Beyond Causal Sufficiency: When Is Optimal Invariant Prediction Possible?
Abstract
Out-of-distribution prediction requires models that remain reliable when the test distribution differs from the training environments. Stabilized Regression addresses this problem causally by combining invariance across multiple environments with regression-optimality. However, this approach relies on the causal sufficiency assumption, limiting its applicability to realistic distribution generalization settings. In this work, we relax this assumption by analyzing invariant prediction in partially observed causal systems with latent confounding. We study the targetindependence assumption, a graphical condition that characterizes whether the ADMG admits an observed intervention-stable set and hence whether invariant prediction can be guaranteed across the considered class of environments. Building on this, we define the Mixed Stable Blanket (MSB), proven to be the optimal invariant predictor among all subsets of admissible variables in partially observed linear additive structural models. Experiments on synthetic data demonstrate the applicability of Stabilized Regression in partially observed settings.
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BibTeX
@misc{goff2026beyond,
title = {{Beyond Causal Sufficiency: When Is Optimal Invariant Prediction Possible?}},
author = {Théotime Le Goff and Émilie Devijver},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05734696v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond Causal Sufficiency: When Is Optimal Invariant Prediction Possible?
AU - Théotime Le Goff
AU - Émilie Devijver
PY - 2026
DA - 2026/09/01
PB - HAL
UR - https://hal.science/hal-05734696v1
AB - Out-of-distribution prediction requires models that remain reliable when the test distribution differs from the training environments. Stabilized Regression addresses this problem causally by combining invariance across multiple environments with regression-optimality. However, this approach relies on the causal sufficiency assumption, limiting its applicability to realistic distribution generalization settings. In this work, we relax this assumption by analyzing invariant prediction in partially observed causal systems with latent confounding. We study the targetindependence assumption, a graphical condition that characterizes whether the ADMG admits an observed intervention-stable set and hence whether invariant prediction can be guaranteed across the considered class of environments. Building on this, we define the Mixed Stable Blanket (MSB), proven to be the optimal invariant predictor among all subsets of admissible variables in partially observed linear additive structural models. Experiments on synthetic data demonstrate the applicability of Stabilized Regression in partially observed settings.
ER -