{"id":"a1cc5a79-d187-433e-af57-880766da8084","arxiv_id":"2607.10456","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"Integrating adjacency, orientation, and gap background knowledge during PC, SNAP, MB-by-MB, LDECC, and LOAD reduces CI tests and improves causal-effect estimates under standard assumptions.","lead":"This paper shows how to fold expert knowledge about edges into causal discovery while the algorithm is still searching, not only after it finishes. That cuts the number of independence tests and often improves effect estimates on large graphs.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper's strongest claim is carefully scoped: under oracle CI tests and consistent direct-relation BK, the listed BK-aware algorithms are sound (and, except LDECC-BK, complete) for their targets, and empirically reduce CI tests/runtime while improving or preserving intervention distance (Thms. 3.1–3.4, Fig. 1). The consistency premise is stated up front, used uniformly in the proofs (App. C), and ablated (App. J). The only non-complete method (LDECC-BK) is explicitly flagged (Cor. 3.2, Ex. C.4). Gap handling is the main technical novelty relative to existing libraries and is justified by counter-examples (App. D) plus the delayed-search construction. Post-processing baselines are compared (App. H) and shown to be computationally inferior once BK is non-trivial. No derivation gap, circularity, or untested regime appears that would overturn the ACCEPT verdict. The concrete test above is a modest robustness check, not a refutation condition.","tokens_in":42541,"tokens_out":506,"duration_ms":7779,"concrete_test":"Re-run the imperfect-BK ablation of Fig. 14 / App. J with SNAP(∞)-BK under a 5% (instead of 10%) orientation-error rate at BK rate 0.5; if runtime remains within a small constant factor of the zero-error baseline and intervention distance does not rise above the zero-BK level, residual sensitivity is modest and the scalability claim holds under mild expert noise.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (consistent BK) is already the paper's explicit premise for all main theorems (Thms. 3.1–3.4, Sec. 2) and is stress-tested in App. J with imperfect-BK ablations that show the expected degradation (especially SNAP(∞)-BK runtime and intervention distance). The central claim is therefore conditional on that premise, which the paper states clearly and does not overclaim beyond. Gap-handling (delayed MissingSepsets-BK rather than naive fixedGaps removal) is motivated by concrete library failures (App. D) and is covered by the soundness proofs. No internal inconsistency, missing case, or unacknowledged failure mode undermines the algorithmic or empirical claims as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper develops a framework for integrating background knowledge (BK) about direct causal relations (adjacencies, orientations, and gaps) into the causal discovery process itself, rather than only as post-processing. It focuses on scalable methods that recover only relevant subgraphs or local structure. The authors instantiate the framework for PC, SNAP(k)/SNAP(∞), MB-by-MB, LDECC, LOAD, and two Markov-blanket algorithms (Grow-Shrink, Total Conditioning). Core design choices include skipping CI tests for known adjacencies, restricting candidate separators to possible parents under BK, and delaying (rather than naively removing) known gaps so that separating sets remain well-defined for v-structure orientation. Under oracle CI tests and consistent BK they prove soundness for all variants and completeness for all except LDECC-BK (Thms. 3.1–3.4, Cor. 3.1–3.2, App. C). Experiments on Erdős–Rényi graphs and bnlearn networks show reductions in CI tests and runtime, with improved or preserved intervention distance as the BK rate rises (Fig. 1, Apps. G–K), plus ablations on BK type, imperfect BK, and post-processing baselines.","tokens_in":42722,"tokens_out":926,"duration_ms":20570,"significance":"The work addresses a genuine practical bottleneck: constraint-based discovery becomes expensive at scale, yet expert or experimental BK is often available and currently under-used during search. The technical contribution is concrete and reusable—shared subroutines (SkelStep-BK, MissingSepsets-BK, PossPa, PossMB) plus algorithm-specific adaptations that avoid known failure modes of library implementations (App. D). Soundness/completeness proofs with counter-examples for incorrect designs (Ex. C.1–C.4), reproducible code, and multi-metric evaluation (CI counts, time, intervention distance, SHD for global methods) strengthen the claim. The imperfect-BK ablations (App. J) and post-processing comparisons (App. H) make the scope of the claims transparent. If the results hold, the framework is immediately useful for practitioners who already run PC/SNAP/local methods and have partial edge knowledge.","major_comments":[],"minor_comments":[{"comment":"In Sec. 3.1 the definition of PossPa_G(X,B) is given inline; a numbered equation would make later references (e.g., the adjusted PossPa* in Eq. (1) for MB-by-MB) cleaner.","section":null},{"comment":"Fig. 1 packs five algorithms × three data regimes; the caption and legend are dense. A short table of relative CI-test reductions at BK rate 0.5 would help readers extract the main quantitative message.","section":null},{"comment":"App. E.2 (FCI-BK) is preliminary and correctly labeled as such; a one-sentence pointer in the main conclusions that latent-variable completeness remains open would set expectations more clearly for readers who skip the appendix.","section":null},{"comment":"A few typos: “SkelStep-BK” vs “SkelStep” consistency in Alg. 4 line 5; “WaiList” in Ex. C.3; “or all CI tests” (missing “f”) in Sec. 5.","section":null},{"comment":"Related work could briefly note how the delayed-gap strategy differs from fixedGaps in pcalg/causal-learn/pgmpy (already illustrated in App. D) so that the novelty relative to existing library options is explicit in the main text.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is solid, well-scoped, and ready for acceptance. The reader’s and skeptic’s assessments align with mine: the consistent-BK premise is stated and stress-tested; no load-bearing error remains. Fit for a methods-oriented ML/stats venue is good."