003e \u003cp\u003e4.7.4 The Ridge-type R-estimator 167\u003c\/p\u003e \u003cp\u003e4.8 Subset Selection Penalty R-estimators 169\u003c\/p\u003e \u003cp\u003e4.8.1 Preliminary Test Subset Selector R-estimator 169\u003c\/p\u003e \u003cp\u003e4.8.2 Saleh-type R-estimator 170\u003c\/p\u003e \u003cp\u003e4.8.3 Positive-rule Saleh Subset Selector (PRSS) 171\u003c\/p\u003e \u003cp\u003e4.8.4 The Adaptive LASSO (aLASSO) 173\u003c\/p\u003e \u003cp\u003e4.8.5 Elastic-net-type R-estimator 177\u003c\/p\u003e \u003cp\u003e4.9 Comparison of the R-estimators 178\u003c\/p\u003e \u003cp\u003e4.9.1 Comparison of URE and RRE 179\u003c\/p\u003e \u003cp\u003e4.9.2 Comparison of URE and Stein–Saleh-type R-estimators 179\u003c\/p\u003e \u003cp\u003e4.9.3 Comparison of URE and Ridge-type R-estimators 179\u003c\/p\u003e \u003cp\u003e4.9.4 Comparison of URE and PTSSRE 180\u003c\/p\u003e \u003cp\u003e4.9.5 Comparison of LASSO-type and Ridge-type R-estimators 180\u003c\/p\u003e \u003cp\u003e4.9.6 Comparison of URE, RRE and LASSO 181\u003c\/p\u003e \u003cp\u003e4.9.7 Comparison of LASSO with PTRE 181\u003c\/p\u003e \u003cp\u003e4.9.8 Comparison of LASSO with SSRE 182\u003c\/p\u003e \u003cp\u003e4.9.9 Comparison of LASSO with PRSSRE 182\u003c\/p\u003e \u003cp\u003e4.9.10 Comparison of nEnetRE with URE 183\u003c\/p\u003e \u003cp\u003e4.9.11 Comparison of nEnetRE with RRE 183\u003c\/p\u003e \u003cp\u003e4.9.12 Comparison of nEnetRE with HTRE 183\u003c\/p\u003e \u003cp\u003e4.9.13 Comparison of nEnetRE with SSRE 184\u003c\/p\u003e \u003cp\u003e4.9.14 Comparison of Ridge-type vs. nEnetRE 184\u003c\/p\u003e \u003cp\u003e4.10 Summary 185\u003c\/p\u003e \u003cp\u003e4.11 Problems 185\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Seemingly Unrelated Simple Linear Models \u003c\/b\u003e\u003cb\u003e191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 191\u003c\/p\u003e \u003cp\u003e5.1.1 Problem Formulation 193\u003c\/p\u003e \u003cp\u003e5.2 Signed and Signed Rank Estimators of Parameters 194\u003c\/p\u003e \u003cp\u003e5.2.1 General Shrinkage R-estimator of 𝛽 198\u003c\/p\u003e \u003cp\u003e5.2.2 Ridge-type R-estimator of 𝛽 199\u003c\/p\u003e \u003cp\u003e5.2.3 Preliminary Test R-estimator of 𝛽 201\u003c\/p\u003e \u003cp\u003e5.3 Stein–Saleh-type R-estimator of 𝛽 202\u003c\/p\u003e \u003cp\u003e5.3.1 Positive-rule Stein–Saleh R-estimators of 𝛽 202\u003c\/p\u003e \u003cp\u003e5.4 Saleh-type R-estimator of 𝛽 203\u003c\/p\u003e \u003cp\u003e5.4.1 LASSO-type R-estimator of the 𝛽 205\u003c\/p\u003e \u003cp\u003e5.5 Elastic-net-type R-estimators 206\u003c\/p\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e5.6 R-estimator of Intercept When Slope Has Sparse Subset 207\u003c\/p\u003e \u003cp\u003e5.6.1 General Shrinkage R-estimator of Intercept 207\u003c\/p\u003e \u003cp\u003e5.6.2 Ridge-type R-estimator of 𝜃 209\u003c\/p\u003e \u003cp\u003e5.6.3 Preliminary Test R-estimators of 𝜃 209\u003c\/p\u003e \u003cp\u003e5.7 Stein–Saleh-type