{"id":"a228146e-4810-4288-a0fe-918db726b3a6","arxiv_id":"2501.18060","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"An adaptive conformal classification method estimates the coverage inflation caused by label noise and corrects the threshold, achieving nominal marginal coverage with tighter prediction sets.","lead":"This paper introduces a conformal prediction method that keeps its promised coverage probability even when the labels used for calibration are corrupted by random noise, while producing smaller prediction sets than standard conformal methods. It addresses a common data-quality problem in machine learning uncertainty quantification.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3's proof uses beta0=-1/(1-eps), beta_k=eps/(1-eps), making W=beta0*I+beta_k/K*J the negative of the true inverse; the step E sup beta*f = beta*E sup f is invalid for negative beta, so delta_FS >= delta* and the finite-sample coverage guarantee are unproven.","rationale":"The paper's central claim is that Algorithm 1, with the finite-sample correction factor delta_FS(n) from Theorem 4, provably attains marginal coverage. That claim depends on Theorem 4, whose proof follows the same decomposition as Theorem 3 and inherits the sign error: the parametrization of W uses the negative of the true inverse, and the linearity step for suprema fails when coefficients are negative. This is a correctness risk in the proof of the main theoretical guarantee, not merely a presentation issue. The reader's overall REJECT verdict is therefore appropriate, and my read does not change it. I mark partial agreement because the reader's formal weakest_assumption field identifies Assumption 2 (known and invertible T) rather than the proof flaw; however, the reader's rationale independently flags the same sign error and invalid inequality, which is the most load-bearing concern. A corrected proof may exist, and the empirical demonstrations are encouraging, but as written the finite-sample validity result is unsupported.","tokens_in":1030,"tokens_out":1100,"duration_ms":79426,"concrete_test":"Independently verify the algebra in Appendix C.3 for randomized response with K=2 and eps=0.2: compute the true inverse W and the proposed beta0=-1/(1-eps), beta_k=eps/(1-eps), and check whether W = beta0*I + beta_k/K*J holds entrywise; it fails by a global sign. Then, with the corrected signs beta0=+1/(1-eps), beta_k=-eps/(1-eps), re-derive E sup_t psi(t) and compare delta_FS(n) from (14) with delta*(n) from (13) for n=100 by Monte Carlo simulation; if the infimum in (14) is below delta* in any configuration, Theorem 4 is false as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.1 states W = T^{-1} = 1/(1-eps)*I - eps/[K(1-eps)]*J. In the proof of Theorem 3 (Appendix C.3), the authors write W = beta0*I + beta_k/K*J and define beta0 := -1/(1-eps), beta_k := eps/(1-eps). These definitions give beta0*I + beta_k/K*J = -1/(1-eps)*I + eps/[K(1-eps)]*J, which is the negative of the true W, not W itself. Consequently, beta0 + (sum_k beta_k)/K = -1, contradicting the proof's claim that this sum equals 1. The proof then asserts E sup psi1 = beta0*c(n); this identity is valid only for beta0 >= 0, but here beta0 < 0, and for negative beta0 the supremum of beta0*f is beta0 times the infimum, not the supremum. The same issue affects the psi2 term when sum_k beta_k is negative. Because Theorem 4 uses the same decomposition and the same c(n)*(beta0 + sum_k beta_k/K) term, the claimed upper bound delta_FS(n) >= delta*(n) is not justified. For the randomized-response case, the proposed beta actually makes the first term negative (-c(n)), so delta_FS(n) cannot be a conservative upper bound. Thus the central finite-sample coverage theorem rests on a sign error and an invalid inequality. The empirical results and the available code are useful, but they do not repair the proof of the headline guarantee.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a split-conformal classification method that aims to maintain marginal coverage when calibration labels are corrupted by random label noise. Under Assumptions 1–2 (noise conditionally independent of features given the true label, and a known invertible transition matrix T), the method estimates the coverage inflation factor Δ(t) and chooses a threshold using a correction factor δ(n); Theorem 2 states that coverage ≥ 1 − α whenever δ(n) ≥ δ*(n). Sections 3–4 propose two ways of choosing δ(n): a finite-sample upper bound δFS(n) based on the constant c(n) plus a chaining error term, and an asymptotic Monte Carlo approximation. Section 5 gives an upper coverage bound under additional assumptions. The method is