# Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing

arXiv: https://arxiv.org/abs/2301.12930 · HTML: https://mlsanity.com/paper/2301.12930/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [High-Dimensional Poisson DAG Model Learning Using ℓ1-Regularized Regression](https://mlsanity.com/paper/1810.02501/) (2018)
- [On the pitfalls of Gaussian likelihood scoring for causal discovery](https://mlsanity.com/paper/2210.11104/) (2022)
- [Diagnosis of Autism Spectrum Disorder by Causal Influence Strength Learned from Resting-State fMRI Data](https://mlsanity.com/paper/1902.10073/) (2019)

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

- [Structural restrictions in local causal discovery: identifying direct causes of a target variable](https://mlsanity.com/paper/2307.16048/) (2023)
- [Causal Discovery via Quantile Partial Effect](https://mlsanity.com/paper/2509.12981/) (2025)
- [Why Online Reinforcement Learning is Causal](https://mlsanity.com/paper/2403.04221/) (2024)
- [Skewness-Robust Causal Discovery in Location-Scale Noise Models](https://mlsanity.com/paper/2511.14441/) (2025)
- [Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables](https://mlsanity.com/paper/2606.08196/) (2026)
- [Counterfactual Residual Data Augmentation for Regression](https://mlsanity.com/paper/2606.28460/) (2026)
- [No Dtrain: Model-Agnostic Counterfactual Explanations Using Reinforcement Learning](https://mlsanity.com/paper/2405.18563/) (2024)

## Abstract (arXiv)

A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise term, which allows us to leverage assumptions about the generating function class. The recently introduced heteroscedastic location-scale noise functional models (LSNMs) combine expressive power with identifiability guarantees. LSNM model selection based on maximizing likelihood achieves state-of-the-art accuracy, when the noise distributions are correctly specified. However, through an extensive empirical evaluation, we demonstrate that the accuracy deteriorates sharply when the form of the noise distribution is misspecified by the user. Our analysis shows that the failure occurs mainly when the conditional variance in the anti-causal direction is smaller than that in the causal direction. As an alternative, we find that causal model selection through residual independence testing is much more robust to noise misspecification and misleading conditional variance.