{"id":"3f3e829a-52eb-4c6b-a928-6538e14c4fa5","arxiv_id":"2411.17033","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"QuACC tests whether two variables jointly exceed or fall below their conditional quantiles and is plugged into the PC algorithm, but the paper's proof of the test's variance is incorrect.","lead":"This paper introduces QuACC, a statistic that measures whether two variables tend to fall together at the same extreme of their conditional distributions, and uses it to learn quantile-specific graphical models. The paper claims a normal limit theorem and valid hypothesis tests, but the central variance derivation contains an algebraic error that breaks the inferential claim.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lemma 2's variance identity is false: Var(IY IX) ≠ Var((IY−τ)(IX−τ)); under independence the true null variance is τ²(1−τ²), not τ²(1−τ)², so the QuACC Wald test and all downstream PC p-values are anti-conservative.","rationale":"I independently re-derived the variance of the Bernoulli product and confirmed the reader's algebra: Var(IY IX) is not Var((IY−τ)(IX−τ)), and under independence the paper's V(τ) is too small by a factor of (1−τ²)/(1−τ)², reaching 3 at τ=0.5. This is not a minor typo affecting a secondary term; it enters the null variance used in the test statistic and therefore invalidates Theorem 1, Corollary 1.1, the Wald intervals, and every p-value fed into the PC algorithm. The simulations do report rejection rates for small copula parameters, but a dedicated size-at-the-null experiment with the paper's variance formula would expose the inflation. The Section 2.3 semantic concern—that accepting H0: ρτ = c justifies PC's edge-removal—is also legitimate, because a single tail-probability constraint is not conditional independence; however, the variance error alone is sufficient to reject the paper's inferential claim. I see independent value in the cross-fitting plug-in idea and in the quantile-tail graphical application, and a corrected derivation might make the method usable, but as written the central statistical machinery is unsound. The reader's REJECT verdict stands unchanged.","tokens_in":22220,"tokens_out":7801,"duration_ms":70653,"concrete_test":"Analytic check: under H0 with independent Y and X and known conditional quantiles, compute Var(I(Y<QY)I(X<QX)) directly as τ²(1−τ²) and compare it with Lemma 2's τ²(1−τ)²; at τ=0.5 the two differ by a factor of 3. Computational confirmation: simulate Y,X,Z with Y and X conditionally independent given Z (e.g., standard normal margins, Z=∅, known quantiles Φ⁻¹(τ)), compute the paper's z-statistic over 10,000 replicates at n=200 and τ=0.5, and record the empirical rejection rate at α=0.05. With the paper's variance it should be roughly 25% instead of the nominal 5%; with the correct variance τ²(1−τ²)/n it should be 5%.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is Theorem 1 / Corollary 1.1: asymptotic normality with variance Στ = κYσ²QYκY + κXσ²QXκX + 2κYκX VXY(τ) + V(τ), which is used to build Wald intervals and a standard-normal test of H0: ρτ = (1−τ)² or τ². Lemma 2, which supplies V(τ), states V(τ) = Var(I(Y<QY)I(X<QX)) and then rewrites it as Var((I(Y<QY)−τ)(I(X<QX)−τ)). These are not equal. Write A = I(Y<QY), B = I(X<QX), each Bernoulli(τ), with p = P(A=B=1). Then Var(AB) = p(1−p), whereas Var((A−τ)(B−τ)) = E[(A−τ)²(B−τ)²] − (p−τ²)². Under independence p = τ², so Var(AB) = τ²(1−τ²), while the paper's expression reduces to τ²(1−τ)². At τ = 0.5 the true variance is 0.1875 and the paper's is 0.0625, a factor of 3. The hypothesis-test section explicitly uses τ²(1−τ)² (or the symmetric upper-tail version) as the null variance, so the denominator of the z-statistic is too small and the Type I error is badly inflated. Because the PC algorithm's edge removals are driven by these p-values, the graphical outputs and the All of Us QGM comparisons inherit the error. The proof also contains a second algebraic slip: it sets (E[W1W2])² = τ²(1−4τ+4τ²), whereas E[W1W2] = p−τ². The variance formula requires a full re-derivation, not a cosmetic correction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces QuACC (Quantile Association via Conditional Concordance), a measure of quantile-specific conditional association defined as the probability that two variables jointly exceed (or fall below) their conditional quantile functions at level tau. The