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Validation protocol

Causal estimates are only useful if they are right, and a wrong number with a confident interval is worse than no number. graphdml is validated in five layers. Each layer answers a different question, and each has a fixed pass criterion written down before the evidence is collected. Results for the current version are in validation-results.md.

Layer Question Where
1. Specification Is the estimator precisely defined? methodology.md
2. Correctness Does the code compute that estimator? pytest (fast suite)
3. Statistical validity Does it behave as the theory says? pytest -m slow, benchmarks/
4. Realism Does it hold up on realistic data? story datasets; real-data benchmarks (planned)
5. User-facing checks Can users tell when their analysis is unreliable? summary() diagnostics, graphdml.diagnostics

Layer 2: correctness (every commit)

  • Reductions to independent implementations.
  • With an edgeless graph and no exposure, estimates and standard errors match DoubleML's DoubleMLPLR (both scores, same folds) to 1e-8.
  • The partialling-out covariance equals statsmodels' HC0 covariance of the final regression.
  • Oracle nuisances. Plugging in the true nuisances recovers the truth.
  • Metamorphic properties.
  • Scaling Y scales the effects.
  • Shifting T leaves them unchanged.
  • Adding a function of X to Y is absorbed.
  • Two disjoint copies of a graph give the same estimate with SE / √2.
  • Relabelling nodes changes nothing.
  • Focal sets. Dependency sets are pairwise disjoint and maximal; for one-hop exposure, pairwise distance ≥ 3, and with a two-hop exposure, distance ≥ 5. Checked across ER, BA and SBM graphs.
  • Robustness claims. Each score's consistency or bias under deliberately wrong nuisances matches the derivation in methodology §4, including the attenuation factor.

Layer 3: statistical validity

Coverage criterion

For each cell (DGP × nuisance type × topology × effect), nominal 95% intervals must cover at 95% up to Monte Carlo error:

  1. Screen: 300 seeds; pass if coverage ∈ 0.95 ± 3·√(0.95·0.05/300) = [0.912, 0.988].
  2. Confirm: any cell outside the screening band is rerun with 2,000 fresh seeds; it passes if coverage ∈ 0.95 ± 3·√(0.95·0.05/2000) = [0.935, 0.965].

The release gate requires every cell to pass at stage 1 or stage 2. Seeds are fixed, so results are reproducible.

Revision log. Both changes below were made after seeing results, so we record them in full.

  1. The original criterion was coverage ∈ [0.925, 0.975] at 300 seeds. That band is about ±2.3 Monte Carlo SEs per cell, so with 18 cells several false failures are expected. The first run (partialling-out default) had three cells at 0.917–0.920. Rerunning the ER oracle cell with 2,000 fresh seeds gave 0.942 (SE/SD 0.98).
  2. We widened the screening band to ±3 Monte Carlo SEs. The next run (IV-type default) flagged one cell: BA, linear nuisances, peer effect, at 0.907. Its 2,000-seed rerun gave 0.940.
  3. We then added the confirmation stage. The final run flagged the same cell at stage 1, and it passed at stage 2 (0.939 direct, 0.944 peer).

Follow-up (3,000 fresh seeds, oracle nuisances, partialling-out). ER graphs cover at the nominal rate, both with about 450 focal nodes (0.950 / 0.954) and about 1,800 (0.950 / 0.947). The Barabási–Albert graph with about 310 focal nodes covers at 0.941 / 0.944, about two Monte Carlo SEs below 0.95. Standard small-sample corrections barely change this: HC1 adds ≤0.1 points, t critical values ≤0.1, and HC3 ≤0.2. So the gap is not explained by the small-sample bias of HC0. It appears specific to hub-heavy graphs, and its cause is not yet known. It is small (under one point) and is tracked as an open question.

Required evidence per release

Benchmark Criterion
benchmarks/coverage.py (oracle and correctly specified nuisances; ER, BA, SBM; continuous and binary T) coverage criterion above
benchmarks/design_choices.py (default ML nuisances on four datasets) default configuration: |relative bias| ≤ 5% and coverage ≥ 0.90 at 100 seeds (criterion set after the first run, which also chose the defaults; future releases must meet it unchanged)
pytest -m slow the ER coverage cells, as a CI-sized version of the gate

Scenarios built to break the method

make_homophily_trap violates no-unobserved-confounding on purpose. The estimator should be wrong there, and the criterion is that negative_control_test flags it. Planned additions: two-hop interference, a misspecified exposure map, and dense graphs where the focal set is tiny.

Layer 4: realism (in progress)

  • Story datasets with realistic structure: spatial, preferential attachment, communities.
  • Planned: semi-synthetic Cora/Pubmed (real topology, simulated outcomes), and a benchmark against a randomized network experiment in which an observational subsample is analysed and compared with the experimental estimate.

Layer 5: user-facing checks

graphdml.selftest() lets anyone re-run a signal check on their own machine: planted effects versus a null twin, against fixed criteria (see the README).

summary() prints diagnostics and the identifying assumptions with every fit, and warns on small focal sets, weak overlap, collinear residuals and isolated focal nodes. The falsification checks in graphdml.diagnostics are tested to pass on clean data and to flag the violations they target.

Running everything

pip install -e ".[dev]"
pytest                       # layer 2 (~30 s)
pytest -m slow               # CI-sized coverage gate (~1 min)
cd benchmarks
python coverage.py           # full coverage gate (minutes, parallel)
python design_choices.py     # default-configuration evidence