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

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 o...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Dimotikalis, Yannis
Otros Autores: Karagrigoriou, Alex, Parpoula, Christina, Skiadas, Christos H.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2021.
Temas:
Quantitative research > Data processing.
Recherche quantitative > Informatique.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

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