Big data in omics and imaging: association analysis
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| Format: | Buch |
| Sprache: | English |
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Boca Raton ; London ; New York
CRC Press
[2018]
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| Schriftenreihe: | Chapman & Hall/CRC mathematical and computational biology
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis und Index: Seite 645-668 |
| Beschreibung: | xxxi, 668 Seiten Diagramme |
| ISBN: | 9781498725781 |
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| 245 | 1 | 0 | |a Big data in omics and imaging |b association analysis |c Momiao Xiong |
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| 490 | 0 | |a Chapman & Hall/CRC mathematical and computational biology | |
| 500 | |a Literaturverzeichnis und Index: Seite 645-668 | ||
| 650 | 4 | |a Biometry |x Data processing | |
| 650 | 4 | |a Imaging systems in biology |x Statistical methods | |
| 650 | 4 | |a Big data |x Statistical methods | |
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Datensatz im Suchindex
| _version_ | 1804178164852719616 |
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| adam_text | Contents
Preface, xxv
Author, xxxi
Chapter 1 ■ Mathematical Foundation_________________________________________l_
1.1 SPARSITY-INDUCING NORMS, DUAL NORMS, AND FENCHEL
CONJUGATE 1
1.1.1 “Entrywise” Norms 4
1.1.LI L21Norm 5
1AA.2 LpqNorm 5
1.1.2 Frobenius Norm 5
1A.2A lfl2 Norm 5
1.1.3 Overlapping Groups 6
1.1.4 Dual Norm 8
1.1.4.1 The Norm Dual to the Group Norm 9
1.1.5 Fenchel Conjugate 10
1.1.6 Fenchel Duality 13
1.2 SUBDIFFERENTIAL 16
1.2.1 Definition of Subgradient 17
1.2.2 Subgradients of Differentiable Functions 18
1.2.3 Calculus of Subgradients 18
1.23.1 Nonnegative Scaling 19
1.23.2 Addition 19
1.233 Affine Transformation of Variables 19
1.23.4 Pointwise Maximum 19
1.23.5 Pointwise Supremum 21
1.23.6 Expectation 21
1.23.7 Chain Rule 22
ix
x ■ Contents
1.23.8 Subdifferential of the Norm 22
1.23.9 Optimality Conditions: Unconstrained 23
1.23.10 Application to Sparse Regularized Convex Optimization
Problems 24
1.3 PROXIMAL METHODS 26
1.3.1 Intro ducti on 26
1.3.2 Basics of Proximate Methods 27
13.2.1 Definition of Proximal Operator 27
1.3.3 Properties of the Proximal Operator 28
133.1 Separable Sum 28
133.2 Moreau-Yosida Regularization 33
1333 Gradient Algorithms for the Calculation of the Proximal
Operator 36
L3.4 Proximal Algorithms 36
13.4.1 Proximal Point Algorithm 37
Î.3A.2 Proximal Gradient Method 37
13.43 Accelerated Proximal Gradient Method 38
13.4.4 Alternating Direction Method of Multipliers 39
13.4.5 Linearized ADMM 41
1.3.5 Computing the Proximal Operator 42
13.5.1 Generic Function 42
13.5.2 Norms 50
1.4 MATRIX CALCULUS 55
1.4.1 Derivative of a Function with Respect to a Vector 55
1.4.2 Derivative of a Function with Respect to a Matrix 56
1.4.3 Derivative of a Matrix with Respect to a Scalar 57
1.4.4 Derivative of a Matrix with Respect to a Matrix or a Vector 58
1.4.5 Derivative of a Vector Function of a Vector 59
1.4.6 Chain Rules 59
1.4.6.1 Vector Function of Vectors 59
1.4.6.2 Scalar Function of Matrices 60
1.4.7 Widely Used Formulae 60
1.4.7.1 Determinants 60
1.4.7.2 Polynomial Functions 61
1.4.73 Trace 61
Contents ■ XI
