论文标题
磁性歧管汉密尔顿蒙特卡洛
Magnetic Manifold Hamiltonian Monte Carlo
论文作者
论文摘要
马尔可夫链蒙特卡洛（MCMC）算法提供了各种抽样策略；采样器的汉密尔顿蒙特卡洛（HMC）家族是MCMC算法，通常表现出改善的混合特性。最近引入的磁HMC是由磁场力影响的颗粒物理学动机的HMC的概括，已被证明可以改善HMC的性能。在许多应用中，人们希望从限于约束集的分布进行采样，通常表现为嵌入式歧管（例如，球体的表面）。我们引入了磁性歧管HMC，这是一种嵌入式歧管上的HMC算法，该歧管的嵌入式歧管是由粒子的物理学限制为歧管的物理学动机，并在磁场力下移动。我们讨论了磁性汉密尔顿动力学在流形上的理论特性，并为HMC更新引入了可逆的和符号的积分器。我们证明，磁歧管HMC相对于歧管受限的HMC的规范变体产生有利的采样行为。
Markov chain Monte Carlo (MCMC) algorithms offer various strategies for sampling; the Hamiltonian Monte Carlo (HMC) family of samplers are MCMC algorithms which often exhibit improved mixing properties. The recently introduced magnetic HMC, a generalization of HMC motivated by the physics of particles influenced by magnetic field forces, has been demonstrated to improve the performance of HMC. In many applications, one wishes to sample from a distribution restricted to a constrained set, often manifested as an embedded manifold (for example, the surface of a sphere). We introduce magnetic manifold HMC, an HMC algorithm on embedded manifolds motivated by the physics of particles constrained to a manifold and moving under magnetic field forces. We discuss the theoretical properties of magnetic Hamiltonian dynamics on manifolds, and introduce a reversible and symplectic integrator for the HMC updates. We demonstrate that magnetic manifold HMC produces favorable sampling behaviors relative to the canonical variant of manifold-constrained HMC.
