Markov Chain Monte Carlo (MCMC) methods are considered one of the most influential algorithms for scientific practice in the 21st century. MCMC methods have facilitated the growth in the adoption of principled Bayesian Inference across numerous disciplines. In particular, Hamiltonian Monte Carlo (HMC) methods have revolutionized probabilistic inference in the fields of Machine Learning and Statistics.
Hamiltonian Monte Carlo Methods in Machine Learning provides a targeted reference on Hamiltonian Monte Carlo (HMC) methods for practitioners and researchers across numerous application domains. The book offers a comprehensive introduction to Hamiltonian Monte Carlo methods. The book further provides a cutting-edge exposition of the current pathologies of HMC-based methods in both tuning and scaling to sampling complex real-world posteriors. These are mainly in the scaling of inference (e.g., Deep Neural Networks), tuning of performance-sensitive sampling parameters and high sample autocorrelation. The book then traverses numerous solutions to these pitfalls. The authors present the advanced HMC methods with applications in renewable energy, finance and image classification for biomedical applications. Readers of the book will be acquainted with both HMC sampling theory and algorithm implementation. A Python-based code repository of all the algorithms considered is supplied to assist readers with the practical implementation of the algorithms in their work.
Hamiltonian Monte Carlo Methods in Machine Learning introduces methods for optimal tuning of HMC parameters, as well as an introduction of Shadow and Non-canonical HMC methods with improvements and speedup. Lastly, the authors address the critical issues of variance reduction for parameter estimates of numerous HMC based samplers.
- Provides in-depth analysis to conduct optimal tuning of Hamiltonian Monte Carlo (HMC) parameters
- Provides readers with an introduction and improvements on Shadow HMC methods as well as non-canonical HMC methods
- Demonstrates how to perform variance reduction for numerous HMC-based samplers
- All source code from the applications and algorithms is available online
1. Introduction to Hamiltonian Monte Carlo
2. Sampling Benchmarks and Performance Metrics
3. Stochastic Volatility Metropolis-Hastings
4. Quantum-Inspired Magnetic Hamiltonian Monte Carlo
5. Generalised Magnetic and Shadow Hamiltonian Monte Carlo
6. Shadow Hamiltonian Monte Carlo Methods
7. Adaptive Shadow Hamiltonian Monte Carlo Methods
8. Adaptive Noncanonical Hamiltonian Monte Carlo
9. Antithetic Hamiltonian Monte Carlo Techniques
10. Application: Bayesian Neural Network Inference in Wind Speed Forecasting
11. Application: A Bayesian Analysis of Lockdown Alert Level Framework for Combating COVID-19
12. Application: Probabilistic Inference of Equity Option Prices Under Jump-Di
13. Application: Bayesian Inference of Local Government Audit Outcomes
14. Open Problems in Sampling
Appendix A: Separable Shadow Hamiltonian B: Automatic Relevance Determination C: Audit Outcome Literature Survey
Dr. Tshilidzi Marwala is the Rector of the United Nations (UN) University and the UN Under-Secretary-General from 1 March 2023. He was previously the Vice-Chancellor and Principal of the University of Johannesburg, Deputy Vice-Chancellor for Research and Executive Dean of the Faculty of Engineering at the University of Johannesburg. He was Associate Professor, Full Professor, the Carl and Emily Fuchs Chair of Systems and Control Engineering at the University of the Witwatersrand. He holds a Bachelor of Science in Mechanical Engineering (magna cum laude) from Case Western Reserve University, a Master of Mechanical Engineering from the University of Pretoria, PhD in Artificial Intelligence from the University of Cambridge and a Post-Doc at Imperial College (London). He is a registered professional engineer, a Fellow of TWAS (The World Academy of Sciences), the Academy of Science of South Africa, the African Academy of Sciences and the South African Academy of Engineering. He is a Senior Member of the IEEE and a distinguished member of the ACM. His research interests are multi-disciplinary and they include the theory and application of artificial intelligence to engineering, computer science, finance, social science and medicine. He has supervised 28 Doctoral students published 15 books in artificial intelligence (one translated into Chinese), over 300 papers in journals, proceedings, book chapters and magazines and holds five patents. He is an associate editor of the International Journal of Systems Science (Taylor and Francis Publishers). He has been a visiting scholar at Harvard University, University of California at Berkeley, Wolfson College of the University of Cambridge, Nanjing Tech University and Silesian University of Technology in Poland. His opinions have appeared in the New Scientist, The Economist, Time Magazine, BBC, CNN and the Oxford Union. Dr. Marwala is the author of Rational Machines and Artificial Intelligence from Elsevier Academic Press. Dr. Rendani Mbuvha is a lecturer in Statistics and Actuarial Science at the University of Witwatersrand, Johannesburg, South Africa. He is a qualified Actuary and a holder of the Chartered Enterprise Risk Actuary designation. He holds a BSc with Honors in Actuarial Science and Statistics from the University of Cape Town, an MSc in Machine Learning from KTH, Royal Institute of Technology in Sweden, and a Ph.D. in Probabilistic Parameter Inference at the University of Johannesburg. He was a recipient of the Google Ph.D. fellowship for his research at the University of Johannesburg. He has previously served in various analytics and actuarial roles in large financial services and AI consulting organizations in both South Africa and Sweden. Wilson Tsakane Mongwe is a Researcher at the University of Johannesburg, South Africa, specializing in Bayesian machine learning and Markov Chain Monte Carlo methods. He received his BSc in Computing from the University of South Africa, his BBusSci in Actuarial Science from the University of Cape Town, and his MSc in Mathematical Finance from the University of Cape Town. He was the recipient of the Google PhD fellowship in machine learning, which is supporting his PhD research.
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