authors propose a cross-fitted plug-in estimator, claim asymptotic normality of the estimator (Theorem 1 and Corollary 1.1), and use this result to build Wald tests for the null hypothesis of independence, rho_tau = (1-tau)^2 or tau^2. These tests are then plugged into the PC algorithm to estimate undirected skeletons for what the authors call QuACC graphical models (QGMs). The method is evaluated in simulations and applied to All of Us biobank data for mitochondrial disorders.","tokens_in":22581,"tokens_out":5560,"duration_ms":49200,"significance":"If the asymptotic theory were correct, QuACC would provide a practically useful tool for detecting tail-specific conditional associations and for constructing quantile-level graphical models, complementing existing quantile graphical model approaches. The paper has several strengths: it uses cross-fitting to separate nuisance estimation from inference, it accommodates both linear and random-forest quantile regressions, it includes simulation studies across copula settings, and it demonstrates a real-data application. However, the central variance derivation in Lemma 2 is algebraically incorrect, and the resulting test statistic and graphical outputs are not valid. The paper's main contribution therefore rests on an unsupported claim.","major_comments":[{"comment":"The proof of Lemma 2 asserts that Var(I(Y<QY)I(X<QX)) = Var((I(Y<QY)-tau)(I(X<QX)-tau)). This identity is false: for independent Bernoulli(tau) indicators A and B, Var(AB) = tau^2(1-tau^2), whereas Var((A-tau)(B-tau)) = tau^2(1-tau)^2. At tau=0.5 the former is 0.1875 and the latter 0.0625, a factor of three. The subsequent algebra also sets (E[W1W2])^2 = tau^2(1-4tau+4tau^2), but E[W1W2] = p(Y<QY, X<QX) - tau^2, which is zero under independence, not tau^2(1-2tau)^2. Because V(tau) enters Theorem 1 and Corollary 1.1, the null variance used in the z-statistic (Section 2.2, Hypothesis test) is too small, leading to inflated Type I error. The simulation rejection rates in Section 3.1 and the QGM graphs in Section 4 therefore do not provide valid evidence of the method's performance.","section":"Appendix F, Lemma 2; Section 2.2, Theorem 1 and hypothesis test"},{"comment":"The PC algorithm requires a test of conditional independence to decide edge removal. The paper instead tests H0: rho_tau = (1-tau)^2 (or tau^2), which is a single condition on the joint exceedance probability, not a statement of full conditional independence of Y and X given Z. The paper does not prove that accepting this null is equivalent to, or even implies, the conditional independence required for the PC algorithm's edge-removal step. Without such a formal connection, the output of the QGM procedure lacks a well-defined interpretation as a conditional independence graph, and the manuscript's central graphical-model claim is unsupported.","section":"Section 2.3, QuACC Graphical Models"}],"minor_comments":[{"comment":"The displayed formula for b-rho_tau after defining b-rho^k_tau appears malformed: \"bρτ = PK k=1 bρk τqPK k=1 V ar(bρkτ )/nk\" is missing an operator and is not a valid expression. Please rewrite it unambiguously.","section":"Section 2.1, equation for overall b-rho"},{"comment":"The sentence \"If they are perfectly discordant, ie. they ever jointly above or below their regression planes, then ρ∗τ is 1\" should say \"never jointly\" and the value should be -1, consistent with the normalization formula.","section":"Appendix C, last paragraph"},{"comment":"The text states that a negative rho_tau indicates discordance and that the smallest possible rho_tau is 0, but the definition of rho_tau as a probability is always nonnegative. Please clarify that only the normalized version rho*_tau can take negative values, and correct the related discussion.","section":"Introduction, Section 1"},{"comment":"The variance term for In2 is written as \"2κYκX nk VXY(τ)\" in the proof but as \"2κYκX VXY(τ)\" in the theorem statement. The factor 1/nk (if intended) should be specified precisely, since it affects the asymptotic variance expression.","section":"Theorem 1 proof, page 21"},{"comment":"There are several typographical errors: \"V owels\" in the references should be \"Vowels\"; \"Ceber's optic atrophy\" should be \"Leber's optic atrophy\"; and the notation \"≶\" in Lemma 2 is unclear without specifying lower versus upper tail cases.","section":"References and