{"id":"5accdcfa-6614-4132-81a2-f29708eaa653","arxiv_id":"2606.20514","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A hypergraph variable selection procedure with a generalized FDR for set-based hypotheses achieves higher power than prior methods while maintaining FDR control.","lead":"The paper proposes a hypergraph-based variable selection method that generalizes false discovery rate control to hypotheses defined on sets of predictors. This could improve power when predictors have overlapping or unstructured correlations compared to hierarchical clustering approaches.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's UNVERDICTED verdict stems directly from the absence of the full text. No additional load-bearing concern can be formulated without the technical content, so the assessment remains unchanged.","tokens_in":1534,"tokens_out":222,"duration_ms":18423,"concrete_test":"Obtain the full manuscript and verify whether the proof of FDR control (likely in the methods or theory section) holds under the stated conditions on the hypergraph and generalized FDR; if the control proof is valid and simulations confirm power gains, the central claim stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract states that a generalized FDR for set-based hypotheses and a hypergraph selection method achieve higher power while preserving rigorous FDR control. Without access to the full manuscript (definitions of the generalized FDR, hypergraph construction, selection algorithm, theoretical proofs, or simulation details), no internal inconsistency, hidden assumption, or correctness risk can be isolated. The reader's weakest_assumption cannot be stress-tested further from the given information.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces a generalized false discovery rate (FDR) definition for hypotheses defined on sets of predictors and proposes a hypergraph-based variable selection procedure. Building on prior work with hierarchically clustered groups, the method targets overlapping predictor sets for less structured correlations and claims to deliver higher power than existing approaches across diverse settings while preserving rigorous FDR control.","tokens_in":1587,"tokens_out":283,"duration_ms":14699,"significance":"If the generalized FDR admits a valid selection procedure and the hypergraph construction accurately captures relevant dependencies, the work would strengthen FDR-controlling variable selection for high-dimensional data with complex dependence, extending group-based methods to more flexible overlapping structures.","major_comments":[],"minor_comments":[{"comment":"The abstract states the central claim but provides no indication of the precise definition of the generalized FDR, the hypergraph construction algorithm, or the theoretical guarantee; these details are needed to assess whether the power gain is achieved without compromising control.","section":null},{"comment":"No simulation design, baseline comparators, or dependence scenarios are described, making it impossible to evaluate the 'diverse settings' claim or reproducibility of the higher-power result.","section":null}],"recommendation":"uncertain","confidential_remarks":"Review performed from abstract and reader notes only; full manuscript text was referenced but not supplied in the query, preventing section-specific technical assessment."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their review of our manuscript on hypergraph variable selection with generalized FDR control. We appreciate the recognition of the potential significance in extending group-based methods to overlapping structures. The recommendation is listed as uncertain, but no specific major comments are provided in the report. We are prepared to address any detailed concerns if they are supplied.","responses":[],"tokens_in":1012,"tokens_out":87,"duration_ms":12062,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main move here is generalizing the authors' earlier hierarchical group selection to hypergraphs so that overlapping sets of predictors can be handled under a generalized false discovery rate. The abstract positions this as a way to recover more power when correlations do not fit a nested structure.\n\nThe useful part is the recognition that tree-based groups are restrictive and that a hypergraph formulation could better match some dependence patterns. That is a direct response to a known limitation in group FDR methods.\n\nThe soft spots are clear from the given text. No definition of the generalized FDR appears, no description of how the hypergraph is built from the data, no algorithm for selection, and no theoretical argument or simulation that would show control is maintained while power increases. The central claim therefore rests on unexamined assumptions about hypergraph construction and the validity of the new rate. Without those pieces it is not possible to tell whether the procedure is sound or merely stated.\n\nThis is for people working on FDR procedures for high-dimensional selection with dependence. A reader already following the authors' prior papers might want to see the full development, but the current version does not yet supply enough to judge its contribution.\n\nI would send it for peer review if the full manuscript contains the missing definitions, proofs, and checks; the direction addresses a real gap even if the present evidence is thin.","headline":"Extends their hierarchical clustering FDR work to hypergraphs for overlapping predictor groups but the abstract supplies no definitions, proofs, or results to check the higher-power claim.","tokens_in":2032,"tokens_out":350,"would_cite":false,"duration_ms":14291,"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":"Hypergraph-based selection on predictor sets raises power while controlling false discovery rate.","keywords":["false discovery rate","variable selection","hypergraph","multiple testing","predictor dependence","statistical power","group selection"],"falsifier":"A simulation in which the supplied hypergraph mismatches the true dependence pattern and the procedure returns a set of discoveries whose empirical false discovery proportion exceeds the nominal target.","tokens_in":2431,"feed_emoji":"","tokens_out":511,"duration_ms":12504,"temperature":0.7,"pith_summary":"Variable selection methods that control the false discovery rate often lose power when predictors have complex dependence structures. Earlier work used hierarchically clustered groups to recover some power, but this works less well when correlations lack clear hierarchical structure. The paper defines a generalized false discovery rate for hypotheses on sets of predictors and introduces a hypergraph-based procedure that selects overlapping groups. The resulting method delivers higher power across a range of settings while still guaranteeing rigorous false discovery rate control.","feed_headline":"Hypergraph selection raises power while controlling false discoveries","feed_subtitle":"Generalized FDR defined on predictor sets enables overlapping groups for unstructured correlations.","key_machinery":"Hypergraph-based selection procedure that operates on a generalized false discovery rate defined for sets of predictors.","core_discovery":"We introduce a generalized false discovery rate for hypotheses defined on sets of predictors and propose a hypergraph-based selection method. This approach achieves higher power across diverse settings while preserving rigorous false discovery rate control.","pith_inferences":["The same generalized false discovery rate idea could be paired with other graphical representations of dependence beyond hypergraphs.","In high-dimensional applications such as genomics the method may identify biologically meaningful overlapping groups that standard approaches miss.","Data-driven construction of the hypergraph from sample correlations could be explored as an extension."],"forward_implications":["Power loss is reduced for variable selection under complex predictor dependence.","Overlapping predictor sets become usable when correlations lack hierarchical structure.","The generalized false discovery rate remains controlled in the selected sets.","The procedure applies across a range of simulation and data settings without loss of the control guarantee."],"fun_headline_variants":["Hypergraph selection controls FDR on predictor sets","Generalized FDR extends to hypergraph variable selection","Hypergraph method for set-based FDR in variable selection","FDR-controlled selection via hypergraphs on overlapping groups"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The hypergraph can be specified so that it accurately encodes the relevant predictor dependencies and the generalized false discovery rate definition supports a valid selection procedure.","fun_headline_variants_meta":{"raw":{"variants":["Hypergraph selection controls FDR on predictor sets","Generalized FDR extends to hypergraph variable selection","Hypergraph method for set-based FDR in variable selection","FDR-controlled selection via hypergraphs on overlapping groups"]},"model":"grok-4.3","cost_usd":0.005525,"raw_usage":{"total_tokens":2552,"prompt_tokens":469,"num_sources_used":0,"completion_tokens":58,"cost_in_usd_ticks":55249500,"prompt_tokens_details":{"text_tokens":469,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2025,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":469,"tokens_out":58,"duration_ms":11056,"temperature":1.0,"reasoning_tokens":2025,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T15:59:30.628438+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A simulation in which the supplied hypergraph mismatches the true dependence pattern and the procedure returns a set of discoveries whose empirical false discovery proportion exceeds the nominal target.","supporting_citations":[],"review_version":1}