1.5 FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS (FPCA) 63
1.5.1 Principal Component Analysis (PCA) 64
1.5.1.1 Least Square Formulation ofPCA 64
1.5.1.2 Variance-Maximization Formulation ofPCA 65
1.5.2 Basic Mathematical Tools for Functional Principal Component
Analysis 68
1.5.2.1 Calculus of Variation 68
1.5.2.2 Stochastic Calculus 69
1.5.3 Unsmoothed Functional Principal Component Analysis 71
1.5.4 Smoothed Principal Component Analysis 73
1.5.5 Computations for the Principal Component Function and the
Principal Component Score 75
1.6 CANONICAL CORRELATION ANALYSIS 77
1.6.1 Mathematical Formulation of Canonical Correlation Analysis 77
1.6.2 Correlation Maximization Techniques for Canonical Correlation
Analysis 78
1.6.3 Single Value Decomposition for Canonical Correlation Analysis 82
1.6.4 Test Statistics 83
1.6.5 Functional Canonical Correlation Analysis 87
APPENDIX 1A 90
EXERCISES 92
Chapter 2 ■ Linkage Disequilibrium__________________________________________95
2.1 CONCEPTS OF LINKAGE DISEQUILIBRIUM 95
2.2 MEASURES OFTWO-LOCUS LINKAGE DISEQUILIBRIUM 96
2.2.1 Linkage Disequilibrium Coefficient D 96
2.2.2 Normalized Measure of Linkage Disequilibrium D 97
2.2.3 Correlation Coefficient r 97
2.2.4 Composite Measure of Linkage Disequilibrium 101
2.2.5 Relationship between the Measure of LD and Physical Distance 102
2.3 HAPLOTYPE RECONSTRUCTION 103
2.3.1 Clarks Algorithm 104
2.3.2 EM algorithm 104
2.3.3 Bayesian and Coalescence-Based Methods 104
2.4 MULTILOCUS MEASURES OF LINKAGE DISEQUILIBRIUM 1 05
2.4.1 Mutual Information Measure of LD 105
xii ■ Contents
2.4.2 Multi-Information and Multilocus Measure of LD 107
2.4.3 Joint Mutual Information and a Measure of LD between a Marker
and a Haplotype Block or between Two Haplotype Blocks 109
2.4.4 Interaction Information 112
2.4.5 Conditional Interaction Information 114
2.4.6 Normalized Multi-Information 115
2.4.7 Distribution of Estimated Mutual Information, Multi-Information
and Interaction Information 115
2.5 CANONICAL CORRELATION ANALYSIS MEASURE FOR LD
BETWEEN TWO GENOMIC REGIONS 11 9
2.5.1 Association Measure between Two Genomic Regions Based on CCA 119
2.5.2 Relationship between Canonical Correlation and Joint Information 122
SOFTWARE PACKAGE 123
BIBLIOGRAPHICAL NOTES 123
APPENDIX 2A 124
APPENDIX 2B 125
APPENDIX 2C 126
EXERCISES 128
Chapter 3 . Association Studies for Qualitative Traits_________________1 31
3.1 POPULATION-BASED ASSOCIATION ANALYSIS FOR
COMMON VARIANTS 131
3.1.1 Introduction 131
3.1.2 The Hardy-Weinberg Equilibrium 133
3.1.3 Genetic Models 136
3.1.4 Odds Ratio 139
3.1.5 Single Marker Association Analysis 143
3.1.5.1 Contingency Tables 143
3.1.5.2 Fishers Exact Test 146
3.1.5.3 The Traditional x2 Test Statistic 147
3.1.6 Multimarker Association Analysis 150
3.1.6.1 Generalized T2 Test Statistic 151
3.1.6.2 The Relationship between the Generalized T2 Test and
Fishers Discriminant Analysis 152
3.2 POPULATION-BASED MULTIVARIATE ASSOCIATION ANALYSIS
FOR NEXT-GENERATION SEQUENCING 1 54
3.2.1 Multivariate Group Tests 155
Contents ■ xiii
3.2.1.1 Collapsing Method 155
3.2.1.2 Combined Multivariate and Collapsing Method 156
3.2.1.3 Weighted Sum Method 157
3.2.2 Score Tests and Logistic Regression 158
3.2.2.1 Score Function 158
3.2.2.2 Score Tests 160
3.2.3 Application of Score Tests for Association of Rare Variants 161
