# C-MI-GAN : Estimation of Conditional Mutual Information using MinMax formulation

arXiv: https://arxiv.org/abs/2005.08226 · HTML: https://mlsanity.com/paper/2005.08226/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2020.

## Built on by (most cited first, 10 of 10)

- [Multimodal Variational Auto-encoder based Audio-Visual Segmentation](https://mlsanity.com/paper/2310.08303/) (2023)
- [Synthetic Data in Human Analysis: A Survey](https://mlsanity.com/paper/2208.09191/) (2022)
- [Conditional Mutual Information for Disentangled Representations in Reinforcement Learning](https://mlsanity.com/paper/2305.14133/) (2023)
- [Decomposed Mutual Information Estimation for Contrastive Representation Learning](https://mlsanity.com/paper/2106.13401/) (2021)
- [Conditional Contrastive Learning with Kernel](https://mlsanity.com/paper/2202.05458/) (2022)
- [Disentanglement and Generalization Under Correlation Shifts](https://mlsanity.com/paper/2112.14754/) (2021)
- [SemCal: Semantic LiDAR-Camera Calibration using Neural MutualInformation Estimator](https://mlsanity.com/paper/2109.10270/) (2021)
- [Can Information Flows Suggest Targets for Interventions in Neural Circuits?](https://mlsanity.com/paper/2111.05299/) (2021)
- [Calibrating LiDAR and Camera using Semantic Mutual information](https://mlsanity.com/paper/2104.12023/) (2021)
- [From Generalist to Specialist Representation](https://mlsanity.com/paper/2605.12733/) (2026)

## Abstract (arXiv)

Estimation of information theoretic quantities such as mutual information and its conditional variant has drawn interest in recent times owing to their multifaceted applications. Newly proposed neural estimators for these quantities have overcome severe drawbacks of classical kNN-based estimators in high dimensions. In this work, we focus on conditional mutual information (CMI) estimation by utilizing its formulation as a minmax optimization problem. Such a formulation leads to a joint training procedure similar to that of generative adversarial networks. We find that our proposed estimator provides better estimates than the existing approaches on a variety of simulated data sets comprising linear and non-linear relations between variables. As an application of CMI estimation, we deploy our estimator for conditional independence (CI) testing on real data and obtain better results than state-of-the-art CI testers.