Hamiltonian Monte Carlo Methods in Machine Learning introduces methods for optimal tuning of HMC parameters, along with 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. The book offers a comprehensive introduction to Hamiltonian Monte Carlo methods and provides a cutting-edge exposition of the current pathologies of HMC-based methods in both tuning, scaling and 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.
Other sections provide numerous solutions to potential pitfalls, presenting advanced HMC methods with applications in renewable energy, finance and image classification for biomedical applications. Readers will get acquainted with both HMC sampling theory and algorithm implementation.
1. 1 : Introduction to Hamiltonian Monte Carlo - p. Page xxii 2. 2 : Sampling benchmarks and performance metrics - p. Page 29 3. 3 : Stochastic volatility Metropolis-Hastings - p. Page 40 4. 4 : Quantum-inspired magnetic Hamiltonian Monte Carlo - p. Page 52 5. 5 : Generalised magnetic and shadow Hamiltonian Monte Carlo - p. Page 62 6. 6 : Shadow Magnetic Hamiltonian Monte Carlo - p. Page 72 7. 7 : Adaptive Shadow Hamiltonian Monte Carlo - p. Page 82 8. 8 : Adaptive noncanonical Hamiltonian Monte Carlo - p. Page 90 9. 9 : Antithetic Hamiltonian Monte Carlo techniques - p. Page 100 10. 10 : Bayesian neural network inference in wind speed nowcasting - p. Page 108 11. 11 : A Bayesian analysis of the efficacy of Covid-19 lockdown measures - p. Page 122 12. 12 : Probabilistic inference of equity option prices under jump-diffusion processes - p. Page 138 13. 13 : Bayesian inference of local government audit outcomes - p. Page 147 14. 14 : Conclusions - p. Page 158 15. A : Separable shadow Hamiltonian - p. Page 162 16. B : ARD posterior variances - p. Page 165 17. C : ARD committee feature selection - p. Page 167 18. D : Summary of audit outcome literature survey - p. Page 171 19. References - p. Page 174 20. Index - p. Page 174
Hamiltonian Monte Carlo Methods in Machine Learning introduces methods for optimal tuning of HMC parameters, along with 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. The book offers a comprehensive introduction to Hamiltonian Monte Carlo methods and provides a cutting-edge exposition of the current pathologies of HMC-based methods in both tuning, scaling and 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.
Other sections provide numerous solutions to potential pitfalls, presenting advanced HMC methods with applications in renewable energy, finance and image classification for biomedical applications. Readers will get acquainted with both HMC sampling theory and algorithm implementation.
1. 1 : Introduction to Hamiltonian Monte Carlo - p. Page xxii 2. 2 : Sampling benchmarks and performance metrics - p. Page 29 3. 3 : Stochastic volatility Metropolis-Hastings - p. Page 40 4. 4 : Quantum-inspired magnetic Hamiltonian Monte Carlo - p. Page 52 5. 5 : Generalised magnetic and shadow Hamiltonian Monte Carlo - p. Page 62 6. 6 : Shadow Magnetic Hamiltonian Monte Carlo - p. Page 72 7. 7 : Adaptive Shadow Hamiltonian Monte Carlo - p. Page 82 8. 8 : Adaptive noncanonical Hamiltonian Monte Carlo - p. Page 90 9. 9 : Antithetic Hamiltonian Monte Carlo techniques - p. Page 100 10. 10 : Bayesian neural network inference in wind speed nowcasting - p. Page 108 11. 11 : A Bayesian analysis of the efficacy of Covid-19 lockdown measures - p. Page 122 12. 12 : Probabilistic inference of equity option prices under jump-diffusion processes - p. Page 138 13. 13 : Bayesian inference of local government audit outcomes - p. Page 147 14. 14 : Conclusions - p. Page 158 15. A : Separable shadow Hamiltonian - p. Page 162 16. B : ARD posterior variances - p. Page 165 17. C : ARD committee feature selection - p. Page 167 18. D : Summary of audit outcome literature survey - p. Page 171 19. References - p. Page 174 20. Index - p. Page 174