3.2.3.1 Weighted Function Method 161
3.2.3.2 Sum Test and Adaptive Association Test 164
3.2.3.3 The Sum Test 165
3.2.4 Variance-Component Score Statistics and Logistic Mixed Effects
Models 167
3.2.4.1 Logistic Mixed Effects Models for Association Analysis 167
3.2.4.2 Sequencing Kernel Association Test 177
3.3 POPULATION-BASED FUNCTIONAL ASSOCIATION ANALYSIS FOR
NEXT-GENERATION SEQUENCING 1 78
3.3.1 Intro duction 179
3.3.2 Functional Principal Component Analysis for Association Test 180
3.3.2.1 Model and Principal Component Functions 180
3.3.2.2 Computations for the Principal Component Function and
the Principal Component Score 182
3.3.2.3 Test Statistic 184
3.3.3 Smoothed Functional Principal Component Analysis for
Association Test 186
3.3.3.1 A General Framework for the Smoothed Functional
Principal Component Analysis 187
3.3.3.2 Computations for the Smoothed Principal Component
Function 188
3.3.3.3 Test Statistic 190
3.3.3.4 Power Comparisons 190
3.3.3.5 Application to Real Data Examples 193
SOFTWARE PACKAGE 196
APPENDIX 3A: FISHER INFORMATION MATRIX FOR y 1 96
APPENDIX 3B: VARIANCE FUNCTION v(p) 198
APPENDIX 3C: DERIVATION OF SCORE FUNCTION FOR UT 1 99
APPENDIX 3D: FISHER INFORMATION MATRIX OF PQL 200
APPENDIX 3E: SCORING ALGORITHM 202
xiv ■ Contents
APPENDIX 3F: EQUIVALENCE BETWEEN ITERATIVELY SOLVING
LINEAR MIXED MODEL AND ITERATIVELY SOLVING THE
NORMAL EQUATION 203
APPENDIX 3G: EQUATION REDUCTION 204
EXERCISES 207
Chapter 4 ■ Association Studies for Quantitative Traits____________________211
4.1 FIXED EFFECT MODEL FOR A SINGLE TRAIT 211
4.1.1 Introduction 211
4.1.2 Genetic Effects 211
4.1.2.1 Variation Partition 211
4.1.2.2 Genetic Additive and Dominance Effects 213
4.1.2.3 Genetic Variance 215
4.1.3 Linear Regression for a Quantitative Trait 216
4.1.4 Multiple Linear Regression for a Quantitative Trait 220
4.2 GENE-BASED QUANTITATIVE TRAIT ANALYSIS 223
4.2.1 Functional Linear Model for a Quantitative Trait 223
4.2.1.1 Model 223
4.2.1.2 Parameter Estimation 224
4.2.1.3 Test Statistics 229
4.2.2 Canonical Correlation Analysis for Gene-Based Quantitative
Trait Analysis 231
4.2.2.1 Multivariate Canonical Correlation Analysis 231
4.2.2.2 Functional Canonical Correlation Analysis 233
4.3 KERNEL APPROACH TO GENE-BASED QUANTITATIVE TRAIT
ANALYSIS 233
4.3.1 Kernel and RKHS 233
4.3.1.1 Kernel and Nonlinear Feature Mapping 233
4.3.1.2 The Reproducing Kernel Hilbert Space 237
4.3.2 Covariance Operator and Dependence Measure 244
4.3.2.1 Hilbert-Schmidt Operator and Norm 244
4.3.2.2 Tensor Product Space and Rank-One Operator 246
4.3.2.3 Cross-Covariance Operator 250
4.3.2.4 Dependence Measure and Covariance Operator 254
4.3.2.5 Dependence Measure and Hilbert-Schmidt Norm of
Covariance Operator 255
4.3.2.6 Kernel-Based Association Tests 257
Contents ■ xv
4.4 SIMULATIONS AND REAL DATA ANALYSIS 260
4.4.1 Power Evaluation 260
4.4.2 Application to Real Data Examples 261
SOFTWARE PACKAGE 264
APPENDIX 4A: CONVERGENCE OF THE LEAST SQUARE ESTIMATOR
OF THE REGRESSION COEFFICIENTS 267
APPENDIX 4B: CONVERGENCE OF REGRESSION COEFFICIENTS IN
THE FUNCTIONAL LINEAR MODEL 272
APPENDIX 4C: NONCENTRALITY PARAMETER OF THE CCA TEST 275
APPENDIX 4D: SOLUTION TO THE CONSTRAINED NONLINEAR
COVARIANCE OPTIMIZATION PROBLEM AND DEPENDENCE
MEASURE 275
EXERCISES 278
