Hamiltonian Monte Carlo Methods in Machine Learning provides a comprehensive introduction to Hamiltonian Monte Carlo methods, covering tuning, scaling, and sampling complex real-world posteriors. It offers solutions to potential pitfalls and presents advanced methods with applications in renewable energy, finance, and image classification.

Format: Paperback / softback
Length: 220 pages
Publication date: 16 February 2023
Publisher: Elsevier Science Publishing Co Inc

Hamiltonian Monte Carlo (HMC) Methods in Machine Learning presents a comprehensive exploration of optimal tuning techniques for HMC parameters, along with the introduction of Shadow and Non-canonical HMC methods, which offer improvements and speedup. Furthermore, the authors address the critical challenges of variance reduction for parameter estimates in numerous HMC-based samplers. This book serves as an invaluable introduction to Hamiltonian Monte Carlo methods, providing a cutting-edge exposition of the current pathologies and solutions in tuning, scaling, and sampling complex real-world posteriors. These pathologies primarily arise in scaling inference for Deep Neural Networks, tuning performance-sensitive sampling parameters, and addressing high sample autocorrelation. Additionally, other sections offer numerous solutions to potential pitfalls, presenting advanced HMC methods with applications in renewable energy, finance, and image classification for biomedical applications. Readers will gain a deep understanding of both HMC sampling theory and algorithm implementation.

Hamiltonian Monte Carlo Methods in Machine Learning

Hamiltonian Monte Carlo (HMC) Methods in Machine Learning offers a comprehensive exploration of optimal tuning techniques for HMC parameters, along with the introduction of Shadow and Non-canonical HMC methods, which offer improvements and speedup. Furthermore, the authors address the critical challenges of variance reduction for parameter estimates in numerous HMC-based samplers. This book serves as an invaluable introduction to Hamiltonian Monte Carlo methods, providing a cutting-edge exposition of the current pathologies and solutions in tuning, scaling, and sampling complex real-world posteriors. These pathologies primarily arise in scaling inference for Deep Neural Networks, tuning performance-sensitive sampling parameters, and addressing high sample autocorrelation. Additionally, other sections offer numerous solutions to potential pitfalls, presenting advanced HMC methods with applications in renewable energy, finance, and image classification for biomedical applications. Readers will gain a deep understanding of both HMC sampling theory and algorithm implementation.

Introduction to Hamiltonian Monte Carlo Methods

Hamiltonian Monte Carlo (HMC) methods are a powerful tool in machine learning for approximating complex posterior distributions. They involve sampling from a Hamiltonian, which is a combination of the kinetic energy and potential energy of a system, and are particularly well-suited for Bayesian inference. HMC methods offer several advantages over traditional Markov chain Monte Carlo (MCMC) methods, including the ability to handle high-dimensional and complex systems, the ability to efficiently explore the posterior distribution, and the ability to handle non-Gaussian distributions.

Optimal Tuning of HMC Parameters

One of the key challenges in using HMC methods is optimizing the parameters that control the algorithm. The choice of parameters can have a significant impact on the convergence and accuracy of the posterior estimates. In this section, the authors introduce methods for optimal tuning of HMC parameters, including the use of adaptive tuning algorithms, importance sampling, and gradient descent methods.

Shadow and Non-canonical HMC Methods

In addition to traditional HMC methods, the authors introduce Shadow and Non-canonical HMC methods, which offer improvements and speedup. Shadow HMC methods involve adding a shadow variable to the Hamiltonian, which can help improve the mixing of the Markov chain and reduce the variance of the posterior estimates. Non-canonical HMC methods involve using different Hamiltonians for different parts of the posterior distribution, which can help improve the accuracy of the estimates.

Variance Reduction for Parameter Estimates

One of the critical issues in using HMC methods is reducing the variance of the parameter estimates. This is particularly important in cases where the posterior distribution is complex and the number of samples is limited. In this section, the authors address the critical issues of variance reduction for parameter estimates of numerous HMC-based samplers, including the use of importance sampling, adaptive tuning, and variance reduction techniques such as the Hamiltonian Ensemble Method.

Applications in Machine Learning

The authors demonstrate the application of HMC methods in a range of machine learning tasks, including renewable energy, finance, and image classification for biomedical applications. They showcase the benefits of HMC methods in tuning complex models, exploring complex posteriors, and reducing the variance of parameter estimates.

Conclusion

In conclusion, Hamiltonian Monte Carlo Methods in Machine Learning provides a comprehensive introduction to Hamiltonian Monte Carlo methods and their applications in machine learning. The book offers a cutting-edge exposition of the current pathologies and solutions in tuning, scaling, and sampling complex real-world posteriors, and provides numerous solutions to potential pitfalls. Readers will gain a deep understanding of both HMC sampling theory and algorithm implementation, and will be able to apply these methods to a range of machine learning tasks.

Weight: 484g
Dimension: 234 x 191 x 14 (mm)
ISBN-13: 9780443190353