# Assessing the overall and partial causal well-specification of nonlinear additive noise models

arXiv: https://arxiv.org/abs/2310.16502 · HTML: https://mlsanity.com/paper/2310.16502/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [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)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Data](https://mlsanity.com/paper/2210.17283/) (2022)
- [On the pitfalls of Gaussian likelihood scoring for causal discovery](https://mlsanity.com/paper/2210.11104/) (2022)
- [On the Intersection Property of Conditional Independence and its Application to Causal Discovery](https://mlsanity.com/paper/1403.0408/) (2014)
- [Higher-order least squares: assessing partial goodness of fit of linear causal models](https://mlsanity.com/paper/2109.14544/) (2021)

## Built on by (most cited first, 3 of 3)

- [Causal Additive Models with Unobserved Causal Paths and Backdoor Paths](https://mlsanity.com/paper/2502.07646/) (2025)
- [Achievable distributional robustness when the robust risk is only partially identified](https://mlsanity.com/paper/2502.02710/) (2025)
- [Kolmogorov-Arnold causal generative models](https://mlsanity.com/paper/2603.20184/) (2026)

## Abstract (arXiv)

We propose a method to detect model misspecifications in nonlinear causal additive and potentially heteroscedastic noise models. We aim to identify predictor variables for which we can infer the causal effect even in cases of such misspecification. We develop a general framework based on knowledge of the multivariate observational data distribution. We then propose an algorithm for finite sample data, discuss its asymptotic properties, and illustrate its performance on simulated and real data.