# Constraint-based difference graph discovery in a linear setting

arXiv: https://arxiv.org/abs/2606.13947 · HTML: https://mlsanity.com/paper/2606.13947/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2026.

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

- [Root cause analysis via difference graph discovery from linear time-series data](https://mlsanity.com/paper/2608.21117/) (2026)

## Abstract (arXiv)

Comparing causal relationships across populations is essential in many scientific domains. This paper studies the problem of inferring a difference graph between two environments and proposes a causal discovery method for linear structural causal models based on equality tests of regression coefficients. We show that invariance of regression coefficients is governed by graphical conditions that go beyond standard d-separation. Therefore, we introduce diff-separation, a graphical criterion that characterizes when a conditioning set blocks all paths capable of inducing differences in regression coefficients across environments. Building on this criterion, we introduce a corresponding diff-faithfulness assumption, linking graphical diff-separation statements to equality constraints on regression coefficients. Finally, we propose LDiffPC, a PC-style algorithm that uses equality tests of regression coefficients to recover the differences from multi-environment data.