{"id":"3fb5e1ae-781a-4671-ae87-1acc2ac3ec79","arxiv_id":"2607.14814","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"After a multivariate change-point is detected, a grid-based or sample-splitting two-sample test determines whether a pre-specified block of coordinates changed, with Type I error bounded by α0+α1.","lead":"This paper proposes two statistical procedures for deciding which block of variables caused a detected change-point in a multivariate time series, while keeping false alarms under control. The methods target practitioners who need to explain detected breaks in sensor, medical, or financial data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Operational δn from calibrated C0=0.15 is not proven to satisfy Assumption 1, so the finite-sample level guarantee of Theorems 3 and 9 may not hold for the implemented procedure.","rationale":"I read the paper in good faith and find the conditional mathematical claims internally consistent. The proofs of Theorem 3 and Theorem 9 are valid under Assumptions 1–2 and 3–5 respectively: on the localization event, the oracle projected segments belong to the candidate grid and are i.i.d. under H0, so the product test is bounded by a single level-α1 test; the hold-out proof correctly exploits the independence of the inference set from the detection set. The load-bearing soft spot is the operationalization of Assumption 1: the value of δn used in the algorithm is obtained from an empirically calibrated constant C0=0.15 rather than from the proven conservative bound. The paper does not prove that this plug-in δn satisfies the high-probability localization requirement, and Appendix C only provides finite simulation evidence over a limited family of distributions and kernels. This is precisely the weakest assumption identified by the reader, and it is a legitimate concern because the central guarantee is conditional on an event that may not hold for the implemented procedure. A direct check of P(d∞>δ̂n)≤α0, or a sensitivity analysis of C0, would settle whether the concern lands. The reader's CONDITIONAL verdict remains appropriate; no further adjustment is needed.","tokens_in":37407,"tokens_out":11257,"duration_ms":95244,"concrete_test":"In the simulation pipeline of Section 4.3.1 with n=500, jump=0.3, d=5, κ⋆=2, 10,000 repetitions, compute the KCP estimate τ̂ and the operational δ̂n from C0=0.15 using the plug-in Δ̂² and Λ̂. Record the maximum localization error d∞(τ⋆,τ̂)=|τ⋆−τ̂|. Check whether at least 95% of repetitions satisfy d∞(τ⋆,τ̂)≤δ̂n (i.e., empirical P(Ωα0)≥0.95). If the frequency is below 1−α0, Assumption 1 fails for the calibrated δ̂n, and the theoretical level guarantee does not apply to the implemented GTST/hold-out procedures. Additionally, repeat with C0∈{0.05,0.15,0.5,1.48,14.8,148} and verify that empirical Type I error on Block 2 remains ≤α0+α1; if it increases with C0, the guarantee is sensitive to misspecification of δn.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central guarantee is conditional on Assumption 1: on an event Ωα0 with probability ≥1−α0, the detector must output κ⋆ change-points with localization error ≤δn. The operational pipeline (Section 4.3.1, Algorithm 1) does not use a proven δn. It replaces the constant 148 in the Garreau–Arlot bound with an empirically calibrated C0=0.15 (Appendix C) and computes δn := C0 κ⋆M²/Δ̂² (log(1/α0)+log n+1), where Δ̂ is a plug-in MMD estimate. No theorem shows that this data-driven δn satisfies P(d∞(τ⋆,τ̂)>δn)≤α0. The calibration study in Appendix C is finite and distribution-specific; it does not establish a valid high-probability localization event for the actual data-generating process. If the true localization quantile exceeds δn with probability >α0, then the event Ωα0 fails, and the bound α0+α1 in Theorems 3 and 9 is no longer justified. Because the simulations themselves use the calibrated δn, the reported Type I error near 0.05 may not reflect the worst-case guarantee, and the claim of valid error control is not established for the implemented algorithm.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes two post hoc procedures, GTST and hold-out, for attributing a detected multivariate change-point to one of two predefined coordinate blocks. The GTST procedure builds a grid of candidate segment pairs around estimated change-points and rejects the block-level null only if every local two-sample test rejects; the hold-out procedure splits the series into detection and inference sets and performs the local test only on the inference set. The main theoretical results, Theorems 3 and 9, claim that each block-level test controls the Type I error at level α0 + α1, where α0 is the localization failure probability and α1 is the nominal level of the local two-sample test, under Assumptions 1–5. The empirical section