evaluated on synthetic data and on CIFAR-10H and BigEarthNet. The advertised central contribution is a finite-sample marginal coverage guarantee with a correction factor that decays as 1/√n independently of the number of classes.","tokens_in":45061,"tokens_out":12592,"duration_ms":148298,"significance":"If the main theorems were correct, the paper would offer a useful and nontrivial extension of conformal inference under label noise, and the comparison to label-conditional methods would be informative. Credit is due for the clean structural result in Theorem 2, the Donsker-style asymptotic argument in Theorem 5, and the public code and extensive experiments. However, the central theoretical result is not established: the proof of Theorem 3 contains a sign error, and the same error undermines Theorem 4, so the proposed finite-sample correction δFS(n) is not proven to be conservative. Since the advertised coverage guarantee depends on δ(n) ≥ δ*(n), the paper's main claim is unsupported. The empirical results do not repair the proof.","major_comments":[{"comment":"In the proof of Theorem 3, the randomized-response inverse is W = 1/(1−ε)I − ε/[K(1−ε)]J, but the proof sets β0 = −1/(1−ε) and β_k = ε/(1−ε), so β0 I + (β_k/K)J equals −W, not W. Consequently β0 + (1/K)Σ_k β_k = −1, contradicting the proof's claim that this sum equals 1. The subsequent identities E sup ψ1 = β0 c(n) and E sup ψ2 ≤ (Σ β_k/K)c(n) require nonnegative coefficients, whereas here β0 < 0. Hence the conclusion c(n) ≥ δ*(n) is not proven.","section":"Appendix C.3 / Section 3.1"},{"comment":"The same sign issue invalidates the proof of Theorem 4. The first term in δFS(n) is c(n)(β0 + Σ_k β_k/K) without absolute values, and the derivation uses E sup ψ1 = β0 c(n) and E sup ψ2 ≤ (Σ_k β_k/K)c(n), which are only valid for nonnegative β0 and β_k. The minimization over all β ∈ R^{K+1} can exploit negative values of the first term, so the argument does not establish δFS(n) ≥ δ*(n). Additionally, Assumption 3 is stated in Theorem 4 but is not used in the proof.","section":"Section 3.2, Eq. (14), and Appendix C.3"},{"comment":"There is a formal inconsistency in the definition of d(n): Assumption 6 in the main text defines d(n) = n^{−1/4} · inf_β {√(π/2)(|β0| + Σ_k|β_k|/K) + B(K,n,β)}, while the proof of Theorem 6 defines d(n) = inf_β {1/(4√n)√(π/2)(|β0| + Σ_k|β_k|/K) + 1/(4√n)B(K,n,β)}. Because the upper bound in Theorem 6 depends on d(n), the assumption and the proof are not aligned.","section":"Section 5 (Assumption 6) and Appendix C.5"},{"comment":"In the real-data experiments, the transition matrix T is estimated from training data, so Assumption 2 fails and the finite-sample coverage guarantee of Theorem 2 does not apply. The paper acknowledges this limitation, but as a result the empirical coverage plots, while encouraging, are not direct evidence for the main theoretical claim.","section":"Section 7"}],"minor_comments":[{"comment":"The notation for the clean and noisy label frequencies is mistyped: both are written as ~ρ_k; the clean-label frequency should be denoted ρ_k and the noisy-label frequency ~ρ_k.","section":"Appendix C.1 (Proof of Theorem 1)"},{"comment":"Assumption 3 is stated as a hypothesis but is never invoked in the proof of Theorem 4 or in Lemma A1; the authors should either use it or remove it.","section":"Theorem 4 / Assumption 3"},{"comment":"The rule-of-thumb choices for the Monte Carlo parameters h, M, and the Richardson extrapolation order are presented only in the appendix; stating them in the main text would make the asymptotic implementation reproducible without reading the supplement.","section":"Section 4 / Appendix B.5"}],"recommendation":"reject","confidential_remarks":"The sign error in the proof of Theorem 3 is decisive: the central finite-sample coverage guarantee is not established, and the same issue propagates to Theorem 4. I am recommending rejection not because of disagreement with the noise-adaptive approach, but because the advertised theoretical guarantee is unsupported. If the authors can provide a corrected proof with the same or a suitably modified correction constant, the empirical methodology may still be worth reconsidering."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper gives the first adaptive conformal method for marginal coverage under label noise that promises a 1/sqrt(n) inflation factor independent of K. The empirical process machinery (chaining, Donsker) is a genuine improvement over the union-bound approach in Sesia et al. 2024, and the experiments on CIFAR-10H and BigEarthNet are thorough, with code available. That part is worth taking seriously.