# Causal versions of Maximum Entropy and Principle of Insufficient Reason

arXiv: https://arxiv.org/abs/2102.03906 · HTML: https://mlsanity.com/paper/2102.03906/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 7 Feb 2021.

## Builds on (most cited first, 7 of 7)

- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Entropic Causal Inference](https://mlsanity.com/paper/1611.04035/) (2016)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [Telling cause from effect in deterministic linear dynamical systems](https://mlsanity.com/paper/1503.01299/) (2015)
- [Justifying Information-Geometric Causal Inference](https://mlsanity.com/paper/1402.2499/) (2014)
- [Error Asymmetry in Causal and Anticausal Regression](https://mlsanity.com/paper/1610.03263/) (2016)
- [Uncertain Reasoning Using Maximum Entropy Inference](https://mlsanity.com/paper/1304.3420/) (2013)

## Built on by (most cited first, 7 of 7)

- [Provably Learning Object-Centric Representations](https://mlsanity.com/paper/2305.14229/) (2023)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Bounding probabilities of causation through the causal marginal problem](https://mlsanity.com/paper/2304.02023/) (2023)
- [The most likely common cause](https://mlsanity.com/paper/2306.17557/) (2023)
- [Estimating Joint Interventional Distributions from Marginal Interventional Data](https://mlsanity.com/paper/2409.01794/) (2024)
- [Causal vs. Anticausal merging of predictors](https://mlsanity.com/paper/2501.08426/) (2025)

## Abstract (arXiv)

The Principle of Insufficient Reason (PIR) assigns equal probabilities to each alternative of a random experiment whenever there is no reason to prefer one over the other. The Maximum Entropy Principle (MaxEnt) generalizes PIR to the case where statistical information like expectations are given. It is known that both principles result in paradoxical probability updates for joint distributions of cause and effect. This is because constraints on the conditional P(effect|cause) result in changes of P(cause) that assign higher probability to those values of the cause that offer more options for the effect, suggesting "intentional behaviour". Earlier work therefore suggested sequentially maximizing (conditional) entropy according to the causal order, but without further justification apart from plausibility on toy examples. We justify causal modifications of PIR and MaxEnt by separating constraints into restrictions for the cause and restrictions for the mechanism that generates the effect from the cause. We further sketch why Causal PIR also entails "Information Geometric Causal Inference". We briefly discuss problems of generalizing the causal version of MaxEnt to arbitrary causal DAGs.