Applied Modeling Techniques and Data Analysis 1 : Computational Data Analysis Methods and Tools

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Title:

Author:

Dimotikalis, Yannis.

ISBN:

9781119821588

9781119821564

9781119821571

Publication Information:

London : ISTE, Ltd. ; Hoboken : Wiley, 2021.

Physical Description:

1 online resource (297 pages)

Series:

Big Data, Artificial Intelligence and Data Analysis Set ; v. 7

Innovation, entrepreneurship and management series. Big data, artificial intelligence and data analysis set ; v. 7.

General Note:

5.2.5. PageRank centrality.

Contents:

Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface -- PART 1: Computational Data Analysis -- 1 A Variant of Updating PageRank in Evolving Tree Graphs -- 1.1. Introduction -- 1.2. Notations and definitions -- 1.3. Updating the transition matrix -- 1.4. Updating the PageRank of a tree graph -- 1.4.1. Updating the PageRank of tree graph when a batch of edges changes -- 1.4.2. An example of updating the PageRank of a tree -- 1.5. Maintaining the levels of vertices in a changing tree graph -- 1.6. Conclusion -- 1.7. Acknowledgments -- 1.8. References

2 Nonlinearly Perturbed Markov Chains and Information Networks -- 2.1. Introduction -- 2.2. Stationary distributions for Markov chains with damping component -- 2.2.1. Stationary distributions for Markov chains with damping component -- 2.2.2. The stationary distribution of the Markov chain X0,n -- 2.3. A perturbation analysis for stationary distributions of Markov chains with damping component -- 2.3.1. Continuity property for stationary probabilities -- 2.3.2. Rate of convergence for stationary distributions -- 2.3.3. Asymptotic expansions for stationary distributions

2.3.4. Results of numerical experiments -- 2.4. Coupling and ergodic theorems for perturbed Markov chains with damping component -- 2.4.1. Coupling for regularly perturbed Markov chains with damping component -- 2.4.2. Coupling for singularly perturbed Markov chains with damping component -- 2.4.3. Ergodic theorems for perturbed Markov chains with damping component in the triangular array mode -- 2.4.4. Numerical examples -- 2.5. Acknowledgments -- 2.6. References -- 3 PageRank and Perturbed Markov Chains -- 3.1. Introduction -- 3.2. PageRank of the first-order perturbed Markov chain

3.3. PageRank of the second-order perturbed Markov chain -- 3.4. Rates of convergence of PageRanks of first- and second-order perturbed Markov chains -- 3.5. Conclusion -- 3.6. Acknowledgments -- 3.7. References -- 4 Doubly Robust Data-driven Distributionally Robust Optimization -- 4.1. Introduction -- 4.2. DD-DRO, optimal transport and supervised machine learning -- 4.2.1. Optimal transport distances and discrepancies -- 4.3. Data-driven selection of optimal transport cost function -- 4.3.1. Data-driven cost functions via metric learning procedures -- 4.4. Robust optimization for metric learning

Abstract:

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.

Local Note:

John Wiley and Sons

Subject Term:

Quantitative research.

Mathematical statistics.

Quantitative research -- Data processing.

Recherche quantitative -- Informatique.

Recherche quantitative.

Management.

BUSINESS & ECONOMICS.

Entrepreneurship.

Mathematical statistics