typos"}],"recommendation":"reject","confidential_remarks":"This manuscript addresses a timely and interesting problem, and the authors have assembled a substantial simulation and application suite. However, the central inferential claim is not supported by the provided proofs. The variance identity in Lemma 2 is demonstrably wrong, and the error propagates to the main theorem, the test statistic, and all downstream graphical results. This is not a presentation issue; it requires a full re-derivation of the asymptotic variance. The PC-algorithm interpretation also needs a formal justification that the QuACC null corresponds to conditional independence. These are load-bearing problems that cannot be resolved within a routine minor revision. I recommend rejection of the current version, though the authors could potentially resubmit a corrected manuscript if they can supply a valid variance formula and a rigorous semantic connection to conditional independence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take on 2411.17033. The paper defines QuACC, a quantile-specific concordance measure, and wires it into PC for graphical structure learning. The All of Us mitochondrial disease application is a nice demonstration of the workflow. I'll be direct: the central inferential machinery has a load-bearing error, so the p-values and graphs as reported are not reliable.\n\nWhat's new and good: the idea of using a fixed-quantile exceedance concordance as a conditional association test and feeding it to PC is useful. The cross-fitting plug-in estimator is a sensible way to handle nuisance quantile regression. The simulations are thoughtfully set up to show tail-only dependence, and the comparison with partial correlation graphs is a fair illustration.\n\nThe problem is Lemma 2. It rewrites Var(I(Y<QY) I(X<QX)) as Var((I(Y<QY)-tau)(I(X<QX)-tau)). Those are not the same. For Bernoulli(tau) indicators, the first variance under independence is tau^2(1-tau^2); the paper's expression is tau^2(1-tau)^2. At tau=0.5 that's 0.1875 vs 0.0625, a factor of 3. The hypothesis test in Section 2.2 uses the wrong value, so the z-statistic denominator is too small and Type I error is inflated. The proof also sets (E[W1W2])^2 = tau^2(1-4tau+4tau^2), which is false; E[W1W2] = p - tau^2. These aren't cosmetic slips; they drive the Wald intervals and the PC edge-removal decisions.\n\nThere's a second issue, more conceptual. The null tested is that the two exceedance indicators are independent at a single tau. That's not conditional independence of Y and X given Z. So a missing edge in a QGM doesn't have the usual PC meaning. The paper sometimes calls them 'quantile-specific graphical models' and sometimes talks as if the skeleton is a standard CI graph. That overclaim should be fixed.\n\nI don't see this paper as a waste of time. The idea is worth pursuing, and the application is plausible. But the variance derivation has to be redone, the simulations should include empirical size under the null, and the graph semantics need to be stated precisely. As is, I wouldn't cite it. If it lands in my inbox, I'd send it to review with instructions that the referee focus on Lemma 2 and the interpretation of edges. The concept deserves serious development, but not in its current form.","headline":"QuACC is a sensible idea for tail-specific association graphs, but the key variance term in the test statistic is wrong, and the graph semantics are looser than claimed.","tokens_in":23191,"tokens_out":4006,"would_cite":false,"duration_ms":34091,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62H20","62G05","62G10","62H12"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper introduces QuACC, a statistic measuring whether two variables are jointly above (or below) their conditional quantiles, proves asymptotic normality for plug-in estimators, and uses it as a conditional-association test inside a…","keywords":["quantile association","conditional concordance","graphical models","tail dependence","quantile regression","conditional independence testing","cross-fitting","structure learning"],"falsifier":"Take independent standard normal variables with no conditioning set and $\\tau=0.5$: the paper's Lemma 2 gives $V(\\tau)=\\tau^2(1-\\tau)^2=0.0625$, while direct computation gives $\\mathrm{Var}(I(Y<0)I(X<0))=(0.25)(0.75)=0.1875$, showing the variance formula in Theorem 1 does not match the variance