## Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks

** Joris M. Mooij, Jonas Peters, Dominik Janzing, Jakob Zscheischler, Bernhard Schölkopf**; 17(32):1−102, 2016.

### Abstract

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: methods based on Additive Noise Models (ANMs) and Information Geometric Causal Inference (IGCI). We present the benchmark`CauseEffectPairs`

that
consists of data for 100 different cause-effect pairs selected
from 37 data sets 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 method based on Additive Noise
Models that has originally been proposed by Hoyer et al. (2009),
which obtains an accuracy of 63 $\pm$ 10 % and an AUC of 0.74
$\pm$ 0.05 on the real-world benchmark. As the main theoretical
contribution of this work we prove the consistency of that
method.