Tearing Apart NOTEARS: Controlling the Graph Prediction via Variance Manipulation

TL;DR

This paper investigates how variance manipulation can influence the graph structures learned by the NOTEARS algorithm, revealing vulnerabilities and proposing methods to control graph predictions through targeted variance attacks.

Contribution

It provides theoretical proofs and empirical evidence that variance manipulation can control graph structures in continuous-optimization DAG learning methods like NOTEARS.

Findings

Variance manipulation affects graph predictions in NOTEARS.

Theoretical results in multivariate cases support empirical observations.

Partial variance control can still influence graph outcomes.

Abstract

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.