论文标题
分段确定性蒙特卡洛算法的自适应方案
Adaptive schemes for piecewise deterministic Monte Carlo algorithms
论文作者
论文摘要
有弹性粒子采样器（BPS）和Zig-Zag采样器（ZZ）是基于分段确定性马尔可夫过程的连续时间，不可逆的蒙特卡洛方法。实验表明，这些采样器的收敛速度可能会受到目标分布形状的影响，例如在各向异性目标的情况下。我们提出了一种自适应方案，该方案迭代地学习目标的协方差矩阵的全部或部分，并利用获得的信息来修改基础过程，以提高收敛速度。此外，我们定义了一种自适应方案，该方案会自动调整BPS或ZZ的茶点率。我们证明了所有提议的自适应算法的怪异性和大量定律。最后，我们通过几个数值模拟显示了自适应采样器的好处。
The Bouncy Particle sampler (BPS) and the Zig-Zag sampler (ZZS) are continuous time, non-reversible Monte Carlo methods based on piecewise deterministic Markov processes. Experiments show that the speed of convergence of these samplers can be affected by the shape of the target distribution, as for instance in the case of anisotropic targets. We propose an adaptive scheme that iteratively learns all or part of the covariance matrix of the target and takes advantage of the obtained information to modify the underlying process with the aim of increasing the speed of convergence. Moreover, we define an adaptive scheme that automatically tunes the refreshment rate of the BPS or ZZS. We prove ergodicity and a law of large numbers for all the proposed adaptive algorithms. Finally, we show the benefits of the adaptive samplers with several numerical simulations.
