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BIG DATA, ARTIFICIAL INTELLIGENCE AND DATA ANALYSIS SET Coordinated by Jacques Janssen Data analysis is a scientific field that continues to grow enormously, most notably over the last few decades, following rapid growth within the tech industry, as well as the wide applicability of computational techniques alongside new advances in analytic tools. Modeling enables data analysts to identify relationships, make predictions, and to understand, interpret and visualize the extracted information more strategically. This book includes the most recent advances on this topic, meeting increasing demand…mehr
BIG DATA, ARTIFICIAL INTELLIGENCE AND DATA ANALYSIS SET Coordinated by Jacques Janssen Data analysis is a scientific field that continues to grow enormously, most notably over the last few decades, following rapid growth within the tech industry, as well as the wide applicability of computational techniques alongside new advances in analytic tools. Modeling enables data analysts to identify relationships, make predictions, and to understand, interpret and visualize the extracted information more strategically. This book includes the most recent advances on this topic, meeting increasing demand from wide circles of the scientific community. Applied Modeling Techniques and Data Analysis 1 is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians, working on the front end of data analysis and modeling applications. The chapters cover a cross section of current concerns and research interests in the above scientific areas. The collected material is divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with appropriate applications.
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Yannis Dimotikalis is Assistant Professor within the Department of Management Science and Technology at the Hellenic Mediterranean University, Greece. Alex Karagrigoriou is Professor of Probability and Statistics, Deputy Director of Graduate Studies in Statistics and Actuarial-Financial Mathematics, and Director of the Laboratory of Statistics and Data Analysis within the Department of Statistics and Actuarial-Financial Mathematics at the University of the Aegean, Greece. Christina Parpoula is Assistant Professor of Applied Statistics and Research Methodology within the Department of Psychology at the Panteion University of Social and Political Sciences, Greece. Christos H. Skiadas is Former Vice-Rector at the Technical University of Crete, Greece, and founder of its Data Analysis and Forecasting Laboratory. He continues his research in ManLab, within the faculty�s Department of Production Engineering and Management.
Inhaltsangabe
Preface xi Yannis DIMOTIKALIS, Alex KARAGRIGORIOU, Christina PARPOULA and Christos H. SKIADAS
Part 1. Computational Data Analysis 1
Chapter 1. A Variant of Updating PageRank in Evolving Tree Graphs 3 Benard ABOLA, Pitos Seleka BIGANDA, Christopher ENGSTRÖM, John Magero MANGO, Godwin KAKUBA and Sergei SILVESTROV
1.1. Introduction 3
1.2. Notations and definitions 5
1.3. Updating the transition matrix 5
1.4. Updating the PageRank of a tree graph 10
1.4.1. Updating the PageRank of tree graph when a batch of edges changes 12
1.4.2. An example of updating the PageRank of a tree 15
1.5. Maintaining the levels of vertices in a changing tree graph 17
1.6. Conclusion 21
1.7. Acknowledgments 21
1.8. References 21
Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks 23 Benard ABOLA, Pitos Seleka BIGANDA, Sergei SILVESTROV, Dmitrii SILVESTROV, Christopher ENGSTRÖM, John Magero MANGO and Godwin KAKUBA
2.1. Introduction 23
2.2. Stationary distributions for Markov chains with damping component 26
2.2.1. Stationary distributions for Markov chains with damping component 26
2.2.2. The stationary distribution of the Markov chain X0,n 28
2.3. A perturbation analysis for stationary distributions of Markov chains with damping component 29
2.3.1. Continuity property for stationary probabilities 29
2.3.2. Rate of convergence for stationary distributions 29
2.3.3. Asymptotic expansions for stationary distributions 30
2.3.4. Results of numerical experiments 32
2.4. Coupling and ergodic theorems for perturbed Markov chains with damping component 39
2.4.1. Coupling for regularly perturbed Markov chains with damping component 39
2.4.2. Coupling for singularly perturbed Markov chains with damping component 41
2.4.3. Ergodic theorems for perturbed Markov chains with damping component in the triangular array mode 42
2.4.4. Numerical examples 43
2.5. Acknowledgments 51
2.6. References 51
