# MINE: Mutual Information Neural Estimation

arXiv: https://arxiv.org/abs/1801.04062 · HTML: https://mlsanity.com/paper/1801.04062/

## Key facts

- Cited by 683 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2018.

## Built on by (most cited first, 30 of 683)

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- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
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- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [Self-supervised Learning on Graphs: Contrastive, Generative,or Predictive](https://mlsanity.com/paper/2105.07342/) (2021)
- [Domain Generalization by Mutual-Information Regularization with Pre-trained Models](https://mlsanity.com/paper/2203.10789/) (2022)
- [Improving Multimodal Fusion with Hierarchical Mutual Information Maximization for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2109.00412/) (2021)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
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- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [To Compress or Not to Compress- Self-Supervised Learning and Information Theory: A Review](https://mlsanity.com/paper/2304.09355/) (2023)
- [Rethinking Minimal Sufficient Representation in Contrastive Learning](https://mlsanity.com/paper/2203.07004/) (2022)
- [AniTalker: Animate Vivid and Diverse Talking Faces through Identity-Decoupled Facial Motion Encoding](https://mlsanity.com/paper/2405.03121/) (2024)
- [VQMIVC: Vector Quantization and Mutual Information-Based Unsupervised Speech Representation Disentanglement for One-shot Voice Conversion](https://mlsanity.com/paper/2106.10132/) (2021)
- [Decoding Visual Neural Representations by Multimodal Learning of Brain-Visual-Linguistic Features](https://mlsanity.com/paper/2210.06756/) (2022)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Farewell to Mutual Information: Variational Distillation for Cross-Modal Person Re-Identification](https://mlsanity.com/paper/2104.02862/) (2021)

## Abstract (arXiv)

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.