R-estimator of 𝜃 210\u003c\/p\u003e \u003cp\u003e5.7.1 Positive-rule Stein–Saleh-type R-estimator of 𝜃 211\u003c\/p\u003e \u003cp\u003e5.7.2 LASSO-type R-estimator of 𝜃 213\u003c\/p\u003e \u003cp\u003e5.8 Summary 213\u003c\/p\u003e \u003cp\u003e5.8.1 Problems 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Multiple Linear Regression Models \u003c\/b\u003e\u003cb\u003e215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 215\u003c\/p\u003e \u003cp\u003e6.2 Multiple Linear Model and R-estimation 215\u003c\/p\u003e \u003cp\u003e6.3 Model Sparsity and Detection 218\u003c\/p\u003e \u003cp\u003e6.4 General Shrinkage R-estimator of 𝛽 221\u003c\/p\u003e \u003cp\u003e6.4.1 Preliminary Test R-estimator 222\u003c\/p\u003e \u003cp\u003e6.4.2 Stein–Saleh-type R-estimator 224\u003c\/p\u003e \u003cp\u003e6.4.3 Positive-rule Stein–Saleh-type R-estimator 225\u003c\/p\u003e \u003cp\u003e6.5 Subset Selectors 226\u003c\/p\u003e \u003cp\u003e6.5.1 Preliminary Test Subset Selector R-estimator 226\u003c\/p\u003e \u003cp\u003e6.5.2 Stein–Saleh-type R-estimator 228\u003c\/p\u003e \u003cp\u003e6.5.3 Positive-rule Stein–Saleh-type R-estimator (LASSO-type) 229\u003c\/p\u003e \u003cp\u003e6.5.4 Ridge-type Subset Selector 231\u003c\/p\u003e \u003cp\u003e6.5.5 Elastic Net-type R-estimator 231\u003c\/p\u003e \u003cp\u003e6.6 Adaptive LASSO 232\u003c\/p\u003e \u003cp\u003e6.6.1 Introduction 232\u003c\/p\u003e \u003cp\u003e6.6.2 Asymptotics for LASSO-type R-estimator 233\u003c\/p\u003e \u003cp\u003e6.6.3 Oracle Property of aLASSO 235\u003c\/p\u003e \u003cp\u003e6.7 Summary 238\u003c\/p\u003e \u003cp\u003e6.8 Problems 239\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Partially Linear Multiple Regression Model \u003c\/b\u003e\u003cb\u003e241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 241\u003c\/p\u003e \u003cp\u003e7.2 Rank Estimation in the PLM 242\u003c\/p\u003e \u003cp\u003e7.2.1 Penalty R-estimators 246\u003c\/p\u003e \u003cp\u003e7.2.2 Preliminary Test and Stein–Saleh-type R-estimator 248\u003c\/p\u003e \u003cp\u003e7.3 ADB and ADL2-risk 249\u003c\/p\u003e \u003cp\u003e7.4 ADL2-risk Comparisons 253\u003c\/p\u003e \u003cp\u003e7.5 Summary: L2-risk Efficiencies 260\u003c\/p\u003e \u003cp\u003e7.6 Problems 262\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Liu Regression Models \u003c\/b\u003e\u003cb\u003e263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 263\u003c\/p\u003e \u003cp\u003e8.2 Linear Unified (Liu) Estimator 263\u003c\/p\u003e \u003cp\u003e8.2.1 Liu-type R-estimator 266\u003c\/p\u003e \u003cp\u003e8.3 Shrinkage Liu-type R-estimators 268\u003c\/p\u003e \u003cp\u003e8.4 Asymptotic Distributional Risk 269\u003c\/p\u003e \u003cp\u003e8.5 Asymptotic Distributional Risk Comparisons 271\u003c\/p\u003e \u003cp\u003e8.5.1 Comparison of SSLRE and PTLRE 272\u003c\/p\u003e \u003cp\u003e8.5.2 Comparison of PRSLRE and PTLRE 274\u003c\/p\u003e \u003cp\u003e8.5.3 Comparison of PRLRE and SSLRE 276\u003c\/p\u003e \u003cp\u003e8.5.4 Comparison of Liu-Type Rank Estimators With Counterparts 277\u003c\/p\u003e \u003cp\u003e8.6 Estimation of d 279\u003c\/p\u003e \u003cp\u003e8.7 Diabetes Data Analysis 280\u003c\/p\u003e \u003cp\u003e8.7.1 Penalty Estimators 281\u003c\/p\u003e \u003cp\u003e8.7.2 Performance Analysis 284\u003c\/p\u003e \u003cp\u003e8.8 Summary 288\u003c\/p\u003e \u003cp\u003e8.9 Problems 288\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Autoregressive Models \u003c\/b\u003e\u003cb\u003e291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 291\u003c\/p\u003e \u003cp\u003e9.2 R-estimation of 𝜌 for the AR(𝑝)-Model 292\u003c\/p\u003e \u003cp\u003e9.3 LASSO, Ridge, Preliminary Test and Stein–Saleh-type R-estimators 294\u003c\/p\u003e \u003cp\u003e9.4 Asymptotic Distributional L2-risk 296\u003c\/p\u003e \u003cp\u003e9.5 Asymptotic Distributional L2-risk Analysis 299\u003c\/p\u003e \u003cp\u003e9.5.1 Comparison of Unrestricted vs. Restricted R-estimators 300\u003c\/p\u003e \u003cp\u003e9.5.2 Comparison of Unrestricted vs. Preliminary Test R-estimator 300\u003c\/p\u003e \u003cp\u003e9.5.3 Comparison of Unrestricted vs. Stein–Saleh-type R-estimators 300\u003c\/p\u003e \u003cp\u003e9.5.4 Comparison of the Preliminary Test vs. Stein–Saleh-type R-estimators 302\u003c\/p\u003e \u003cp\u003e9.6 Summary 303\u003c\/p\u003e \u003cp\u003e9.7 Problems 304\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 High-Dimensional Models \u003c\/b\u003e\u003cb\u003e307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 307\u003c\/p\u003e \u003cp\u003e10.2 Identifiability of 𝛽∗ and Projection 309\u003c\/p\u003e \u003cp\u003e10.3 Parsimonious Model Selection 309\u003c\/p\u003e \u003cp\u003e10.4 Some Notation and Separation 311\u003c\/p\u003e \u003cp\u003e10.4.1 Special Matrices 311\u003c\/p\u003e \u003cp\u003e10.4.2 Steps Towards Estimators 312\u003c\/p\u003e \u003cp\u003e10.4.3 Post-selection Ridge Estimation of 𝛽∗ 𝒮1 and 𝜷∗ 𝒮2 312\u003c\/p\u003e \u003cp\u003e10.4.4 Post-selection Ridge R-estimators for 𝛽∗ 𝒮1 and 𝜷∗ 𝒮2 313\u003c\/p\u003e \u003cp\u003e10.5 Post-selection Shrinkage R-estimators 315\u003c\/p\u003e \u003cp\u003e10.6 Asymptotic Properties of the Ridge R-estimators 316\u003c\/p\u003e \u003cp\u003e10.7 Asymptotic Distributional L2-Risk Properties 321\u003c\/p\u003e \u003cp\u003e10.8 Asymptotic Distributional Risk Efficiency 324\u003c\/p\u003e \u003cp\u003e10.9 Summary 326\u003c\/p\u003e \u003cp\u003e10.10 Problems 327\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Rank-based Logistic Regression \u003c\/b\u003e329\u003c\/p\u003e \u003cp\u003e11.1 Introduction 329\u003c\/p\u003e \u003cp\u003e11.2 Data Science and Machine Learning 329\u003c\/p\u003e \u003cp\u003e11.2.1 What is Robust Data Science? 329\u003c\/p\u003e \u003cp\u003e11.2.2 What is Robust Machine Learning? 