A General Metric for Riemannian Manifold Hamiltonian Monte Carlo

机译：黎曼流形哈密顿量蒙特卡洛的一般度量

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Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo (RMHMC), has demonstrated success in many challenging problems. Current RMHMC implementations, however, rely on a Riemannian metric that limits their application. In this paper I propose a new metric for RMHMC without these limitations and verify its success on a distribution that emulates many hierarchical and latent models.

机译：马尔可夫链蒙特卡洛（MCMC）是使用复杂模型进行推理的一种宝贵手段，汉密尔顿蒙特卡洛，尤其是黎曼流形汉密尔顿蒙特卡洛（RMHMC）在许多挑战性问题上都取得了成功。但是，当前的RMHMC实现依赖于限制其应用的黎曼度量。在本文中，我提出了一种不受这些限制的RMHMC新指标，并在模拟许多分层模型和潜在模型的分布上验证了其成功性。

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《International conference on geometric science of information》|2013年|327-334|共8页
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Michael Betancourt;
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1. k-STEP SUB-RIEMANNIAN MANIFOLD WHOSE SUB-RIEMANNIAN METRIC ADMITS A CANONICAL EXTENSION TO A RIEMANNIAN METRIC [J] . M. M. DINIZ, J. M. M. VELOSO Journal of Dynamical and Control Systems . 2010,第4期

机译：k-STEP亚黎曼流形，亚黎曼度量矩阵的典范扩展
2. k-Step Sub-Riemannian Manifold whose Sub-Riemannian Metric Admits a Canonical Extension to a Riemannian Metric [J] . Journal of Dynamical and Control Systems . 2010,第4期

机译：k步次黎曼流形，其次黎曼度量允许对黎曼度量的规范扩展
3. Stochastic Volatility in Mean: Empirical evidence from Latin-American stock markets using Hamiltonian Monte Carlo and Riemann Manifold HMC methods [J] . Abanto-Valle Carlos A., Rodriguez Gabriel, Garrafa-Aragon Hernan B. The quarterly review of economics and finance . 2021,第May期

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4. A General Metric for Riemannian Manifold Hamiltonian Monte Carlo [C] . Michael Betancourt International SEE Conference on Geometric science of information . 2013

机译：Riemannian多方汉密尔顿蒙特卡洛的一般指标
5. The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning [D] . Faraki, Masoud. 2018

机译：黎曼流形在计算机视觉中的作用：从编码到深度度量学习
6. Quantum Monte Carlo simulation of a particular class of non-stoquastic Hamiltonians in quantum annealing [O] . Masayuki Ohzeki -1

机译：量子退火中一类非随机哈密顿量的量子蒙特卡罗模拟
7. A General Metric for Riemannian Manifold Hamiltonian Monte Carlo [O] . Betancourt, M. J. 2013

机译：黎曼流形哈密顿蒙特卡罗的一般度量
8. Monte Carlo Procedure for Hamiltonians with Small Nonlocal Correction Terms [R] . Mack, G., Pinn, K. 1986

机译：具有小非局部修正项的Hamiltonian蒙特卡罗程序

A General Metric for Riemannian Manifold Hamiltonian Monte Carlo

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