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Assumption Glossary

Every causalrl Certificate records the assumptions it consumed as typed Assumption entries (name, params, checkable, diagnostic). This page explains each one: what it means, whether it is checkable from data, and how a violation is handled. The library is one-sidedly honest — outside a supported class it returns a hedge or a typed exception, never a silent point estimate.

Epistemic kinds

A certificate's kind is never conflated across these three:

  • IDENTIFIED — a point claim backed by identification under the stated graph/assumptions.
  • BOUNDED — partial identification: an interval valid under an explicit sensitivity budget.
  • EMPIRICAL — simulation/sample evidence only, with no identification guarantee.

Assumptions

backdoor

The adjustment set blocks all back-door paths from treatment to outcome. params.adjustment_set lists the covariates. Checkable given the graph (the graph is the witness); the numeric estimate additionally assumes correct nuisance models (relaxed by the doubly-robust aipw / dml methods).

overlap (positivity)

Every unit has propensity bounded away from 0 and 1 (or, for importance sampling, a finite effective sample size). params.eps / params.min_ess_fraction set the threshold; diagnostic reports the observed extremes / ESS. Checkable — a violation downgrades to a hedge (overlap-violation) rather than returning an unstable inverse-weighted estimate.

MSM (marginal sensitivity model)

Unmeasured confounding shifts the true propensity from the nominal one by at most an odds-ratio gamma >= 1 (Tan's model). params.gamma is the budget. Not checkable from data — it is a stated sensitivity parameter; the certificate is BOUNDED and the interval widens monotonically in gamma, collapsing to the point estimate at gamma = 1.

logged-propensities

The importance weights / nominal propensities used for off-policy evaluation are the true logging probabilities (up to the MSM budget when one is declared). Not checkable from the logs alone.

moment-condition

The target functional's moments exist (e.g. a finite mean). Checkable via a heavy-tail diagnostic; when it fails, the mean target downgrades to a valid quantile/tail target with the downgrade recorded (hedge.downgraded_from).

mi-cap / pivotality

A cap on how much a hidden confounder can move the decision, expressed as a mutual-information or odds-ratio budget (the pivotality layer). BOUNDED; certify_decision reports the tipping gamma at which the decision would flip.

selection-nodes-S (transport)

The named selection nodes mark exactly where the source and target regimes differ (population or mechanism). The transport formula / regret certificate is valid when the marked diagram is correct; Regime selection nodes are the witness. Non-transportable queries hedge.

quantile-sketch

A streamed quantile is answered by a Greenwald–Khanna sketch whose true rank is within epsilon * n of the requested rank. params.epsilon is the guaranteed rank-error budget, recorded in provenance so the approximation travels with the claim.

fqe-model

A fitted-Q-evaluation off-policy value estimate. Model-based with no identification guarantee under hidden confounding, so the certificate is EMPIRICAL; upgrade to certify_effect or bound it with certify_policy when the structure licenses it.

Provenance

Every certificate also records reproducibility metadata (Provenance): the library version, seeds, a data fingerprint, a graph hash, and a timestamp — so a claim can be reproduced and audited.