332\u003c\/p\u003e \u003cp\u003e11.3 Logistic Regression 333\u003c\/p\u003e \u003cp\u003e11.3.1 Log-likelihood Setup 334\u003c\/p\u003e \u003cp\u003e11.3.2 Motivation for Rank-based Logistic Methods 338\u003c\/p\u003e \u003cp\u003e11.3.3 Nonlinear Dispersion Function 341\u003c\/p\u003e \u003cp\u003e11.4 Application to Machine Learning 342\u003c\/p\u003e \u003cp\u003e11.4.1 Example: Motor Trend Cars 344\u003c\/p\u003e \u003cp\u003e11.5 Penalized Logistic Regression 347\u003c\/p\u003e \u003cp\u003e11.5.1 Log-likelihood Expressions 347\u003c\/p\u003e \u003cp\u003e11.5.2 Rank-based Expressions 348\u003c\/p\u003e \u003cp\u003e11.5.3 Support Vector Machines 349\u003c\/p\u003e \u003cp\u003e11.5.4 Example: Circular Data 353\u003c\/p\u003e \u003cp\u003e11.6 Example: Titanic Data Set 359\u003c\/p\u003e \u003cp\u003e11.6.1 Exploratory Data Analysis 359\u003c\/p\u003e \u003cp\u003e11.6.2 RLR vs. LLR vs. SVM 365\u003c\/p\u003e \u003cp\u003e11.6.3 Shrinkage and Selection 367\u003c\/p\u003e \u003cp\u003e11.7 Summary 370\u003c\/p\u003e \u003cp\u003e11.8 Problems 371\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Rank-based Neural Networks \u003c\/b\u003e\u003cb\u003e377\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 377\u003c\/p\u003e \u003cp\u003e12.2 Set-up for Neural Networks 379\u003c\/p\u003e \u003cp\u003e12.3 Implementing Neural Networks 381\u003c\/p\u003e \u003cp\u003e12.3.1 Basic Computational Unit 382\u003c\/p\u003e \u003cp\u003e12.3.2 Activation Functions 382\u003c\/p\u003e \u003cp\u003e12.3.3 Four-layer Neural Network 384\u003c\/p\u003e \u003cp\u003e12.4 Gradient Descent with Momentum 386\u003c\/p\u003e \u003cp\u003e12.4.1 Gradient Descent 386\u003c\/p\u003e \u003cp\u003e12.4.2 Momentum 388\u003c\/p\u003e \u003cp\u003e12.5 Back Propagation Example 389\u003c\/p\u003e \u003cp\u003e12.5.1 Forward Propagation 390\u003c\/p\u003e \u003cp\u003e12.5.2 Back Propagation 392\u003c\/p\u003e \u003cp\u003e12.5.3 Dispersion Function Gradients 394\u003c\/p\u003e \u003cp\u003e12.5.4 RNN Algorithm 395\u003c\/p\u003e \u003cp\u003e12.6 Accuracy Metrics 396\u003c\/p\u003e \u003cp\u003e12.7 Example: Circular Data Set 400\u003c\/p\u003e \u003cp\u003e12.8 Image Recognition: Cats vs. Dogs 405\u003c\/p\u003e \u003cp\u003e12.8.1 Binary Image Classification 406\u003c\/p\u003e \u003cp\u003e12.8.2 Image Preparation 406\u003c\/p\u003e \u003cp\u003e12.8.3 Over-fitting and Under-fitting 409\u003c\/p\u003e \u003cp\u003e12.8.4 Comparison of LNN vs. RNN 410\u003c\/p\u003e \u003cp\u003e12.9 Image Recognition: MNIST Data Set 414\u003c\/p\u003e \u003cp\u003e12.10 Summary 421\u003c\/p\u003e \u003cp\u003e12.11 Problems 421\u003c\/p\u003e \u003cp\u003eBibliography 433\u003c\/p\u003e \u003cp\u003eAuthor Index 443\u003c\/p\u003e \u003cp\u003eSubject Index445\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407102320983,"sku":"9781119625391","price":97.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119625391.jpg?v=1730498185","url":"https:\/\/bookcurl.com\/products\/rankbased-methods-for-shrinkage-and-selection-9781119625391","provider":"Book Curl","version":"1.0","type":"link"}