We propose two extensions to existing importance sampling based methods for lossy compression. First, we introduce an importance sampling based compression scheme that is a variant of ordered random coding (Theis and Ahmed, 2022) and is amenable to direct evaluation of the achievable compression rate for a finite number of samples. Our second and major contribution is the importance matching lemma, which is a finite proposal counterpart of the recently introduced Poisson matching lemma (Li and Anantharam, 2021). By integrating with deep learning, we provide a new coding scheme for distributed lossy compression with side information at the decoder. We demonstrate the effectiveness of the proposed scheme through experiments involving synthetic Gaussian sources, distributed image compression with MNIST and vertical federated learning with CIFAR-10.

翻译：我们针对基于重要性采样的有损压缩方法提出两项扩展。首先，我们引入一种基于重要性采样的压缩方案，该方案是有序随机编码（Theis和Ahmed，2022）的变体，并且便于在有限样本数量下直接评估可达压缩率。第二项也是我们的主要贡献是重要性匹配引理，这是最近提出的泊松匹配引理（Li和Anantharam，2021）的有限提议对应物。通过与深度学习相结合，我们为解码端带辅助信息的分布式有损压缩提供了一种新的编码方案。我们通过涉及合成高斯源、基于MNIST的分布式图像压缩以及基于CIFAR-10的纵向联邦学习的实验，展示了所提方案的有效性。