Chapter 5 ■ Multiple Phenotype Association Studies____ 281
5.1 PLEIOTROPIC ADDITIVE AND DOMINANCE EFFECTS 281
5.2 MULTIVARIATE MARGINAL REGRESSION 283
5.2.1 Models 283
5.2.2 Estimation of Genetic Effects 284
5.2.2.1 Least Square Estimation 284
5.2.2.2 Maximum Likelihood Estimator 289
5.2.3 Test Statistics 294
5.2.3.1 Classical Null Hypothesis 294
5.23.2 The Multivariate General Linear Hypothesis 295
5.23.3 Estimation of the Parameter Matrix under Constraints 296
5.23.4 Multivariate Analysis of Variance (MANOVA) 297
5.23.5 Other Multivariate Test Statistics 298
5.3 LINEAR MODELS FOR MULTIPLE PHENOTYPES AND MULTIPLE
MARKERS 304
5.3.1 Multivariate Multiple Linear Regression Models 304
5.3.2 Multivariate Functional Linear Models for Gene֊Based Genetic
Analysis of Multiple Phenotypes 306
5.3.2.1 Parameter Estimation 307
53.2.2 Null Hypothesis and Test Statistics 308
5.3.23 Other Multivariate Test Statistics 309
53.2.4 Wilks* Lambda 310
53.2.5 F Approximation to the Distribution of Three Test Statistics 310
xvi ■ Contents
5.4 CANONICAL CORRELATION ANALYSIS FOR GENE-BASED
GENETIC PLEIOTROPIC ANALYSIS 311
5.4.1 Multivariate Canonical Correlation Analysis (CCA) 311
5.4.2 Kernel CCA 312
5.4.3 Functional CCA 314
5.4.4 Quadratically Regularized Functional CCA 317
5.5 DEPENDENCE MEASURE AND ASSOCIATION TESTS OF
MULTIPLE TRAITS 319
5.6 PRINCIPAL COMPONENT FOR PHENOTYPE DIMENSION
REDUCTION 321
5.6.1 Principal Component Analysis 321
5.6.2 Kernel Principal Component Analysis 322
5.6.3 Quadratically Regularized PCA or Kernel PCA 325
5.7 OTHER STATISTICS FOR PLEIOTROPIC GENETIC ANALYSIS 326
5.7.1 Sum of Squared Score Test 326
5.7.2 Unified Score-Based Association Test (USAT) 328
5.7.3 Combining Marginal Tests 329
5.7.4 FPCA-Based Kernel Measure Test of Independence 329
5.8 CONNECTION BETWEEN STATISTICS 330
5.9 SIMULATIONS AND REAL DATA ANALYSIS 335
5.9.1 Type 1 Error Rate and Power Evaluation 335
5.9.2 Application to Real Data Example 336
SOFTWARE PACKAGE 337
APPENDIX 5A OPTIMIZATION FORMULATION OF KERNEL CCA 337
APPENDIX 5B DERIVATION OF THE REGRESSION COEFFICIENT
MATRIX IN THE FUNCTIONAL LINEAR MODE, SUM OF
SQUARES DUETO REGRESSION, AND RFCCA MATRIX 339
EXERCISES 340
Chapter 6 ■ Family-Based Association Analysis________________________________343
6.1 GENETIC SIMILARITY AND KINSHIP COEFFICIENTS 344
6.1.1 Kinship Coefficients 344
6.1.2 Identity Coefficients 347
6.1.3 Relation between Identity Coefficients and Kinship Coefficients 348
6.1.4 Estimation of Genetic Relations from the Data 350
6ЛАЛ A General Framework for Identity by Descent 350
6.1.4.2 Kinship Matrix or Genetic Relationship Matrix in the
Homogeneous Population 352
Contents ■ xvii
6.1 A3 Kinship Matrix or Genetic Relationship Matrix in the
General Population 353
6.1 AA Coefficient of Fraternity 357
6.2 GENETIC COVARIANCE BETWEEN RELATIVES 358
6.2.1 Assumptions and Genetic Models 358
6.2.2 Analysis for Genetic Covariance between Relatives 359
6.3 MIXED LINEAR MODEL FOR A SINGLE TRAIT 362
6.3.1 Genetic Random Effect 362
63.1.1 Single Random Variable 362
63.1.2 Multiple Genetic Random Effects 365
6.3.2 Mixed Linear Model for Quantitative Trait Association Analysis 366
63.2.1 Mixed Linear Model 366
63.2.2 Estimating Fixed and Random Effects 367
6.3.3 Estimating Variance Components 370
63.3.1 ML Estimation of Variance Components 370
