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：我们提出了现有基于重要性采样的有损压缩方法的两种扩展。首先，我们引入了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 and Ahmed, 2022）的一个变体，并且适用于有限样本数下可达压缩率的直接评估。我们的第二个也是主要贡献是重要性匹配引理，它是近期提出的泊松匹配引理（Li and Anantharam, 2021）在有限提议情况下的对应物。通过与深度学习集成，我们为解码端具有边信息的分布式有损压缩提供了一种新的编码方案。我们通过在合成高斯源、MNIST分布式图像压缩以及CIFAR-10纵向联邦学习上的实验，展示了所提方案的有效性。