论文标题
来自条件可逆变换的非可逆MCMC：具有收敛保证的完整食谱
Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees
论文作者
论文摘要
Markov Chain Monte Carlo（MCMC）是一类算法，用于采样复杂和高维概率分布。 MCMC的主力军Metropolis-Hastings（MH）算法提供了一个简单的配方来构建可逆的Markov内核。可逆性是一种可容纳的属性，暗示着这里不太可行但必不可少的属性（不变性）。但是，在考虑性能时，不一定需要可逆性。这引发了最近对破坏该属性的内核设计的兴趣。同时，一项积极的研究流着集中于MH内核的新版本的设计，这种研究依赖于使用复杂的可逆确定性变换。尽管对MH内核的标准实施进行了充分的了解，但上述发展尚未获得相同的系统处理以确保其有效性。本文通过开发通用工具来填补空白，以确保一类可能依靠复杂变换的非可逆马尔可夫内核具有所需的不变性属性并导致收敛算法。这导致一组简单且实际可验证的条件。
Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible Markov kernels. Reversibility is a tractable property that implies a less tractable but essential property here, invariance. Reversibility is however not necessarily desirable when considering performance. This has prompted recent interest in designing kernels breaking this property. At the same time, an active stream of research has focused on the design of novel versions of the MH kernel, some nonreversible, relying on the use of complex invertible deterministic transforms. While standard implementations of the MH kernel are well understood, the aforementioned developments have not received the same systematic treatment to ensure their validity. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms. This leads to a set of simple and practically verifiable conditions.