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a clean methods paper that does what it claims. The real novelty is not inventing background knowledge for causal discovery—Meek, Perković, tetrad, tPC, and the libraries already do pieces of that—but a unified, careful treatment of gaps (delay MissingSepsets-BK instead of naive fixedGaps removal) plus systematic integration into scalable/local algorithms (PC-BK, SNAP-BK, MB-by-MB-BK, LDECC-BK, LOAD-BK, GrowShrink-BK) with soundness/completeness proofs and concrete counterexamples for the wrong designs (Ex. C.1–C.4, App. D). That gap handling is the part that actually fixes real library bugs.\n\nWhat they do well: assumptions are stated up front (Markov, faithfulness, no latents in the main results, consistent B). Theorems 3.1–3.4 and the appendix proofs are careful; they show where naive parent-pruning or early pruning breaks SNAP and MB-by-MB and fix it. Experiments measure the right things for these algorithms (CI count, wall time, intervention distance on held-out data) across oracle/Fisher-Z/G², synthetic ER graphs, and bnlearn nets, with ablations on BK type, post-processing baselines, and imperfect BK. The gains are real: fewer tests, often better or equal effect estimates as BK rate rises, and some graphs (ARTH150) only become runnable once BK is used during search.\n\nSoft spots, in proportion: the main theorems assume consistent B; App. J shows SNAP can get much slower and intervention distance degrades under noisy BK, so the scalability claim is conditional. LDECC-BK is only sound, not complete, for orientations (they say so). Latent-variable extension is preliminary (App. E.2). None of this is hidden or load-bearing for the stated claims.\n\nThis is for people who run constraint-based discovery on hundreds of variables and already have some edge knowledge. Math, data, and citations look solid; self-cites are to the methods being extended. I would send it to referees. Worth engaging if you care about practical causal discovery at scale.","headline":"Solid engineering paper: careful during-search BK (especially delayed gap handling) for PC/SNAP/local methods, with proofs and clear CI/runtime gains under consistent BK.","tokens_in":43333,"tokens_out":561,"would_cite":true,"duration_ms":10292,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Background knowledge used during causal discovery can cut CI tests by an order of magnitude while improving effect estimates.","keywords":["causal discovery","background knowledge","PC algorithm","SNAP","Markov blanket","MPDAG","conditional independence tests","local causal discovery"],"falsifier":"Run the same suite of algorithms on graphs with deliberately injected BK errors (as in the paper’s own App. J) and check whether the claimed reductions in CI-test count and intervention distance still appear once the error rate exceeds roughly 10–20 percent.","tokens_in":43460,"feed_emoji":"🔗","tokens_out":548,"duration_ms":9386,"temperature":0.7,"pith_summary":"Causal discovery from data alone becomes expensive as the number of variables grows, and most pipelines only apply expert knowledge after the fact to tidy the learned graph. This paper shows that knowledge of which edges exist, which are missing, and which are oriented can be injected into the search itself, pruning candidate conditioning sets and skipping known adjacencies. The authors build this idea into both global algorithms (PC, SNAP) and local algorithms that recover only the structure around a few targets (MB-by-MB, LDECC, LOAD), plus Markov-blanket discovery. Under oracle conditional-independence tests and consistent knowledge they prove the modified procedures remain sound and, with one exception, complete. Empirically, both the number of tests and wall-clock time fall as more knowledge is supplied, while the accuracy of downstream causal-effect estimates stays the same or improves. The practical payoff is that graphs with hundreds of variables become tractable once modest expert constraints are available.","feed_headline":"Expert edge knowledge cuts causal-discovery tests by 10x","feed_subtitle":"Injecting adjacency and orientation constraints during search, not after, speeds algorithms and sharpens effect estimates","key_machinery":"The three operating principles (skip known adjacencies, restrict separators to possible parents given the current skeleton and BK, and search for separators of known gaps only after the first skeleton pass) together with the b-possible-ancestral pruning rule that lets SNAP keep only the variables still needed for the targets.","core_discovery":"When background knowledge about direct causal relations is used inside the discovery loop—skipping known adjacencies, restricting candidate separators to possible parents, and delaying gap tests until the skeleton is sparse—the resulting algorithms recover the same (or a correctly restricted) MPDAG or local structure while performing substantially fewer conditional-independence tests.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Expert edges mid-search cut causal-discovery CI tests 10x","Background knowledge inside the loop shrinks discovery test load","Known adjacencies during search cut tests and sharpen MPDAG recovery","Inject constraints early to skip separators and delay gap tests","Utilizing edge knowledge in discovery reduces compute, improves structure"],"cache_read_input_tokens":32896,"weakest_assumption_plain":"The supplied background knowledge never contradicts the true causal graph; if it does, edges may be kept or mis-oriented and some algorithms become slower rather than faster.","fun_headline_variants_meta":{"raw":{"variants":["Expert edges mid-search cut causal-discovery CI tests 10x","Background knowledge inside the loop shrinks discovery test load","Known adjacencies during search cut tests and sharpen MPDAG recovery","Inject constraints early to skip separators and delay gap tests","Utilizing edge knowledge in discovery reduces compute, improves structure"]},"model":"grok-4.5","effort":"low","cost_usd":0.00654,"raw_usage":{"total_tokens":1538,"prompt_tokens":672,"num_sources_used":0,"completion_tokens":87,"cost_in_usd_ticks":65400000,"prompt_tokens_details":{"text_tokens":672,"audio_tokens":0,"image_tokens":0,"cached_tokens":0},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":779,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":672,"tokens_out":87,"duration_ms":10369,"temperature":1.0,"reasoning_tokens":779,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T11:34:07.396478+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Run the same suite of algorithms on graphs with deliberately injected BK errors (as in the paper’s own App. J) and check whether the claimed reductions in CI-test count and intervention distance still appear once the error rate exceeds roughly 10–20 percent.","supporting_citations":[],"review_version":1}