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Cham : Springer International Publishing AG, 2022

1 online resource (707 pages)

ISBN 9783030890100 (electronic bk.)

ISBN 9783030890094

Print version: Montesinos Lopez, Osval Antonio Multivariate Statistical Machine Learning Methods for Genomic Prediction Cham : Springer International Publishing AG,c2022 ISBN 9783030890094

Intro -- Foreword -- Preface -- Acknowledgments -- Contents -- Chapter 1: General Elements of Genomic Selection and Statistical Learning -- 1.1 Data as a Powerful Weapon -- 1.2 Genomic Selection -- 1.2.1 Concepts of Genomic Selection -- 1.2.2 Why Is Statistical Machine Learning a Key Element of Genomic Selection? -- 1.3 Modeling Basics -- 1.3.1 What Is a Statistical Machine Learning Model? -- 1.3.2 The Two Cultures of Model Building: Prediction Versus Inference -- 1.3.3 Types of Statistical Machine Learning Models and Model Effects -- 1.3.3.1 Types of Statistical Machine Learning Models -- 1.3.3.2 Model Effects -- 1.4 Matrix Algebra Review -- 1.5 Statistical Data Types -- 1.5.1 Data Types -- 1.5.2 Multivariate Data Types -- 1.6 Types of Learning -- 1.6.1 Definition and Examples of Supervised Learning -- 1.6.2 Definitions and Examples of Unsupervised Learning -- 1.6.3 Definition and Examples of Semi-Supervised Learning -- References -- Chapter 2: Preprocessing Tools for Data Preparation -- 2.1 Fixed or Random Effects -- 2.2 BLUEs and BLUPs -- 2.3 Marker Depuration -- 2.4 Methods to Compute the Genomic Relationship Matrix -- 2.5 Genomic Breeding Values and Their Estimation -- 2.6 Normalization Methods -- 2.7 General Suggestions for Removing or Adding Inputs -- 2.8 Principal Component Analysis as a Compression Method -- Appendix 1 -- Appendix 2 -- References -- Chapter 3: Elements for Building Supervised Statistical Machine Learning Models -- 3.1 Definition of a Linear Multiple Regression Model -- 3.2 Fitting a Linear Multiple Regression Model via the Ordinary Least Square (OLS) Method -- 3.3 Fitting the Linear Multiple Regression Model via the Maximum Likelihood (ML) Method -- 3.4 Fitting the Linear Multiple Regression Model via the Gradient Descent (GD) Method -- 3.5 Advantages and Disadvantages of Standard Linear Regression Models (OLS and MLR).

10.8 The King Algorithm for Training Artificial Neural Networks: Backpropagation -- 10.8.1 Backpropagation Algorithm: Online Version -- 10.8.1.1 Feedforward Part -- 10.8.1.2 Backpropagation Part -- 10.8.2 Illustrative Example 10.1: A Hand Computation -- 10.8.3 Illustrative Example 10.2-By Hand Computation -- References -- Chapter 11: Artificial Neural Networks and Deep Learning for Genomic Prediction of Continuous Outcomes -- 11.1 Hyperparameters to Be Tuned in ANN and DL -- 11.1.1 Network Topology -- 11.1.2 Activation Functions -- 11.1.3 Loss Function -- 11.1.4 Number of Hidden Layers -- 11.1.5 Number of Neurons in Each Layer -- 11.1.6 Regularization Type -- 11.1.7 Learning Rate -- 11.1.8 Number of Epochs and Number of Batches -- 11.1.9 Normalization Scheme for Input Data -- 11.2 Popular DL Frameworks -- 11.3 Optimizers -- 11.4 Illustrative Examples -- Appendix 1 -- Appendix 2 -- Appendix 3 -- Appendix 4 -- Appendix 5 -- References -- Chapter 12: Artificial Neural Networks and Deep Learning for Genomic Prediction of Binary, Ordinal, and Mixed Outcomes -- 12.1 Training DNN with Binary Outcomes -- 12.2 Training DNN with Categorical (Ordinal) Outcomes -- 12.3 Training DNN with Count Outcomes -- 12.4 Training DNN with Multivariate Outcomes -- 12.4.1 DNN with Multivariate Continuous Outcomes -- 12.4.2 DNN with Multivariate Binary Outcomes -- 12.4.3 DNN with Multivariate Ordinal Outcomes -- 12.4.4 DNN with Multivariate Count Outcomes -- 12.4.5 DNN with Multivariate Mixed Outcomes -- Appendix 1 -- Appendix 2 -- Appendix 3 -- Appendix 4 -- Appendix 5 -- References -- Chapter 13: Convolutional Neural Networks -- 13.1 The Importance of Convolutional Neural Networks -- 13.2 Tensors -- 13.3 Convolution -- 13.4 Pooling -- 13.5 Convolutional Operation for 1D Tensor for Sequence Data -- 13.6 Motivation of CNN.

