Probabilistic Data-Driven Modeling
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Product details:
- Publisher Cambridge University Press
- Date of Publication 31 March 2025
- ISBN 9781009221856
- Binding Hardback
- No. of pages420 pages
- Language English 700
Categories
Short description:
A probabilistic data-driven modeling toolbox to help students and researchers characterize, classify and model real complex systems.
MoreLong description:
This book introduces relevant and established data-driven modeling tools currently in use or in development, which will help readers master the art and science of constructing models from data and dive into different application areas. It presents statistical tools useful to individuate regularities, discover patterns and laws in complex datasets, and demonstrates how to apply them to devise models that help to understand these systems and predict their behaviors. By focusing on the estimation of multivariate probabilities, the book shows that the entire domain, from linear regressions to deep learning neural networks, can be formulated in probabilistic terms. This book provides the right balance between accessibility and mathematical rigor for applied data science or operations research students, graduate students in CSE, and machine learning and uncertainty quantification researchers who use statistics in their field. Background in probability theory and undergraduate mathematics is assumed.
'I really enjoyed reading this book. It offers an expansive tour to the realm of probabilistic data-driven systems modeling, as well as an easily accessible reference for those, such as students, researchers and practitioners, aiming to understand the nature and behaviors of complex systems, as often encountered in the real world.' Jiming Liu, Hong Kong Baptist University
Table of Contents:
List of symbols; Preface; Part I. Preliminary: 1. Introduction; 2. Fundamentals of Probability; 3. Fundamentals of machine learning; 4. Fundamentals of networks; Part II. Foundations of Probabilistic Modeling: 5. Univariate probabilities; 6. Multivariate probabilities; 7. Entropies; 8. Dependence; 9. Stochastic processes and scaling laws; 10. Causation; 11. Networks as representations of complex systems; 12. Probabilistic modeling with network representations; Part III. Model Construction from Data: 13. Nonparametric estimation of univariate probabilities from data; 14. Parametric estimation of univariate probabilities from data; 15. Estimation of multivariate probabilities from data; 16. Time series and probabilistic modeling; 17. Construction of network representations from data; 18. Assessing the goodness of models; Part IV. Closing: 19. Conclusions; Part V. Appendices: Appendix A. Essentials on probability theory; Appendix B. Finding roots of non-linear equations; Appendix C. Some optimization problems and methods; Appendix D. Principal components analysis; Appendix E. Random forest; Appendix F. Expectation maximization (EM); Appendix G. Bad modeling; References; Index.
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