In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

通过基于Girsanov定理的新方法，我们提出了一种估计随机变量之间互信息（MI）的方法。我们的方法基于分数函数的扩散模型来估计两个密度之间的Kullback Leibler散度，并衍生出估计随机变量熵的方法。我们的结果表明，我们的方法在挑战性分布情况下比文献中的主要替代方法更准确，并通过自洽性测试，包括数据处理和独立性下的可加性。

MINDE: 互信息神经扩散估计