3.6 Regularized Linear Multiple Regression Model -- 3.6.1 Ridge Regression -- 3.6.2 Lasso Regression -- 3.7 Logistic Regression -- 3.7.1 Logistic Ridge Regression -- 3.7.2 Lasso Logistic Regression -- Appendix 1: R Code for Ridge Regression Used in Example 2 -- References -- Chapter 4: Overfitting, Model Tuning, and Evaluation of Prediction Performance -- 4.1 The Problem of Overfitting and Underfitting -- 4.2 The Trade-Off Between Prediction Accuracy and Model Interpretability -- 4.3 Cross-validation -- 4.3.1 The Single Hold-Out Set Approach -- 4.3.2 The k-Fold Cross-validation -- 4.3.3 The Leave-One-Out Cross-validation -- 4.3.4 The Leave-m-Out Cross-validation -- 4.3.5 Random Cross-validation -- 4.3.6 The Leave-One-Group-Out Cross-validation -- 4.3.7 Bootstrap Cross-validation -- 4.3.8 Incomplete Block Cross-validation -- 4.3.9 Random Cross-validation with Blocks -- 4.3.10 Other Options and General Comments on Cross-validation -- 4.4 Model Tuning -- 4.4.1 Why Is Model Tuning Important? -- 4.4.2 Methods for Hyperparameter Tuning (Grid Search, Random Search, etc.) -- 4.5 Metrics for the Evaluation of Prediction Performance -- 4.5.1 Quantitative Measures of Prediction Performance -- 4.5.2 Binary and Ordinal Measures of Prediction Performance -- 4.5.3 Count Measures of Prediction Performance -- References -- Chapter 5: Linear Mixed Models -- 5.1 General of Linear Mixed Models -- 5.2 Estimation of the Linear Mixed Model -- 5.2.1 Maximum Likelihood Estimation -- 5.2.1.1 EM Algorithm -- E Step -- M Step -- 5.2.1.2 REML -- 5.2.1.3 BLUPs -- 5.3 Linear Mixed Models in Genomic Prediction -- 5.4 Illustrative Examples of the Univariate LMM -- 5.5 Multi-trait Genomic Linear Mixed-Effects Models -- 5.6 Final Comments -- Appendix 1 -- Appendix 2 -- Appendix 3 -- Appendix 4 -- Appendix 5 -- Appendix 6 -- Appendix 7 -- References.

