Title: Channel Simulation and Distributed Compression with Ensemble Rejection Sampling Show Chinese title

Title: 信道模拟与基于集合拒绝采样的分布式压缩

Abstract: We study channel simulation and distributed matching, two fundamental problems with several applications to machine learning, using a recently introduced generalization of the standard rejection sampling (RS) algorithm known as Ensemble Rejection Sampling (ERS). For channel simulation, we propose a new coding scheme based on ERS that achieves a near-optimal coding rate. In this process, we demonstrate that standard RS can also achieve a near-optimal coding rate and generalize the result of Braverman and Garg (2014) to the continuous alphabet setting. Next, as our main contribution, we present a distributed matching lemma for ERS, which serves as the rejection sampling counterpart to the Poisson Matching Lemma (PML) introduced by Li and Anantharam (2021). Our result also generalizes a recent work on importance matching lemma (Phan et al, 2024) and, to our knowledge, is the first result on distributed matching in the family of rejection sampling schemes where the matching probability is close to PML. We demonstrate the practical significance of our approach over prior works by applying it to distributed compression. The effectiveness of our proposed scheme is validated through experiments involving synthetic Gaussian sources and distributed image compression using the MNIST dataset. Show Chinese abstract

Abstract: 我们研究信道模拟和分布式匹配，这两个基本问题在机器学习中有多种应用，使用了一种最近引入的标准拒绝采样（RS）算法的推广方法，称为集合拒绝采样（ERS）。 对于信道模拟，我们提出了一种基于ERS的新编码方案，实现了接近最优的编码速率。 在此过程中，我们证明了标准RS也可以实现接近最优的编码速率，并将Braverman和Garg（2014）的结果推广到连续字母表设置。 接下来，作为我们的主要贡献，我们提出了一个针对ERS的分布式匹配引理，该引理是Li和Anantharam（2021）提出的泊松匹配引理（PML）的拒绝采样对应版本。 我们的结果还推广了关于重要性匹配引理的最新工作（Phan等，2024），据我们所知，这是在匹配概率接近PML的拒绝采样方案家族中关于分布式匹配的第一个结果。 我们通过将其应用于分布式压缩来展示我们方法的实际意义。 我们提出的方案的有效性通过涉及合成高斯源和使用MNIST数据集进行分布式图像压缩的实验得到了验证。