# Tearing Apart NOTEARS: Controlling the Graph Prediction via Variance Manipulation

arXiv: https://arxiv.org/abs/2206.07195 · HTML: https://mlsanity.com/paper/2206.07195/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 7 of 7)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Scaling structural learning with NO-BEARS to infer causal transcriptome networks](https://mlsanity.com/paper/1911.00081/) (2019)
- [Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values](https://mlsanity.com/paper/2002.09573/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Open problems in causal structure learning: A case study of COVID-19 in the UK](https://mlsanity.com/paper/2305.03859/) (2023)
- [Iterative Causal Discovery: Per-Edge Impossibility Certificates, Tier-Aware Oracle Queries, and the 1+K Lower Bound](https://mlsanity.com/paper/2605.27477/) (2026)

## Abstract (arXiv)

Simulations are ubiquitous in machine learning. Especially in graph learning, simulations of Directed Acyclic Graphs (DAG) are being deployed for evaluating new algorithms. In the literature, it was recently argued that continuous-optimization approaches to structure discovery such as NOTEARS might be exploiting the sortability of the variable's variances in the available data due to their use of least square losses. Specifically, since structure discovery is a key problem in science and beyond, we want to be invariant to the scale being used for measuring our data (e.g. meter versus centimeter should not affect the causal direction inferred by the algorithm). In this work, we further strengthen this initial, negative empirical suggestion by both proving key results in the multivariate case and corroborating with further empirical evidence. In particular, we show that we can control the resulting graph with our targeted variance attacks, even in the case where we can only partially manipulate the variances of the data.