Causal inference for group-contaminated structured outcomes: observable quotients, lossless reduction and exact randomization inference
Structured potential outcomes such as microscopy images may be recorded after an unknown, unit-specific transformation. If that transformation can depend on treatment, covariates or the intrinsic outcome, raw-coordinate analyses may mix biological effects with acquisition geometry. We study the unrestricted observation model X = Γ . Y(A) and characterize its observable information: a target is uniformly recoverable exactly when it is constant on group orbits, while a Borel maximal invariant retains every measurable invariant target. We then distinguish observability from statistical losslessness. A quotient-faithful reconstruction theorem shows that quotient reduction is sufficient for th...
| Authors | Usef Faghihi, Amir Saki |
|---|---|
| Primary category | stat.ME |
| Published | 12 August 2026 |
| Last updated at source | 12 August 2026 |
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