CCMI : Classifier based Conditional Mutual Information Estimation
This work addresses a fundamental challenge in data-driven inference problems such as graphical models and causal learning, offering a scalable solution for researchers and practitioners dealing with high-dimensional data.
The paper tackled the problem of conditional mutual information (CMI) estimation, which suffers from the curse of dimensionality in existing methods, by introducing a classifier-based estimator that leverages likelihood ratios and conditional generative models, resulting in significant performance improvements over the widely used KSG estimator and superior state-of-the-art performance in conditional independence testing on simulated and real datasets.
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference problems such as graphical models, causal learning, feature selection and time-series analysis. While k-nearest neighbor (kNN) based estimators as well as kernel-based methods have been widely used for CMI estimation, they suffer severely from the curse of dimensionality. In this paper, we leverage advances in classifiers and generative models to design methods for CMI estimation. Specifically, we introduce an estimator for KL-Divergence based on the likelihood ratio by training a classifier to distinguish the observed joint distribution from the product distribution. We then show how to construct several CMI estimators using this basic divergence estimator by drawing ideas from conditional generative models. We demonstrate that the estimates from our proposed approaches do not degrade in performance with increasing dimension and obtain significant improvement over the widely used KSG estimator. Finally, as an application of accurate CMI estimation, we use our best estimator for conditional independence testing and achieve superior performance than the state-of-the-art tester on both simulated and real data-sets.