633.2 Restricted Maximum Likelihood Estimation 373
6333 Numerical Solutions to the ML/REML Equations 374
6.33.4 Fisher Information Matrix for the ML Estimators 377
6.33.5 Expectation/Maximization (EM) Algorithm for
ML Estimation 378
633.6 Expectation/Maximization (EM) Algorithm for
REML Estimation 382
6.33.7 Average Information Algorithms 383
6.3.4 Hypothesis Test in Mixed Linear Models 383
6.3.5 Mixed Linear Models for Quantitative Trait Analysis with
Sequencing Data 387
63.5.1 Sequence Kernel Association Test (SKAT) 387
6.4 MIXED FUNCTIONAL LINEAR MODELS FOR SEQUENCE-BASED
QUANTITATIVE TRAIT ANALYSIS 390
6.4.1 Mixed Functional Linear Models (Type 1) 390
6.4.2 Mixed Functional Linear Models (Type 2: Functional Variance
Component Models) 393
6.5 MULTIVARIATE MIXED LINEAR MODEL FOR MULTIPLE TRAITS 395
6.5.1 Multivariate Mixed Linear Model 395
6.5.2 Maximum Likelihood Estimate of Variance Components 398
6.5.3 REML Estimate of Variance Components 399
xviii ■ Contents
6.6 HERITABILITY 400
6.6.1 Heritability Estimation for a Single Trait 400
6.6.1.1 Definition of Narrow-Sense Heritability 400
6.6.1.2 Mixed Linear Model for Heritability Estimation 401
6.6.2 Heritability Estimation for Multiple Traits 404
6.6.2.1 Definition of Heritability Matrix for Multiple Traits 404
6.6.2.2 Connection between Heritability Matrix and Multivariate
Mixed Linear Models 405
6.6.23 Another Interpretation of Heritability 406
6.6.2.4 Maximizing Heritability 408
6.7 FAMILY-BASED ASSOCIATION ANALYSIS FOR QUALITATIVE TRAIT 41 0
6.7.1 The Generalized T2 Test with Families and Additional Population
Structures 410
6.7.2 Collapsing Method 414
6.7.3 CMC with Families 416
6.7.4 The Functional Principal Component Analysis and Smooth
Functional Principal Component Analysis with Families 418
SOFTWARE PACKAGE 420
APPENDIX 6A: GENETIC RELATIONSHIP MATRIX 420
APPENDIX 6B: DERIVATION OF EQUATION 6.30 423
APPENDIX 6C: DERIVATION OF EQUATION 6.33 426
APPENDIX 6D: ML ESTIMATION OF VARIANCE COMPONENTS 428
APPENDIX 6E: COVARIANCE MATRIX OF THE ML ESTIMATORS 429
APPENDIX 6F: SELECTION OF THE MATRIX K IN THE REML 431
APPENDIX 6G: ALTERNATIVE FORM OF LOG-LIKELIHOOD FUNCTION
FORTHE REML 433
APPENDIX 6H: ML ESTIMATE OF VARIANCE COMPONENTS IN THE
MULTIVARIATE MIXED LINEAR MODELS 436
APPENDIX 6I: COVARIANCE MATRIX FOR FAMILY-BASED T2 STATISTIC 438
APPENDIX 6J: FAMILY-BASED FUNCTIONAL PRINCIPAL COMPONENT
ANALYSIS 440
EXERCISE 443
Chapter 7 - Interaction Analysis 447
7.1 MEASURES OF GENE-GENE AND GENE-ENVIRONMENT
INTERACTIONS FOR A QUALITATIVE TRAIT 448
7.1.1 Binary Measure of Gene-Gene and Gene-Environment Interactions 448
Contents ■ XIX
7.1.1.1 The Binary Measure of Gene-Gene Interaction for the
Cohort Study Design 448
7.1.1.2 The Binary Measure of Gene-Gene Interaction for the
Case-Control Study Design 452
7.1.2 Disequilibrium Measure of Gene-Gene and Gene-Environment
Interactions 453
7.1.3 Information Measure of Gene-Gene and Gene-Environment
Interactions 455
7.1.4 Measure of Interaction between a Gene and a Continuous
Environment 458
7.1.4.1 Multiplicative Measure of Interaction between a Gene
and a Continuous Environment 458
7.1.4.2 Disequilibrium Measure of Interaction between a Gene
and a Continuous Environment 459
7.1 A3 Mutual Information Measure of Interaction between
a Gene and a Continuous Environment 460
