# Distinguishing cause from effect using observational data: methods and benchmarks

arXiv: https://arxiv.org/abs/1412.3773 · HTML: https://mlsanity.com/paper/1412.3773/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2014.

## Built on by (most cited first, 30 of 33)

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- [Demystifying amortized causal discovery with transformers](https://mlsanity.com/paper/2405.16924/) (2024)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
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- [Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation](https://mlsanity.com/paper/2209.08579/) (2022)
- [Feature Selection for Efficient Local-to-Global Bayesian Network Structure Learning](https://mlsanity.com/paper/2112.10369/) (2021)
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- [Causal Identification with Additive Noise Models: Quantifying the Effect of Noise](https://mlsanity.com/paper/2110.08087/) (2021)
- [DODO: Causal Structure Learning with Budgeted Interventions](https://mlsanity.com/paper/2510.08207/) (2025)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Identifiability of AMP chain graph models](https://mlsanity.com/paper/2106.09350/) (2021)
- [Efficiently Disentangle Causal Representations](https://mlsanity.com/paper/2201.01942/) (2022)

## Abstract (arXiv)

The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: Additive Noise Methods (ANM) and Information Geometric Causal Inference (IGCI). We present the benchmark CauseEffectPairs that consists of data for 100 different cause-effect pairs selected from 37 datasets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the additive-noise method originally proposed by Hoyer et al. (2009), which obtains an accuracy of 63+-10 % and an AUC of 0.74+-0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method.