Chapter 6: Bayesian Genomic Linear Regression -- 6.1 Bayes Theorem and Bayesian Linear Regression -- 6.2 Bayesian Genome-Based Ridge Regression -- 6.3 Bayesian GBLUP Genomic Model -- 6.4 Genomic-Enabled Prediction BayesA Model -- 6.5 Genomic-Enabled Prediction BayesB and BayesC Models -- 6.6 Genomic-Enabled Prediction Bayesian Lasso Model -- 6.7 Extended Predictor in Bayesian Genomic Regression Models -- 6.8 Bayesian Genomic Multi-trait Linear Regression Model -- 6.8.1 Genomic Multi-trait Linear Model -- 6.9 Bayesian Genomic Multi-trait and Multi-environment Model (BMTME) -- Appendix 1 -- Appendix 2: Setting Hyperparameters for the Prior Distributions of the BRR Model -- Appendix 3: R Code Example 1 -- Appendix 4: R Code Example 2 -- Appendix 5 -- R Code Example 3 -- R Code for Example 4 -- References -- Chapter 7: Bayesian and Classical Prediction Models for Categorical and Count Data -- 7.1 Introduction -- 7.2 Bayesian Ordinal Regression Model -- 7.2.1 Illustrative Examples -- 7.3 Ordinal Logistic Regression -- 7.4 Penalized Multinomial Logistic Regression -- 7.4.1 Illustrative Examples for Multinomial Penalized Logistic Regression -- 7.5 Penalized Poisson Regression -- 7.6 Final Comments -- Appendix 1 -- Appendix 2 -- Appendix 3 -- Appendix 4 (Example 4) -- Appendix 5 -- Appendix 6 -- References -- Chapter 8: Reproducing Kernel Hilbert Spaces Regression and Classification Methods -- 8.1 The Reproducing Kernel Hilbert Spaces (RKHS) -- 8.2 Generalized Kernel Model -- 8.2.1 Parameter Estimation Under the Frequentist Paradigm -- 8.2.2 Kernels -- 8.2.3 Kernel Trick -- 8.2.4 Popular Kernel Functions -- 8.2.5 A Two Separate Step Process for Building Kernel Machines -- 8.3 Kernel Methods for Gaussian Response Variables -- 8.4 Kernel Methods for Binary Response Variables -- 8.5 Kernel Methods for Categorical Response Variables.

13.7 Why Are CNNs Preferred over Feedforward Deep Neural Networks for Processing Images?.

8.6 The Linear Mixed Model with Kernels -- 8.7 Hyperparameter Tuning for Building the Kernels -- 8.8 Bayesian Kernel Methods -- 8.8.1 Extended Predictor Under the Bayesian Kernel BLUP -- 8.8.2 Extended Predictor Under the Bayesian Kernel BLUP with a Binary Response Variable -- 8.8.3 Extended Predictor Under the Bayesian Kernel BLUP with a Categorical Response Variable -- 8.9 Multi-trait Bayesian Kernel -- 8.10 Kernel Compression Methods -- 8.10.1 Extended Predictor Under the Approximate Kernel Method -- 8.11 Final Comments -- Appendix 1 -- Appendix 2 -- Appendix 3 -- Appendix 4 -- Appendix 5 -- Appendix 6 -- Appendix 7 -- Appendix 8 -- Appendix 9 -- Appendix 10 -- Appendix 11 -- References -- Chapter 9: Support Vector Machines and Support Vector Regression -- 9.1 Introduction to Support Vector Machine -- 9.2 Hyperplane -- 9.3 Maximum Margin Classifier -- 9.3.1 Derivation of the Maximum Margin Classifier -- 9.3.2 Wolfe Dual -- 9.4 Derivation of the Support Vector Classifier -- 9.5 Support Vector Machine -- 9.5.1 One-Versus-One Classification -- 9.5.2 One-Versus-All Classification -- 9.6 Support Vector Regression -- Appendix 1 -- Appendix 2 -- Appendix 3 -- References -- Chapter 10: Fundamentals of Artificial Neural Networks and Deep Learning -- 10.1 The Inspiration for the Neural Network Model -- 10.2 The Building Blocks of Artificial Neural Networks -- 10.3 Activation Functions -- 10.3.1 Linear -- 10.3.2 Rectifier Linear Unit (ReLU) -- 10.3.3 Leaky ReLU -- 10.3.4 Sigmoid -- 10.3.5 Softmax -- 10.3.6 Tanh -- 10.4 The Universal Approximation Theorem -- 10.5 Artificial Neural Network Topologies -- 10.6 Successful Applications of ANN and DL -- 10.7 Loss Functions -- 10.7.1 Loss Functions for Continuous Outcomes -- 10.7.2 Loss Functions for Binary and Ordinal Outcomes -- 10.7.3 Regularized Loss Functions -- 10.7.4 Early Stopping Method of Training.

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