# Encoding Causal Macrovariables

arXiv: https://arxiv.org/abs/2111.14724 · HTML: https://mlsanity.com/paper/2111.14724/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [Deep Learning of Representations: Looking Forward](https://mlsanity.com/paper/1305.0445/) (2013)
- [Discovering Causal Signals in Images](https://mlsanity.com/paper/1605.08179/) (2016)
- [Visual Causal Feature Learning](https://mlsanity.com/paper/1412.2309/) (2014)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [Unsupervised Discovery of El Nino Using Causal Feature Learning on Microlevel Climate Data](https://mlsanity.com/paper/1605.09370/) (2016)
- [When the map is better than the territory](https://mlsanity.com/paper/1612.09592/) (2016)

## Built on by (most cited first, 4 of 4)

- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [The Causal Information Bottleneck and Optimal Causal Variable Abstractions](https://mlsanity.com/paper/2410.00535/) (2024)
- [Fundamental Properties of Causal Entropy and Information Gain](https://mlsanity.com/paper/2402.01341/) (2024)
- [Causality in the human niche: lessons for machine learning](https://mlsanity.com/paper/2506.13803/) (2025)

## Abstract (arXiv)

In many scientific disciplines, coarse-grained causal models are used to explain and predict the dynamics of more fine-grained systems. Naturally, such models require appropriate macrovariables. Automated procedures to detect suitable variables would be useful to leverage increasingly available high-dimensional observational datasets. This work introduces a novel algorithmic approach that is inspired by a new characterisation of causal macrovariables as information bottlenecks between microstates. Its general form can be adapted to address individual needs of different scientific goals. After a further transformation step, the causal relationships between learned variables can be investigated through additive noise models. Experiments on both simulated data and on a real climate dataset are reported. In a synthetic dataset, the algorithm robustly detects the ground-truth variables and correctly infers the causal relationships between them. In a real climate dataset, the algorithm robustly detects two variables that correspond to the two known variations of the El Nino phenomenon.