instantiates the local tests as MMD permutation tests and computes the operational localization radius δn using a calibrated constant C0 = 0.15 in place of the proven constant 148 from the Garreau–Arlot bound.","tokens_in":37769,"tokens_out":8792,"duration_ms":83160,"significance":"If the operational gap identified below is closed, the paper makes a useful contribution to post-selection inference for change-point attribution. The conditional results are clean: the error decomposition into a localization event and a two-sample testing event is elegant, and the hold-out treatment in the single-change-point case is correctly shown to require only independence, not localization. The grid-based product rule is a conservative but theoretically transparent device. The manuscript also provides code and reproducible simulation code, which is a strength. The central weakness is that the implemented algorithm does not provably satisfy the assumptions under which the theorems are stated.","major_comments":[{"comment":"The operational procedure replaces the proven constant 148 in the Garreau–Arlot localization bound with an empirically calibrated C0 = 0.15 and computes δn = C0 κ⋆ M² / Δ̂² (log(1/α0) + log n + 1), using a plug-in estimate Δ̂ of the minimal MMD jump. No theorem shows that this data-dependent δn satisfies P(d∞(τ⋆, τ̂) > δn) ≤ α0. Theorems 3 and 9 are explicitly conditional on Assumption 1, which requires a δn satisfying exactly this high-probability localization event. Because δn is random and may under-estimate the true localization error, the event Ωα0 may fail with probability greater than α0, and the level α0 + α1 is not guaranteed for the procedure as actually run in the simulations and real-data experiment. Appendix C is a finite calibration study over selected distribution families and dimensions; it does not establish a worst-case bound. This is load-bearing because the paper's ce","section":"Section 4.3.1, Algorithm 1 (definition of δn)"},{"comment":"The separability condition is checked using the plug-in estimate Λ̂τ, but Assumption 2 requires the true minimal spacing nΛτ⋆ > δ′n. If Λ̂τ over-estimates the true spacing, the procedure executes the multi-test grid despite being outside the regime of Lemma 1 and Theorem 3. The paper correctly notes in Remark 5 that Condition (2.3) cannot be checked directly, but it does not provide a valid alternative. For the hold-out method, Remark 7 explicitly acknowledges that if the spacing condition is violated, 'formal guarantees are lost' while the procedure is still applied. This means the theoretical level control applies only to an idealized version of the algorithms in which the true parameters are known; the practical algorithms need either a valid data-dependent check or a clearly stated limitation that the guarantee is conditional on a condition that is not verified.","section":"Algorithm 1, Step 3; Remark 5; Remark 7"},{"comment":"The abstract and conclusion state that the proposed procedures 'provide theoretical guarantees for Type I error control' without qualifying that the guarantees hold only under Assumptions 1–5, which are not established for the implemented operational pipeline using C0 = 0.15 and plug-in estimates. The statements should be softened to describe the guarantees as conditional on a valid localization event, or the operational procedure should be modified to use a proven conservative δn so that the unconditional claim is justified for the implemented algorithm.","section":"Abstract and Section 5"}],"minor_comments":[{"comment":"In Lemma 2, point 3, the restricted grid-set is denoted eE_i0,η (with a tilde) in the statement but the definition immediately before uses eEi0,η without the tilde. The notation should be harmonized.","section":"Section 3.1.2, Lemma 2"},{"comment":"The displayed formula for the theoretical condition has 'log(1/α0)+log n+1' in the numerator of a fraction that is not explicitly parenthesized. It should be written as Δ²/M² > 148 κ⋆(κ⋆+1)(log(1/α0)+log n+1)/(nΛτ⋆) to avoid ambiguity.","section":"Section 4.3.1"},{"comment":"The statement that the permutation test provides an exact non-asymptotic level α1 is correct only when ties are handled appropriately; the reference [27] is about stepdown methods and not specifically about permutation MMD tests. A more direct reference, such as the standard permutation testing literature, would be preferable.","section":"Remark 10"},{"comment":"Assumption 4 uses the notation bκdet before it is defined; it should be introduced as κ̂det for clarity.","section":"Assumption 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest about the calibration being empirical, but the gap between the theoretical guarantees and the implemented algorithm is substantial. The authors could either (i) present the C0 = 0.15 procedure as a heuristic and give the theoretical guarantee only for a version using the proven constant 148, or (ii) provide a valid self-normalized localization guarantee for a data-dependent δn. The conditional theory itself is sound, and the paper is worth revising rather than rejecting."