7.2 STATISTICS FORTESTING GENE-GENE AND
GENE-ENVIRONMENT INTERACTIONS FOR A QUALITATIVE TRAIT
WITH COMMON VARIANTS 462
7.2.1 Relative Risk and Odds-Ratio-Based Statistics for Testing
Interaction between a Gene and a Discrete Environment 462
7.2.2 Disequilibrium-Based Statistics for Testing Gene-Gene Interaction 464
7.2.2.1 Standard Disequilibrium Measure-Based Statistics 464
7.2.2.2 Composite Measure of Linkage Disequilibrium for Testing
Interaction between Unlinked Loci 466
7.2.3 Information՝Based Statistics for Testing Gene-Gene Interaction 469
7.2.4 Haplotype Odds Ratio and Tests for Gene-Gene Interaction 472
7.2A.1 Genotype-Based Odds Ratio Multiplicative Interaction
Measure 473
7.2A.2 Allele-Based Odds Ratio Multiplicative Interaction Measure 474
7.2.4.3 Haplotype-Based Odds Ratio Multiplicative Interaction Measure 476
7.2.4.4 Haplotype-Based Odds Ratio Multiplicative Interaction
Measure-Based Test Statistics 479
7.2.5 Multiplicative Measure-Based Statistics for Testing Interaction
between a Gene and a Continuous Environment 480
7.2.6 Information Measure-Based Statistics for Testing Interaction
between a Gene and a Continuous Environment 481
7.2.7 Real Example 481
XX ■ Contents
7.3 STATISTICS FOR TESTING GENE-GENE AND
GENE-ENVIRONMENT INTERACTION FOR A QUALITATIVE TRAIT
WITH NEXT-GENERATION SEQUENCING DATA 486
7.3.1 Multiple Logistic Regression Model for Gene-Gene Interaction
Analysis 487
7.3.2 Functional Logistic Regression Model for Gene-Gene Interaction
Analysis 488
7.3.3 Statistics for Testing Interaction between Two Genomic Regions 492
7.4 STATISTICS FOR TESTING GENE-GENE AND GENE-ENVIRONMENT
INTERACTION FOR QUANTITATIVE TRAITS 492
7.4.1 Genetic Models for Epistasis Effects of Quantitative Traits 493
7.4.2 Regression Model for Interaction Analysis with Quantitative
Traits 498
7.4.3 Functional Regression Model for Interaction Analysis with a
Quantitative Trait 499
7A. 3,1 Model 499
7A3.2 Parameter Estimation 500
7A3.3 Test Statistics 503
7A3 A Simulations and Applications to Real Example 504
7.4.4 Functional Regression Model for Interaction Analysis with Multiple
Quantitative Traits 507
7AA.1 Model 507
7. A4,2 Parameter Estimation 509
7A A3 Test Statistics 511
7AAA Simulations and Real Example Applications 512
7.5 MULTIVARIATE AND FUNCTIONAL CANONICAL CORRELATION
AS A UNIFIED FRAMEWORK FORTESTING FOR
GENE-GENE AND GENE-ENVIRONMENT INTERACTION FOR
BOTH QUALITATIVE AND QUANTITATIVE TRAITS 516
7.5.1 Data Structure of CCA for Interaction Analysis 517
7.5.1,1 Single Quantitative Trait 517
73,1,2 Multiple Quantitative Trait 518
73A3 A Qualitative Trait 518
7.5.2 CCA and Functional CCA 519
7.5.3 Kernel CCA 521
SOFTWARE PACKAGE 522
APPENDIX 7A: VARIANCE OF LOGARITHM OF ODDS RATIO 522
Contents ■ xxi
APPENDIX 7B: HAPLOTYPE ODDS-RATIO INTERACTION MEASURE 524
APPENDIX 7C: PARAMETER ESTIMATION FOR MULTIVARIATE
FUNCTIONAL REGRESSION MODEL 525
EXERCISE 527
Chapter 8 ■ Machine Learning, Low-Rank Models, and Their
Application to Disease Risk Prediction and Precision
_______________Medicine____________________________________________________531
8J LOGISTIC REGRESSION 532
8.1.1 Two-Class Logistic Regression 532
8.1.2 Multiclass Logistic Regression 534
8.1.3 Parameter Estimation 536
8.1.4 Test Statistics 542
8.1.5 Network-Penalized Two-Class Logistic Regression 543
