{"id":"e5c02d77-0c7e-4dda-9d34-9e46732cee59","arxiv_id":"2606.05919","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"For linear-fractional leave-set-out estimands, most influential set selection reduces to a one-parameter sequence of top-k problems solved efficiently by Dinkelbach's algorithm with global optimality for fixed residuals.","lead":"This paper presents an algorithm to identify the most influential size-k data subsets for certain statistical estimands by reducing the problem to a sequence of top-k selections solvable via Dinkelbach's method. A generalist might read it to see how influence analysis in large datasets can become computationally tractable for linear-fractional objectives.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest-assumption diagnosis matches the scoping of the claim; the reduction and algorithmic guarantees rest on that hypothesis, and the paper states the required conditions for the estimated-nuisance case. No additional load-bearing gap is visible.","tokens_in":1646,"tokens_out":270,"duration_ms":15673,"concrete_test":"Take the explicit formula for the oracle-residualized partial-linear estimand, compute the leave-set-out difference directly, and verify that the resulting expression is exactly linear-fractional in the indicator vector of the removed set.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is explicitly scoped to estimands whose leave-set-out effects are linear-fractional. Under that structural hypothesis the reduction to a one-parameter family of top-k problems is the standard application of Dinkelbach iteration to a ratio objective; finite termination follows because the feasible set is finite and each iteration strictly improves the auxiliary parameter. The O(n) per-iteration cost is consistent with linear-time selection once scores are formed. The subsequent claims about oracle-residualized partial-linear models and first-order approximation under nuisance estimation are likewise conditioned on explicitly named stability and separation assumptions. No internal inconsistency or unsupported inference appears in the argument as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper claims that for estimands with linear-fractional leave-set-out effects, identifying most influential sets (MIS) of size k reduces to a one-parameter sequence of top-k problems. Dinkelbach's method then yields an algorithm with O(n) per-iteration cost and finite termination. For fixed residualized inputs the procedure returns a globally optimal set for the univariate ratio objective (including the oracle-residualized partial-linear model). With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective, with exact recovery under an additional separation condition. Simulations and applications are reported to recover exact MIS that were previously computationally inaccessible.","tokens_in":1774,"tokens_out":332,"duration_ms":33572,"significance":"If the central claims hold, the work converts an intractable combinatorial search into a tractable parametric sequence of linear-time selection problems under an explicitly scoped structural hypothesis. The application of Dinkelbach iteration, the finite-termination argument on a finite feasible set, and the explicit stability/separation conditions for the nuisance-estimation case constitute clear algorithmic and theoretical contributions. The extension to oracle-residualized partial-linear models and the empirical demonstration of exact recovery further strengthen the practical utility for influence diagnostics in statistical and machine-learning settings.","major_comments":[],"minor_comments":[{"comment":"The abstract refers to 'uniform denominator and generated-score stability' without an inline pointer to the precise definition or assumption statement; a parenthetical reference to the relevant section would improve immediate readability.","section":"Abstract"}],"recommendation":"accept","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their thorough and positive review. We are grateful for the recommendation to accept and for the recognition of the algorithmic and theoretical contributions, including the reduction to a parametric sequence of top-k problems, the finite-termination argument for Dinkelbach iteration, and the stability conditions for the nuisance-estimated case.","responses":[],"tokens_in":1216,"tokens_out":83,"duration_ms":4843,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that for estimands whose leave-set-out effect is linear-fractional, the search for the size-k set that changes the target most reduces to a one-parameter family of top-k problems solved by Dinkelbach iteration. That gives an exact global optimum for the oracle-residualized case and an approximation result under nuisance estimation when stability and separation hold.\n\nWhat the paper does cleanly is state the structural assumption up front, apply the standard fractional-programming trick, and note that finite termination follows from the finite feasible set plus strict improvement each step. The O(n) per-iteration claim is consistent once scores are available. The extension to partial-linear models and the first-order orthogonal-score approximation under uniform denominator stability is a reasonable incremental step.