# Generalized Criterion for Identifiability of Additive Noise Models Using Majorization

arXiv: https://arxiv.org/abs/2404.05148 · HTML: https://mlsanity.com/paper/2404.05148/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 8 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity](https://mlsanity.com/paper/1703.01196/) (2017)
- [Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)](https://mlsanity.com/paper/1704.08783/) (2017)
- [Learning directed acyclic graphs based on sparsest permutations](https://mlsanity.com/paper/1307.0366/) (2013)
- [Learning Local Dependence In Ordered Data](https://mlsanity.com/paper/1604.07451/) (2016)

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

- [Generalizing Identifiability Results in Causal Discovery from Complete Data to Missing Data Settings](https://mlsanity.com/paper/2610.19211/) (2026)

## Abstract (arXiv)

The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of directed acyclic graph (DAG) models. In this paper, we introduce a novel identifiability criterion for DAGs that places constraints on the conditional variances of additive noise models. We demonstrate that this criterion extends and generalizes existing identifiability criteria in the literature that employ (conditional) variances as measures of uncertainty in (conditional) distributions. For linear Structural Equation Models, we present a new algorithm that leverages the concept of weak majorization applied to the diagonal elements of the Cholesky factor of the covariance matrix to learn a topological ordering of variables. Through extensive simulations and the analysis of bank connectivity data, we provide evidence of the effectiveness of our approach in successfully recovering DAGs. The code for reproducing the results in this paper is available in Supplementary Materials.