8.1.5.1 Model 543
8.1.5.2 Proximal Method for Parameter Estimation 547
8.1.6 Network-Penalized Multiclass Logistic Regression 548
8.1.6.1 Model 548
8.1.6.2 Proximal Method for Parameter Estimation in Multiclass
Logistic Regression 550
8.2 FISHER S LINEAR DISCRIMINANT ANALYSIS 552
8.2.1 Fishers Linear Discriminant Analysis for Two Classes 552
8.2.2 Multiclass Fishers Linear Discriminant Analysis 556
8.2.3 Connections between Linear Discriminant Analysis, Optimal
Scoring, and Canonical Correlation Analysis (CCA) 558
8.2.3.1 Matrix Formulation of Linear Discriminant Analysis 558
8.2.3.2 Optimal Scoring and Its Connection with Linear
Discriminant Analysis 561
8.2.3.3 Connection between LDA and CCA 561
8.3 SUPPORT VECTOR MACHINE 562
8.3.1 Introduction 563
8.3.2 Linear Support Vector Machines 563
8.3.2. i Separable Case 563
8.3.2.2 Nonseparable Case 566
8.3.2.3 The Karush-Kuhn-Tucker (KKT) Conditions 568
8.3.2A Sequential Minimal Optimization (SMO) Algorithm 570
xxïi ■ Contents
8.3.3 Nonlinear SVM 575
8.3.4 Penalized SVMs 575
8.4 LOW-RANK APPROXIMATION 580
8.4.1 Quadratically Regularized PCA 580
8.4.1 A Formulation 580
8 A. 1.2 Interpretation 582
8.4.2 Generalized Regularization 583
8A.2A Formulation 583
8.4.2.2 Sparse PCA 583
8.5 GENERALIZED CANONICAL CORRELATION ANALYSIS (CCA) 585
8.5.1 Quadratically Regularized Canonical Correlation Analysis 585
8.5.2 Sparse Canonical Correlation Analysis 586
8.5.2A Least Square Formulation of CCA 586
8.5.2.2 CCA for Multiclass Classification 595
8.5.3 Sparse Canonical Correlation Analysis via a Penalized Matrix
Decomposition 596
8.53.1 Sparse Singular Value Decomposition via Penalized Matrix
Decomposition 596
8.53.2 Sparse CCA via Direct Regularization Formulation 599
8.6 INVERSE REGRESSION (IR) AND SUFFICIENT DIMENSION
REDUCTION 601
8.6.1 Sufficient Dimension Reduction (SDR) and Sliced Inverse
Regression (SIR) 601
8.6.2 Sparse SDR 605
8.6.2.1 Coordinate Hypothesis 605
8.6.2.2 Reformulation of SIR for SDR as an Optimization Problem 606
8.6.23 Solve Sparse SDR by Alternative Direction Method of
Multipliers 607
8.6.2A Application to Real Data Examples 610
SOFTWARE PACKAGE 611
APPENDIX 8A: PROXIMAL METHOD FOR PARAMETER ESTIMATION IN
NETWORK-PENALIZED TWO-CLASS LOGISTIC REGRESSION 61 5
APPENDIX 8B: EQUIVALENCE OF OPTIMAL SCORING AND LDA 621
APPENDIX 8C: A DISTANCE FROM A POINT TO THE HYPERPLANE 622
APPENDIX 8D: SOLVING A QUADRATICALLY REGULARIZED PCA
PROBLEM 624
Contents ■ xxiii
APPENDIX 8E: THE ECKART-YOUNG THEOREM 626
APPENDIX 8F POINCARE SEPARATION THEOREM 630
APPENDIX 8G: REGRESSION FOR CCA 632
APPENDIX 8H: PARTITION OF GLOBAL SDR FOR A WHOLE GENOME
INTO A NUMBER OF SMALL REGIONS 634
APPENDIX 81: OPTIMAL SCORING AND ALTERNATIVE DIRECTION
METHODS OF MULTIPLIERS (ADMM) ALGORITHMS 637
EXERCISES 641
REFERENCES, 645
INDEX, 655
|
| any_adam_object | 1 |
| author | Xiong, Momiao |
| author_GND | (DE-588)1152287826 |
| author_facet | Xiong, Momiao |
| author_role | aut |
| author_sort | Xiong, Momiao |
| author_variant | m x mx |
| building | Verbundindex |
| bvnumber | BV044697590 |
| callnumber-first | R - Medicine |
| callnumber-label | R853 |
| callnumber-raw | R853.S7 |
| callnumber-search | R853.S7 |
| callnumber-sort | R 3853 S7 |
| callnumber-subject | R - General Medicine |
| classification_rvk | WC 7700 |
