Causal Inference for Group-Contaminated Structured Outcomes: New Theoretical Framework

A new paper on arXiv (2608.11954) introduces a theoretical framework for causal inference when structured outcomes, such as microscopy images, are subject to unknown unit-specific transformations. The study characterizes observable information under an unrestricted observation model, showing that a target is uniformly recoverable only if it is constant on group orbits. It distinguishes observability from statistical losslessness and presents a quotient-faithful reconstruction theorem. The paper also explores conditional Haar contamination on compact groups, yielding Blackwell equivalence under certain conditions. This work has implications for biological imaging and other fields where acquisition geometry can confound analysis.