# Skewness-Robust Causal Discovery in Location-Scale Noise Models

arXiv: https://arxiv.org/abs/2511.14441 · HTML: https://mlsanity.com/paper/2511.14441/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 71 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 22 of 22)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [cmaes: A Simple yet Practical Python Library for CMA-ES](https://mlsanity.com/paper/2402.01373/) (2024)
- [On the pitfalls of Gaussian likelihood scoring for causal discovery](https://mlsanity.com/paper/2210.11104/) (2022)
- [Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing](https://mlsanity.com/paper/2301.12930/) (2023)
- [Heteroscedastic Causal Structure Learning](https://mlsanity.com/paper/2307.07973/) (2023)
- [A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery](https://mlsanity.com/paper/2410.06407/) (2024)
- [Identifiability of causal graphs under nonadditive conditionally parametric causal models](https://mlsanity.com/paper/2303.15376/) (2023)
- [Robust Estimation of Causal Heteroscedastic Noise Models](https://mlsanity.com/paper/2312.10102/) (2023)
- [Order-based Structure Learning with Normalizing Flows](https://mlsanity.com/paper/2308.07480/) (2023)

## Built on by (most cited first, 1 of 1)

- [On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models](https://mlsanity.com/paper/2609.17942/) (2026)

## Abstract (arXiv)

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause X from effect Y in bivariate models, that is, distinguish the two graphs X → Y and Y → X. Location-scale noise models (LSNMs), in which the effect Y is modeled based on the cause X as Y = f(X) + g(X)N, form a flexible class of models that is general and identifiable in most cases. Estimating these models for arbitrary noise terms N, however, is challenging. Therefore, practical estimators are typically restricted to symmetric distributions, such as the normal distribution. As we showcase in this paper, when N is a skewed random variable, which is likely in real-world domains, the reliability of these approaches decreases. To approach this limitation, we propose SkewD, a likelihood-based algorithm for bivariate causal discovery under LSNMs with skewed noise distributions. SkewD extends the usual normal-distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. For parameter estimation, we employ a combination of a heuristic search and an expectation conditional maximization algorithm. We evaluate SkewD on novel synthetically generated datasets with skewed noise as well as established benchmark datasets. Throughout our experiments, SkewD exhibits a strong performance and, in comparison to prior work, remains robust under high skewness.