Chapter 3. PageRank and Perturbed Markov Chains 57 Pitos Seleka BIGANDA, Benard ABOLA, Christopher ENGSTRÖM, Sergei SILVESTROV, Godwin KAKUBA and John Magero MANGO
3.1. Introduction 57
3.2. PageRank of the first-order perturbed Markov chain 59
3.3. PageRank of the second-order perturbed Markov chain 60
3.4. Rates of convergence of Page Ranks of first- and second-order perturbed Markovchains 70
3.5. Conclusion 72
3.6. Acknowledgments 72
3.7. References 72
Chapter 4. Doubly Robust Data-driven Distributionally Robust Optimization 75 Jose BLANCHET, Yang KANG, Fan ZHANG, Fei HE and Zhangyi HU
4.1. Introduction 75
4.2. DD-DRO, optimal transport and supervised machine learning 79
4.2.1. Optimal transport distances and discrepancies 80
4.3. Data-driven selection of optimal transport cost function 81
4.3.1. Data-driven cost functions via metric learning procedures 81
4.4. Robust optimization for metric learning 83
4.4.1. Robust optimization for relative metric learning 83
4.4.2. Robust optimization for absolute metric learning 86
4.5. Numerical experiments 88
4.6. Discussion and conclusion 89
4.7. References 89
Chapter 5. A Comparison of Graph Centrality Measures Based on Lazy Random Walks 91 Collins ANGUZU, Christopher ENGSTRÖM and Sergei SILVESTROV
Preface xi Yannis DIMOTIKALIS, Alex KARAGRIGORIOU, Christina PARPOULA and Christos H. SKIADAS
Part 1. Computational Data Analysis 1
Chapter 1. A Variant of Updating PageRank in Evolving Tree Graphs 3 Benard ABOLA, Pitos Seleka BIGANDA, Christopher ENGSTRÖM, John Magero MANGO, Godwin KAKUBA and Sergei SILVESTROV
1.1. Introduction 3
1.2. Notations and definitions 5
1.3. Updating the transition matrix 5
1.4. Updating the PageRank of a tree graph 10
1.4.1. Updating the PageRank of tree graph when a batch of edges changes 12
1.4.2. An example of updating the PageRank of a tree 15
1.5. Maintaining the levels of vertices in a changing tree graph 17
1.6. Conclusion 21
1.7. Acknowledgments 21
1.8. References 21
Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks 23 Benard ABOLA, Pitos Seleka BIGANDA, Sergei SILVESTROV, Dmitrii SILVESTROV, Christopher ENGSTRÖM, John Magero MANGO and Godwin KAKUBA
2.1. Introduction 23
2.2. Stationary distributions for Markov chains with damping component 26
2.2.1. Stationary distributions for Markov chains with damping component 26
2.2.2. The stationary distribution of the Markov chain X0,n 28
2.3. A perturbation analysis for stationary distributions of Markov chains with damping component 29
2.3.1. Continuity property for stationary probabilities 29
2.3.2. Rate of convergence for stationary distributions 29
2.3.3. Asymptotic expansions for stationary distributions 30
2.3.4. Results of numerical experiments 32
2.4. Coupling and ergodic theorems for perturbed Markov chains with damping component 39
2.4.1. Coupling for regularly perturbed Markov chains with damping component 39
2.4.2. Coupling for singularly perturbed Markov chains with damping component 41
2.4.3. Ergodic theorems for perturbed Markov chains with damping component in the triangular array mode 42
2.4.4. Numerical examples 43
2.5. Acknowledgments 51
2.6. References 51
Chapter 3. PageRank and Perturbed Markov Chains 57 Pitos Seleka BIGANDA, Benard ABOLA, Christopher ENGSTRÖM, Sergei SILVESTROV, Godwin KAKUBA and John Magero MANGO
3.1. Introduction 57
3.2. PageRank of the first-order perturbed Markov chain 59
3.3. PageRank of the second-order perturbed Markov chain 60
3.4. Rates of convergence of Page Ranks of first- and second-order perturbed Markovchains 70
3.5. Conclusion 72
3.6. Acknowledgments 72
3.7. References 72
Chapter 4. Doubly Robust Data-driven Distributionally Robust Optimization 75 Jose BLANCHET, Yang KANG, Fan ZHANG, Fei HE and Zhangyi HU
4.1. Introduction 75
4.2. DD-DRO, optimal transport and supervised machine learning 79
4.2.1. Optimal transport distances and discrepancies 80
4.3. Data-driven selection of optimal transport cost function 81
4.3.1. Data-driven cost functions via metric learning procedures 81
4.4. Robust optimization for metric learning 83
4.4.1. Robust optimization for relative metric learning 83
4.4.2. Robust optimization for absolute metric learning 86
4.5. Numerical experiments 88
4.6. Discussion and conclusion 89
4.7. References 89
Chapter 5. A Comparison of Graph Centrality Measures Based on Lazy Random Walks 91 Collins ANGUZU, Christopher ENGSTRÖM and Sergei SILVESTROV
5.1. Introduction 91
5.1.1. Notations and abbreviations 93
5.1.2. Linear systems and the Neumann series 94
5.2.
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