| ctrlnum | (OCoLC)1021406441 (DE-599)BVBBV044697590 |
| dewey-full | 610.1/5195 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 610 - Medicine and health |
| dewey-raw | 610.1/5195 |
| dewey-search | 610.1/5195 |
| dewey-sort | 3610.1 45195 |
| dewey-tens | 610 - Medicine and health |
| discipline | Biologie Medizin |
| format | Book |
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| id | DE-604.BV044697590 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:59:38Z |
| institution | BVB |
| isbn | 9781498725781 |
| language | English |
| lccn | 017029924 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030094397 |
| oclc_num | 1021406441 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | xxxi, 668 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall/CRC mathematical and computational biology |
| spelling | Xiong, Momiao Verfasser (DE-588)1152287826 aut Big data in omics and imaging association analysis Momiao Xiong Boca Raton ; London ; New York CRC Press [2018] xxxi, 668 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC mathematical and computational biology Literaturverzeichnis und Index: Seite 645-668 Biometry Data processing Imaging systems in biology Statistical methods Big data Statistical methods Biometrie (DE-588)4124925-2 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Bioinformatik (DE-588)4611085-9 gnd rswk-swf Genomik (DE-588)4776397-8 gnd rswk-swf Genomik (DE-588)4776397-8 s Datenanalyse (DE-588)4123037-1 s Bioinformatik (DE-588)4611085-9 s Biometrie (DE-588)4124925-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-498-72580-4 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030094397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xiong, Momiao Big data in omics and imaging association analysis Biometry Data processing Imaging systems in biology Statistical methods Big data Statistical methods Biometrie (DE-588)4124925-2 gnd Datenanalyse (DE-588)4123037-1 gnd Bioinformatik (DE-588)4611085-9 gnd Genomik (DE-588)4776397-8 gnd |
| subject_GND | (DE-588)4124925-2 (DE-588)4123037-1 (DE-588)4611085-9 (DE-588)4776397-8 |
| title | Big data in omics and imaging association analysis |
| title_auth | Big data in omics and imaging association analysis |
| title_exact_search | Big data in omics and imaging association analysis |
| title_full | Big data in omics and imaging association analysis Momiao Xiong |
| title_fullStr | Big data in omics and imaging association analysis Momiao Xiong |
| title_full_unstemmed | Big data in omics and imaging association analysis Momiao Xiong |
| title_short | Big data in omics and imaging |
| title_sort | big data in omics and imaging association analysis |
| title_sub | association analysis |
| topic | Biometry Data processing Imaging systems in biology Statistical methods Big data Statistical methods Biometrie (DE-588)4124925-2 gnd Datenanalyse (DE-588)4123037-1 gnd Bioinformatik (DE-588)4611085-9 gnd Genomik (DE-588)4776397-8 gnd |
| topic_facet | Biometry Data processing Imaging systems in biology Statistical methods Big data Statistical methods Biometrie Datenanalyse Bioinformatik Genomik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030094397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xiongmomiao bigdatainomicsandimagingassociationanalysis |