用离散桥模型解决离散变量互信息估计难题
Discrete Bridges for Mutual Information Estimation
- 将互信息估计转化为域迁移问题，构建离散桥框架
- 在低维和图像数据上均显著优于传统方法
- 适合处理离散变量互信息估计场景
连续和离散状态空间的扩散桥模型近期成为生成建模的强大工具。本文利用离散状态空间的桥匹配模型，解决机器学习与信息论中的另一关键问题：离散随机变量间互信息（MI）的估计。通过将MI估计巧妙地建模为域迁移问题，我们构建了适用于离散数据的离散桥互信息（DBMI）估计器，解决了传统方法在离散数据上的困难。我们在两个设置下验证了该估计器的表现：低维场景与基于图像的场景。
原文摘要 · Abstract (English)
Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to address another important problem in machine learning and information theory: the estimation of the mutual information (MI) between discrete random variables. By neatly framing MI estimation as a domain transfer problem, we construct a Discrete Bridge Mutual Information (DBMI) estimator suitable for discrete data, which poses difficulties for conventional MI estimators. We showcase the performance of our estimator on two MI estimation settings: low-dimensional and image-based.
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