We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy–Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber–Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.

我们将Zig-Zag采样器的使用介绍给对条件扩散过程（扩散桥）进行采样的问题。之字形采样器是一种基于不可逆的连续分段确定性马尔可夫过程的无拒绝采样方案。类似于Lévy–Ciesielski布朗运动的构造，我们在截短的Faber–Schauder基础上扩展了扩散路径。使用Zig-Zag采样器对基础内的系数进行采样。一项关键创新是将全局部算法用于Zig-Zag采样器，该算法可利用系数的依赖图和子采样技术所隐含的稀疏结构来降低算法的复杂性。我们在许多示例中说明了所提出方法的性能。