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper up front: it gives a principled way to attribute a detected change-point to one of two predefined coordinate blocks while controlling Type I error, and the core theorems are sound under the stated assumptions. The catch is that the practical algorithm replaces a proven localization bound with an empirically calibrated constant, C0 = 0.15, and no theorem shows the resulting δn actually satisfies the high-probability localization event. So the implemented procedure's level guarantee is real only if that calibration happens to hold for your data.\n\nThe genuinely new piece is GTST, a grid-based construction that runs a two-sample test over a discrete family of candidate segments and rejects only if all local tests reject. Combined with the localization bounds from Garreau & Arlot, the product rule gives conservative Type I control. The hold-out method is a nice formalization of sample splitting for this problem, and the proof that the inference segments avoid contamination is clean. The simulations are extensive, cover mean, variance, covariance, sparsity, and multiple change-points, and the code is public. The empirical results support the qualitative claims.\n\nThe soft spot is exactly what the stress-test note flags: the operational δn is computed with C0 = 0.15 and plug-in estimates of κ*, Δ, and Λ. The calibration study in Appendix C is finite, distribution-specific, and does not establish a valid high-probability event for any new data-generating process. If the true localization quantile exceeds the calibrated δn with probability greater than α0, Theorems 3 and 9 no longer justify the bound α0+α1. The paper is honest about this being an empirical tuning parameter, but the abstract and introduction claim theoretical guarantees without this caveat, which overstates what is proven. The assumption that κ* is known is also strong, though the paper acknowledges it. The real-data example does not discriminate between methods, as the authors admit.\n\nOverall, the central argument holds up under its assumptions, and the gap between theory and implementation is clearly identified rather than hidden. This deserves a serious referee. The authors should be asked to either prove a valid data-driven δn, or reframe the contribution as conditional on a calibrated but unproven bound and report sensitivity to C0. I would cite this if I worked on change-point inference, and I'd bring it to a reading group focused on post-selection inference.","headline":"A useful framework for post hoc block attribution with valid guarantees under explicit localization assumptions, but the implemented version swaps in an empirically calibrated constant that is not proven to satisfy the assumptions, so the finite-sample level claim is conditional on unverified calibration.","tokens_in":38202,"tokens_out":1600,"would_cite":true,"duration_ms":16831,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62G10","62H15","62M10"],"pacs":[],"model":"deepseek-v4-flash","headline":"After a change-point is found, two tests identify which blocks of variables caused it while controlling false attribution.","keywords":["post hoc change-point attribution","multivariate time series","two-sample testing","kernel MMD","Type I error control","hold-out validation","grid-based testing","selection bias"],"falsifier":"Simulate weak mean shifts with small n, estimate δn exactly as in the paper, and record the empirical frequency of |τ̂ − τ*| > δn; if that frequency exceeds α0, then Assumption 1 is violated and the GTST Type I error can be checked to see whether it exceeds α0 + α1.","tokens_in":37326,"feed_emoji":"🎯","tokens_out":3343,"duration_ms":31593,"temperature":0.7,"pith_summary":"After an offline change-point detector finds a break in a multivariate time series, the analyst usually wants to know which coordinates drove it. This paper proves that two procedures — a grid-based test on the full series (GTST) and a hold-out split — control the probability of falsely blaming a block. Both procedures use a generic two-sample test (for instance, a kernel MMD test) on segments that are deliberately kept away from the uncertain estimated boundary. The stated guarantee is a bound α0 + α1: α0 for the chance the initial detector mislocalizes, α1 for the local test's false-alarm rate. The paper also shows, in simulations, that a naive test applied directly at the estimated change-point inflates false positives severely.","feed_headline":"A way to say which variables caused a