Evolutionary Statistical Procedures (eBook)

Roberto Baragona received the ‘laurea’ in Mathematics from Sapienza University of Rome, Italy, in 1972. He is currently a professor of Data Analysis at Sapienza University. His main research interests are in time series analysis and multivariate statistics with a special emphasis on meta-heuristic methods. Referee for several international journals and associate editor of Statistical Methods and Applications. Francesco Battaglia is a professor of Statistical Forecasting at Sapienza University of Rome. He has taught at the University of Cagliari and at the Italian Public Administration School, and visited several European universities. He is a former head of Sapienza University’s Department of Statistics, and head of the Time Series Analysis Group of the Italian Statistical Society. Editor-in-chief of Statistical Methods and Applications.Irene Poli is Professor of Statistics at Ca' Foscari University of Venice, and Director of the European Centre for Living Technology (ECLT, www.ecltech.org). Her current research involves developing statistical procedures for high dimensional data and deriving evolutionary experimental designs and multiobjective optimizations mainly for biochemical problems. She is a Fellow of the New York Academy of Science, of the Royal Statistical Society, the Bernoulli Society, and a member of the Italian Statistical Society.

Preface 4
Contents 7
1 Introduction 10
1.1 Bio-inspired Optimization Methods 10
1.2 Topics Organization 13
2 Evolutionary Computation 14
2.1 Introduction 14
2.1.1 Evolutionary Computation Between Artificial Intelligence and Natural Evolution 14
2.1.2 The Contribution of Genetics 17
2.2 Evolutionary Computation Methods 19
2.2.1 Essential Properties 19
2.2.2 Evolutionary Programming 23
2.2.3 Evolution Strategies 25
2.2.4 Genetic Algorithms 27
2.2.5 Estimation of Distribution Algorithms 29
2.2.6 Differential Evolution 32
2.2.7 Evolutionary Behavior Algorithms 34
2.2.8 A Simple Example of Evolutionary Computation 36
2.3 Properties of Genetic Algorithms 45
2.3.1 Genetic Algorithms as a Paradigm of Evolutionary Computation 45
2.3.2 Evolution of Genetic Algorithms 50
2.3.3 Convergence of Genetic Algorithms 53
2.3.4 Issues in the Implementation of Genetic Algorithms 60
2.3.5 Genetic Algorithms and Random Samplingfrom a Probability Distribution 65
3 Evolving Regression Models 71
3.1 Introduction 71
3.2 Identification 72
3.2.1 Linear Regression 72
3.2.2 Generalized Linear Models 75
3.2.3 Principal Component Analysis 76
3.3 Parameter Estimation 77
3.3.1 Regression Models 77
3.3.2 The Logistic Regression Model 78
3.4 Independent Component Analysis 82
3.4.1 ICA algorithms 84
3.4.2 Simple GAs for ICA 85
3.4.3 GAs for Nonlinear ICA 91
4 Time Series Linear and Nonlinear Models 93
4.1 Models of Time Series 94
4.2 Autoregressive Moving Average Models 96
4.2.1 Identification of ARMA Models by Genetic Algorithms 99
4.2.2 More General Models 103
4.3 Nonlinear Models 105
4.3.1 Threshold AR and Double Threshold GARCH Models 105
4.3.2 Exponential Models 108
4.3.3 Piecewise Linear Models 111
4.3.4 Bilinear Models 122
4.3.5 Real Data Applications 124
4.3.6 Artificial Neural Networks 126
5 Design of Experiments 133
5.1 Introduction 133
5.2 Experiments and Design of Experiments 134
5.2.1 Randomization, Replication and Blocking 136
5.2.2 Factorial Designs and Response Surface Methodology 137
5.3 The Evolutionary Design of Experiments 140
5.3.1 High-Dimensionality Search Space 140
5.3.2 The Evolutionary Approach to Design Experiments 141
5.3.3 The Genetic Algorithm Design (GA-Design) 143
5.4 The Evolutionary Model-Based Experimental Design: The Statistical Models in the Evolution 152
5.4.1 The Evolutionary Neural Network Design (ENN-Design) 152
5.4.2 The Model Based Genetic Algorithm Design (MGA-Design) 155
5.4.3 The Evolutionary Bayesian Network Design(EBN-Design) 160
6 Outliers 166
6.1 Outliers in Independent Data 166
6.1.1 Exploratory Data Analysis for Multiple Outliers Detection 167
6.1.2 Genetic Algorithms for Detecting Outliers in an i.i.d.Data Set 169
6.2 Outliers in Time Series 174
6.2.1 Univariate ARIMA Models 176
6.2.2 Multivariate Time Series Outlier Models 188
6.3 Genetic Algorithms for Multiple Outlier Detection 191
6.3.1 Detecting Multiple Outliers in Univariate Time Series 193
6.3.2 Genetic Algorithms for Detecting Multiple Outliers in Multivariate Time Series 194
6.3.3 An Example of Application to Real Data 198
7 Cluster Analysis 205
7.1 The Partitioning Problem 205
7.1.1 Classification 206
7.1.2 Algorithms for Clustering Data 210
7.1.3 Indexes of Cluster Validity 218
7.2 Genetic Clustering Algorithms 225
7.2.1 A Genetic Divisive Algorithm 225
7.2.2 Quick Partition Genetic Algorithms 227
7.2.3 Centroid Evolution Algorithms 233
7.2.4 The Grouping Genetic Algorithm 236
7.2.5 Genetic Clustering of Large Data Sets 239
7.3 Fuzzy Partition 240
7.3.1 The Fuzzy c-Means Algorithm 240
7.3.2 Genetic Fuzzy Partition Algorithms 242
7.4 Multivariate Mixture Models Estimation by Evolutionary Computing 245
7.4.1 Genetic Multivariate Mixture Model Estimates 246
7.4.2 Hybrid Genetic Algorithms and the EM Algorithm 250
7.4.3 Multivariate Mixture Model Estimates with Unknown Number of Mixtures 252
7.5 Genetic Algorithms in Classification and Regression Trees Models 254
7.6 Clusters of Time Series and Directional Data 254
7.6.1 GAs-Based Methods for Clustering Time Series Data 255
7.6.2 GAs-Based Methods for Clustering Directional Data 260
7.7 Multiobjective Genetic Clustering 264
7.7.1 Pareto Optimality 264
7.7.2 Multiobjective Genetic Clustering Outline 265
References 267
Index 279