\n\nThe central limitation is the linear-fractional requirement itself; many common estimands will not satisfy it, so the algorithm simply does not apply. The abstract supplies no derivation or proof sketch, so the tightness of the optimality and termination arguments cannot be checked from the summary alone. Simulations are referenced without reported error rates or runtime comparisons, which leaves the practical gain somewhat underspecified.\n\nThis is for statisticians and econometricians who already work with influence or sensitivity diagnostics on moderately large samples and need an exact method for a restricted but useful class of estimands. A reader who needs to audit influential groups rather than single points would find the reduction useful.\n\nThe work is scoped and the algorithmic claim looks standard once the assumption is granted, so it is worth sending to referees.","headline":"The paper reduces most-influential-set search to a Dinkelbach sequence of top-k problems when leave-set-out effects are linear-fractional, with finite termination and O(n) per iteration.","tokens_in":2242,"tokens_out":395,"would_cite":false,"duration_ms":13668,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"For estimands with linear-fractional leave-set-out effects, most influential set selection reduces to a one-parameter sequence of top-k problems.","keywords":["most influential sets","leave-set-out effects","Dinkelbach's method","top-k problems","orthogonal scores","partial linear model","influence analysis","statistical estimands"],"falsifier":"On a small dataset where the estimand lacks linear-fractional leave-set-out effects, brute-force enumeration of all k-subsets would yield a different set than the one returned by the algorithm.","tokens_in":2549,"feed_emoji":"","tokens_out":671,"duration_ms":17755,"temperature":0.7,"pith_summary":"The paper shows that finding size-k subsets whose removal maximally alters a target estimand is normally intractable due to the binomial number of candidates. When the leave-set-out effect takes a linear-fractional form, the search collapses to a one-parameter family of top-k selection tasks. Dinkelbach's method then solves the resulting univariate ratio problem with linear cost per iteration and guaranteed finite termination. A reader would care because the approach yields globally optimal sets for fixed-residual partial linear models and approximates the orthogonal-score objective under estimated nuisances when stability conditions hold. Simulations confirm that previously inaccessible exact recoveries become feasible.","feed_headline":"Linear-fractional effects turn influential-set search into top-k sequence","feed_subtitle":"Dinkelbach's method solves it with linear cost per iteration and finite termination for qualifying estimands.","key_machinery":"The linear-fractional structure of leave-set-out effects, which reduces MIS selection to a one-parameter sequence of top-k problems solved by Dinkelbach's method.","core_discovery":"For estimands with linear-fractional leave-set-out effects, MIS selection reduces to a one-parameter sequence of top-k problems. Dinkelbach's method yields an algorithm with O(n) cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition.","pith_inferences":["The reduction may extend to other fractional objectives in causal inference if they admit an analogous structural property.","The approach could scale influence diagnostics to larger n in settings where residualization is cheap.","Checking the separation condition on real data would indicate when exact recovery is practically reliable."],"forward_implications":["The algorithm has O(n) cost per iteration and finite termination.","For fixed residualized inputs, it returns a globally optimal set for the univariate ratio objective.","With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective.","Exact set recovery follows under a separation condition.","Simulations and applications recover exact MIS that were previously computationally inaccessible."],"fun_headline_variants":["Linear-fractional effects reduce MIS to top-k sequence","Dinkelbach method finds influential sets in O(n) per iteration","MIS selection simplifies to one-parameter top-k problems","Influential sets via Dinkelbach on linear-fractional effects"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The target estimand must possess linear-fractional leave-set-out effects.","fun_headline_variants_meta":{"raw":{"variants":["Linear-fractional effects reduce MIS to top-k sequence","Dinkelbach method finds influential sets in O(n) per iteration","MIS selection simplifies to one-parameter top-k problems","Influential sets via Dinkelbach on linear-fractional effects"]},"model":"grok-4.3","cost_usd":0.006372,"raw_usage":{"total_tokens":2963,"prompt_tokens":613,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":63724500,"prompt_tokens_details":{"text_tokens":613,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2283,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":613,"tokens_out":67,"duration_ms":13979,"temperature":1.0,"reasoning_tokens":2283,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T23:48:26.510752+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"On a small dataset where the estimand lacks linear-fractional leave-set-out effects, brute-force enumeration of all k-subsets would yield a different set than the one returned by the algorithm.","supporting_citations":[],"review_version":1}