2014
NIPS
NeurIPS 2014
Positive Curvature and Hamiltonian Monte Carlo
Abstract
The Jacobi metric introduced in mathematical physics can be used to analyze Hamiltonian Monte Carlo (HMC). In a geometrical setting, each step of HMC corresponds to a geodesic on a Riemannian manifold with a Jacobi metric. Our calculation of the sectional curvature of this HMC manifold allows us to see that it is positive in cases such as sampling from a high dimensional multivariate Gaussian. We show that positive curvature can be used to prove theoretical concentration results for HMC Markov chains.
🌉
Interdisciplinary Bridge
— Artificial Intelligence and Machine Learning and Mathematics & Optimization
📈
Trend Setter
— Markov Chain Monte Carlo
🧭
Keyword Pioneer
— sectional curvature
🐣
Hot Topic Early Bird
— markov chain
🐝
Cross-Pollinator
— Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Security & Privacy, Speech & Audio
Authors
Topics
Artificial Intelligence > Bayesian & Probabilistic > Bayesian Learning
Machine Learning > Optimization & Theory > Bayesian Inference
Mathematics & Optimization > Mathematics > Geometry
Mathematics & Optimization > Optimization > Stochastic Methods
Artificial Intelligence > Bayesian & Probabilistic > Bayesian Inference
Machine Learning > Bayesian & Probabilistic > Bayesian Inference
Machine Learning > Bayesian & Probabilistic > Markov Chain Monte Carlo