# Conditional distribution variability measures for causality detection

arXiv: https://arxiv.org/abs/1601.06680 · HTML: https://mlsanity.com/paper/1601.06680/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2016.

## Built on by (most cited first, 15 of 15)

- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Nonlinear Invariant Risk Minimization: A Causal Approach](https://mlsanity.com/paper/2102.12353/) (2021)
- [Model-Based Counterfactual Synthesizer for Interpretation](https://mlsanity.com/paper/2106.08971/) (2021)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [Unifying Pairwise Interactions in Complex Dynamics](https://mlsanity.com/paper/2201.11941/) (2022)
- [Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework](https://mlsanity.com/paper/2406.08311/) (2024)
- [Distinguishing Cause from Effect with Causal Velocity Models](https://mlsanity.com/paper/2502.05122/) (2025)
- [Do learned representations respect causal relationships?](https://mlsanity.com/paper/2204.00762/) (2022)
- [Improving Data-driven Heterogeneous Treatment Effect Estimation Under Structure Uncertainty](https://mlsanity.com/paper/2206.12689/) (2022)
- [From Causal Pairs to Causal Graphs](https://mlsanity.com/paper/2211.04312/) (2022)
- [Initial Results for Pairwise Causal Discovery Using Quantitative Information Flow](https://mlsanity.com/paper/2212.01279/) (2022)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [From Observations to Causations: A GNN-based Probabilistic Prediction Framework for Causal Discovery](https://mlsanity.com/paper/2507.20349/) (2025)
- [LxCIM: a new rank-based binary classifier performance metric invariant to local exchange of classes](https://mlsanity.com/paper/2512.10053/) (2025)

## Abstract (arXiv)

In this paper we derive variability measures for the conditional probability distributions of a pair of random variables, and we study its application in the inference of causal-effect relationships. We also study the combination of the proposed measures with standard statistical measures in the the framework of the ChaLearn cause-effect pair challenge. The developed model obtains an AUC score of 0.82 on the final test database and ranked second in the challenge.