of the observed concordance statistic.","tokens_in":21926,"feed_emoji":"📊","tokens_out":8194,"duration_ms":72152,"temperature":0.7,"pith_summary":"The paper is trying to establish that tail-specific dependence between two variables, given a covariate set, can be measured by a single concordance probability: the chance that both variables fall on the same side of their conditional quantiles at a chosen level tau. It calls this quantity QuACC, builds plug-in estimators through cross-fitted quantile regression, and claims these estimators are asymptotically normal with a variance that can be estimated, so confidence intervals and hypothesis tests are available. If the claim holds, researchers can run the PC structure-learning algorithm once per quantile level and obtain a graph of which conditional associations live at the tails rather than only at the mean. This would matter for biomedical settings where two biomarkers may look unrelated on average but move together only in extreme states.","feed_headline":"Tail-only associations get their own conditional test","feed_subtitle":"A new statistic counts when two variables hit their extreme quantiles together, then drives graph discovery.","key_machinery":"The central object is the QuACC concordance probability, defined as the joint probability that two variables fall on the same side of their conditional quantile functions at level $\\tau$. The machinery around it is a cross-fitted plug-in estimator: fit quantile regressions for $Y$ and $X$ on training folds, evaluate indicator concordance on a held-out fold, then pool folds. The proof machinery is a decomposition of estimation error into a testing-set concordance term with variance $V(\\tau)$ and a quantile-estimation term with covariance $V_{XY}(\\tau)$ weighted by density factors $\\kappa_Y,\\kappa_X$; Theorem 1 says the sum is asymptotically normal. This normality is what converts QuACC into a $z$-test and lets the PC algorithm use it as a conditional-independence oracle at each quantile level.","core_discovery":"The central claim is that for fixed $\\tau$, the QuACC statistic $\\rho_\\tau(Y,X|Z)=P(Y>Q_Y(\\tau|Z),\\,X>Q_X(\\tau|Z))$ for $\\tau\\ge 0.5$ (and the analogous lower-tail probability for $\\tau<0.5$) is a meaningful, testable quantile-specific conditional association. Under conditions C1-C4, the cross-fitted plug-in estimator $\\hat{\\rho}^k_\\tau$ satisfies $(b_n)^{1/2}(\\hat{\\rho}^k_\\tau-\\rho_{\\tau 0})\\to N(0,\\Sigma_\\tau)$ with $\\Sigma_\\tau=\\kappa_Y\\sigma^2_{Q_Y}\\kappa_Y+\\kappa_X\\sigma^2_{Q_X}\\kappa_X+2\\kappa_Y\\kappa_X V_{XY}(\\tau)+V(\\tau)$, where $\\kappa_Y,\\kappa_X$ encode derivatives of the concordance probability with respect to the quantile functions, $V_{XY}(\\tau)$ captures the joint estimation error of the two quantile regressions, and $V(\\tau)$ is the variance of the concordance indicators at the true quantiles. For linear quantile regression a root-$n$ version is given, yielding a standard-normal test statistic for $H_0:\\rho_\\tau=(1-\\tau)^2$ (upper) or $\\tau^2$ (lower). The intended use is not just pairwise testing: feeding this test statistic into the PC algorithm produces a quantile-specific graphical model whose missing edges denote conditional independence at that quantile.","pith_inferences":["The paper tests one pair of quantiles at a time; a natural extension would be a joint test over a grid of $\\tau$ values, which would detect dependence appearing at any tail without the multiple-testing burden of separate tests.","The concordance definition could be generalized to asymmetric quantile levels $\\tau_Y\\ne\\tau_X$, allowing questions such as whether upper-tail movement in one variable tracks lower-tail movement in another; the variance decomposition would need a new $V(\\tau)$ term.","If the asymptotic result extends, QuACC could serve as a screening statistic before fitting full conditional copula models, since it targets precisely the corner probabilities that copulas aim to capture.","The graph produced by the PC skeleton at one $\\tau$ should be read as quantile-specific association structure, not as full causal structure; orienting edges and combining layers across $\\tau$ would require additional assumptions the paper does not state."],"forward_implications":["If the central claim is right, researchers can test whether two variables move to their extremes together given a covariate