# Fundamental Properties of Causal Entropy and Information Gain

arXiv: https://arxiv.org/abs/2402.01341 · HTML: https://mlsanity.com/paper/2402.01341/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [Causal Influence Detection for Improving Efficiency in Reinforcement Learning](https://mlsanity.com/paper/2106.03443/) (2021)
- [Encoding Causal Macrovariables](https://mlsanity.com/paper/2111.14724/) (2021)
- [Causal Entropy and Information Gain for Measuring Causal Control](https://mlsanity.com/paper/2309.07703/) (2023)

## Built on by (most cited first, 1 of 1)

- [The Causal Information Bottleneck and Optimal Causal Variable Abstractions](https://mlsanity.com/paper/2410.00535/) (2024)

## Abstract (arXiv)

Recent developments enable the quantification of causal control given a structural causal model (SCM). This has been accomplished by introducing quantities which encode changes in the entropy of one variable when intervening on another. These measures, named causal entropy and causal information gain, aim to address limitations in existing information theoretical approaches for machine learning tasks where causality plays a crucial role. They have not yet been properly mathematically studied. Our research contributes to the formal understanding of the notions of causal entropy and causal information gain by establishing and analyzing fundamental properties of these concepts, including bounds and chain rules. Furthermore, we elucidate the relationship between causal entropy and stochastic interventions. We also propose definitions for causal conditional entropy and causal conditional information gain. Overall, this exploration paves the way for enhancing causal machine learning tasks through the study of recently-proposed information theoretic quantities grounded in considerations about causality.