detected change","feed_subtitle":"Two procedures control false attribution at level α0 + α1 after a change-point is found.","key_machinery":"GTST enumerates candidate pairs of pre/post segments on a grid of step η inside the δn-neighborhood of the estimated break, applies the chosen two-sample test to every pair, and rejects only if every local test rejects; this intersection device lets the paper avoid conditioning on a single random segment. The hold-out method assigns detection to a subset Idet and inference to the complement, so the test statistic is independent of the estimated change-point. The uncertainty radius δn and the minimal-spacing condition nΛτ⋆ > δ′n are what guarantee that the selected segments contain i.i.d. observations from a single distribution.","core_discovery":"The central claim is Theorem 3 and Theorem 9: under a localization event of probability at least 1 − α0 and a minimal spacing condition, GTST and the hold-out test are valid level-α0 + α1 tests of whether a predefined block's distribution changes at the candidate change-point. Validity comes from discarding an uncertainty window of width δn around each estimated change-point; on the high-probability localization event, the remaining segments lie inside true stationary segments, so the i.i.d. assumption of the local two-sample test is restored. GTST additionally checks a separability condition and, if it fails, conservatively retains the null. The hold-out instead runs detection on one subset","pith_inferences":["If the guarantees are correct, the common practice of testing directly on data-driven segments is not merely risky but theoretically invalid; the simulations quantify the inflation, with naive Type I error reaching about 0.25 for a small mean shift.","The hold-out argument suggests a natural extension to online change-point monitoring: detect on a buffer, then test on fresh observations, preserving valid attribution without needing a localization bound.","Because the empirical calibration of the localization radius uses a tuned constant, users should report the observed distribution of localization errors, not just the calibrated δn, to verify Assumption 1 in practice.","For weak signals where GTST's separability condition often fails, the hold-out is the safer default; once the signal is moderate, GTST is more powerful."],"forward_implications":["Any two-sample test with a valid level can be plugged into GTST or the hold-out without re-deriving the main guarantee.","For two blocks, the family-wise error rate is controlled at α0 + 2α1; for L blocks, at α0 + Lα1 via a union bound.","In the single-change-point case, the hold-out test attains level α1 rather than α0 + α1, because inference data are independent of detection.","The framework is nonparametric and applies to variance and covariance changes, not just mean shifts, as shown in simulations.","The exact block recovery rate approaches oracle power once the signal is strong enough, while naive testing produces frequent false attributions."],"fun_headline_variants":["Which variables caused that detected change? New tests tell","Post-hoc tests attribute change-points to specific blocks","Identify culprit coordinates after a multivariate change-point","New procedures pinpoint variables behind a detected shift","Attributing detected changes to specific variable blocks"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"A detection algorithm must output the correct number of change-points and localize them within δn with probability at least 1 − α0, and in the implemented version δn is computed with a calibrated constant rather than the proven bound — if that radius is too small, the guarantee collapses.","fun_headline_variants_meta":{"raw":{"variants":["Which variables caused that detected change? New tests tell","Post-hoc tests attribute change-points to specific blocks","Identify culprit coordinates after a multivariate change-point","New procedures pinpoint variables behind a detected shift","Attributing detected changes to specific variable blocks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000216,"raw_usage":{"total_tokens":1199,"prompt_tokens":607,"completion_tokens":592,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":351,"completion_tokens_details":{"reasoning_tokens":521}},"tokens_in":351,"tokens_out":592,"duration_ms":5433,"temperature":1.0,"reasoning_tokens":521,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T00:59:14.019795+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate weak mean shifts with small n, estimate δn exactly as in the paper, and record the empirical frequency of |τ̂ − τ*| > δn; if that frequency exceeds α0, then Assumption 1 is violated and the GTST Type I error can be checked to see whether it exceeds α0 + α1.","supporting_citations":[],"review_version":1}