AI referee report
on “Minimax Precision for Total Treatment Effects with Partially Observed Interference Networks”
The verified precision characterization is substantial and its headline claims are faithful, but extensive duplication and an underdeveloped explanation of the information mechanism require a substantial editorial revision.
Summary
The paper establishes matching minimax squared-risk bounds for a population total treatment effect under bounded additive interference, half-Bernoulli assignment, and independently retained network arrows. Its strongest contribution is the complete-record converse, which accounts for the information carried jointly by network labels, assignments, and noiseless outcomes. The abstract, consistency characterization, and collection implications accurately reflect the verified results and their conditions. Publication would be warranted after reorganizing the manuscript around its principal contribution, strengthening the conceptual explanation, and resolving several notation and positioning issues.
Strengths
- The characterization is uniform across population size, degree, and retention, including both retention endpoints and an exact consistency criterion.
- The converse covers every measurable randomized estimator using the complete observed record, giving the attainable score a substantive optimality interpretation.
- The manuscript carefully preserves the coefficient envelope, directed degree conventions, compulsory own-treatment coordinates, and fixed-schedule interpretation.
- The closest network-information comparisons engage actual rates and conditions, and the platform discussion accurately describes a prospective calibrated collection experiment.
Findings
The manuscript repeatedly defines and proves essentially the same central objects and conclusions. The upper rule, attaining rule, and precision pair repeat the estimator; the observed-record frontier and explicit frontier repeat the risk and consistency characterization; the block-testing theorem and nonlocal-testing theorem repeat the canonical-design comparison. The deferred proofs then reproduce substantial portions of the frontier argument. This obscures the contribution and makes the paper much longer than its mathematical content requires.
Suggested fix
Use one principal frontier theorem, one definition of the attaining estimator, and one block-testing theorem. Present explicit constants, endpoints, and the degree-two specialization as short deductions or remarks referencing those results through cleveref. Give each substantive argument once, and replace repeated definitions and proofs with precise cross-references. Condense the introduction and collection discussion so each develops a distinct aspect of the result.
The central lower-bound mechanism is introduced mainly through technical names: 'Translation bounds, all-order Walsh energy control, and hidden-allocation contraction yield the testing comparison.' Readers receive considerably less explanation of why a source's association is revealed with probability 1-(1-q)^d, why repeated recipient responses matter, and how unknown fixed baselines preserve ambiguity despite noiseless outcomes. These points explain the substantive novelty of the complete-record converse.
Suggested fix
Add a compact conceptual account of the hard block family before listing its analytic tools. Explain that each source reaches d recipients, any retained outgoing arrow identifies its recipient block, assignments constrain hidden allocations through a global treated count, and the baseline prior selects fixed schedules before the experiment. Connect this mechanism explicitly to the revelation probability and the degree–retention scale, using the existing verified construction.
The fixed-schedule experiment definition sets P_{theta,q}=Law(O,xi), whereas subsequent mixture notation treats fixed-schedule laws as laws of O and then appends an independent seed. The distinction between a record law and its seeded extension is therefore inconsistent across the exposition. This is a notation problem surrounding the verified results, rather than a challenge to their conclusions.
Suggested fix
Introduce a record marginal P^O_{theta,q}=Law(O) and a seeded law P^O_{theta,q} tensor Uniform[0,1], or adopt equivalent consistently distinguished notation. Define block and two-prior mixtures using the record marginal and append the seed exactly once when evaluating randomized estimators. Apply the convention throughout.
The discussion gives useful comparisons with SNIPE and incomplete-network methods, but the estimator lineage jumps directly to SNIPE. Inverse-inclusion correction also belongs to the Horvitz–Thompson tradition, and additive interference estimation has a broader linear-unbiased and representer-based lineage. Engaging these connections would make the attribution of the observable procedure and the distinction between estimator construction and the new minimax converse more precise.
Suggested fix
Add a concise paragraph crediting inverse-inclusion weighting and relevant additive or linear-functional interference estimation, including the pertinent Sussman and Harshaw–Sävje–Wang frameworks. Check their information sets and response restrictions before stating a comparison. Locate the paper's contribution in the joint degree–retention frontier and complete-record converse, while preserving its existing credit to SNIPE and the supplied-graph benchmark.
The attaining rule uses d to evaluate its envelope and choose its branch, but the observation-design exposition explicitly identifies q as known without equally clearly explaining the estimator's access to an admissible degree bound. A retained graph reveals sampled degrees, so readers implementing the planning calculation need to understand what value of d the guarantee assumes.
Suggested fix
State explicitly that n, q, and a valid common upper bound d on the true in- and out-degrees are supplied to the rule. Explain that the guarantee applies for any supplied bound satisfying the schedule restrictions and that the envelope is evaluated at that bound. Include this information alongside the estimator and collection interpretation.
Questions for the authors
- Can the non-archival supplied-graph research note be identified by a stable version and accessible location, with a reader-facing theorem or page locator alongside its internal theorem label?
- Which parts of the supplied-graph comparison are credited earlier results, and which parts are independently established here? A concise statement of this relationship would sharpen the novelty account.
Review history
| Round | Date | Score | Findings |
|---|---|---|---|
| 1 | 3 Oct 2026 | 6.8 | 7 |
| 2 | 3 Oct 2026 | 7.3 | 5 |
| 3 · current | 3 Oct 2026 | 7.1 | 5 |
Every referee draw is kept: scores are noisy, so the history is shown rather than only the last or the best pass.
Read against paper.tex sha256 a1c7b20d1493.