set, using a standard normal statistic at any $\\tau$ and no assumed copula family.","Running the test inside the PC algorithm yields one undirected skeleton per quantile level; edges present at $\\tau=0.9$ but absent at $\\tau=0.5$ would mark tail-only conditional associations.","The same plug-in logic extends the graph framework to nonlinear quantile regressions such as quantile forests, at the cost of a slower $(n/s)^{1/2}$ convergence rate.","Applied to biobank biomarker panels, the method can produce quantile-specific graphs that differ at lower and upper tails, which is where dysregulation is often visible.","Correct estimation of the conditional quantile functions is a precondition for the null benchmark $(1-\\tau)^2$ or $\\tau^2$ to be valid, so the test is only as reliable as the fitted quantile models."],"supporting_citations":[{"why":"Supplies the linear quantile regression asymptotics that yield $\\sigma^2_{Q_Y}$ and $\\sigma^2_{Q_X}$ in Corollary 1.1.","marker":"[Koenker and Hallock, 2001]"},{"why":"Provides the uniform convergence lemma used to control the difference between empirical concordance at estimated versus true quantiles.","marker":"[He and Shao, 2000]"},{"why":"Provides the generalized random forest convergence theory behind the quantile-forest version of QuACC.","marker":"[Athey et al., 2019]"},{"why":"Supplies the PC algorithm that QuACC is plugged into for graph structure learning.","marker":"[Spirtes et al., 2000]"},{"why":"Supplies the high-dimensional PC algorithm implementation and consistency backdrop used in the graph simulations.","marker":"[Kalisch and Bühlman, 2007]"},{"why":"Defines the quantile association regression framework and the simulated data-generating processes that QuACC is tested against.","marker":"[Li et al., 2014]"},{"why":"Supplies the cross-fitting rationale used in the definition of the QuACC estimator.","marker":"[Zivich and Breskin, 2021]"}],"fun_headline_variants":["QuACC: a new test for tail-only conditional dependencies","Quantile-conditioned graphs catch tail associations","New measure reveals links that emerge only in extremes","Conditional concordance spots hidden tail dependencies","Graph discovery that respects quantile-specific ties"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole inference rests on the claim that subtracting each variable's exceedance probability before multiplying does not change the variance of the joint-exceedance indicator; the variance formulas in Theorem 1 are valid only if this algebraic identity holds.","fun_headline_variants_meta":{"raw":{"variants":["QuACC: a new test for tail-only conditional dependencies","Quantile-conditioned graphs catch tail associations","New measure reveals links that emerge only in extremes","Conditional concordance spots hidden tail dependencies","Graph discovery that respects quantile-specific ties"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000335,"raw_usage":{"total_tokens":1907,"prompt_tokens":1046,"completion_tokens":861,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":662,"completion_tokens_details":{"reasoning_tokens":791}},"tokens_in":662,"tokens_out":861,"duration_ms":7347,"temperature":1.0,"reasoning_tokens":791,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:37:25.512301+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take independent standard normal variables with no conditioning set and $\\tau=0.5$: the paper's Lemma 2 gives $V(\\tau)=\\tau^2(1-\\tau)^2=0.0625$, while direct computation gives $\\mathrm{Var}(I(Y<0)I(X<0))=(0.25)(0.75)=0.1875$, showing the variance formula in Theorem 1 does not match the variance of the observed concordance statistic.","supporting_citations":[{"cited_title":"On parameters of increasing dimensions","cited_arxiv_id":null,"evidence_quote":"Provides the uniform convergence lemma used to control the difference between empirical concordance at estimated versus true quantiles."},{"cited_title":"Estimating high-dimensional directed acyclic graphs with the PC -algorithm","cited_arxiv_id":null,"evidence_quote":"Supplies the high-dimensional PC algorithm implementation and consistency backdrop used in the graph simulations."},{"cited_title":"Machine learning for causal inference: on the use of cross-fit estimators","cited_arxiv_id":null,"evidence_quote":"Supplies the cross-fitting rationale used in the definition of the QuACC estimator."}],"review_version":1}