\n\nThe problem is the proof of Theorem 3. The authors parametrize the inverse transition matrix W for the randomized response model as beta0 I + (beta_k/K) J with beta0 = -1/(1-eps), beta_k = eps/(1-eps). But the true W is 1/(1-eps) I - eps/(K(1-eps)) J. Their beta gives -W, not W. So the sum beta0 + (sum beta_k)/K equals -1, not 1, and the step E[sup psi1] = beta0 c(n) is false when beta0 is negative. The same decomposition drives the finite-sample bound delta_FS in Theorem 4, so that result is also unsupported. In other words, the advertised guarantee that delta_FS(n) >= delta*(n) does not go through as written.\n\nI checked the proof carefully and the stress-test note is right: this is not a stylistic complaint, it's a load-bearing sign error. The asymptotic method in Section 4 uses W directly and is not affected, and the empirical results look good, but the paper's central theoretical contribution—the finite-sample coverage guarantee—is unproven in this version. The authors also honestly acknowledge that the real-data experiments use estimated T rather than known T, which is a lesser but real caveat.\n\nWho should read this: anyone working on conformal prediction with noisy labels. The method is likely salvageable by flipping the signs in the parametrization and re-running the constants, and the empirical evidence is encouraging. So I would send it to a serious referee, but with the expectation of major revision: the proof needs to be corrected before the guarantee can be trusted. My own verdict would be reject in current form, not because the idea is bad, but because the main theorem is not proved.","headline":"The marginal-coverage method is a real step forward, but the finite-sample guarantee in Theorem 3 rests on a sign error that invalidates the proof of the headline claim.","tokens_in":45613,"tokens_out":2876,"would_cite":false,"duration_ms":32484,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62G15","62G20","62H30"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper introduces an adaptive conformal prediction method that provably maintains marginal coverage when calibration labels are corrupted by random noise, and shows how to compute a finite-sample correction factor that keeps…","keywords":["conformal inference","classification","label noise","marginal coverage","prediction sets","empirical process","non-exchangeability","adaptive calibration"],"falsifier":"Simulate data with two classes under a two-level randomized response model with known T, run Algorithm 1 with the finite-sample correction delta_FS(n) for n = 1000, 5000, 20000, and verify empirically that marginal coverage stays at or above 1 - alpha. Then repeat the same simulation with a deliberately biased estimate of T (e.g., misspecified noise rate plus 0.05) and check that coverage drops below 1 - alpha by more than Monte Carlo error as n grows; if it does not drop, the method is more robust than the theory claims, while if it drops, the theory's reliance on exact T is confirmed.","tokens_in":44451,"feed_emoji":"🎯","tokens_out":3629,"duration_ms":45619,"temperature":0.7,"pith_summary":"The paper tackles a practical failure mode of conformal prediction: when the labels used for calibration are contaminated by random noise, standard split-conformal sets become over-conservative, wasting informativeness. The authors propose an adaptive calibration algorithm that estimates the gap between coverage computed with noisy labels and coverage with clean labels, then shifts the prediction threshold by a correction factor. They prove that with the right correction factor the method achieves the target marginal coverage in finite samples, and they supply two computable versions of that factor: a finite-sample upper bound and an asymptotic approximation based on a Gaussian limit process. If correct, this gives practitioners a way to keep 90% (or any target) coverage under label noise without needing clean labels at calibration time.","feed_headline":"Conformal prediction survives label noise with a 1/√n correction","feed_subtitle":"Adaptive calibration keeps target marginal coverage and tight sets even when calibration labels are corrupted.","key_machinery":"The core object is the marginal coverage inflation factor $\\Delta$(t) = F(t) - F(tilde-F)(t), and its empirical estimator hat{$\\Delta$}(t) built from the inverse transition matrix W = $T^{{-1}}$, the empirical label frequencies, and conditional empirical CDFs of scores. The ideal correction factor delta*(n) is the expected supremum of the empirical process psi-hat(t) = sum_{k,l} W_{kl}(hat{rho}_l hat{F}_l^k(t) - tilde{rho}_l tilde{F}_l^k(t)). The paper bounds delta*(n) in two ways: a finite-sample chaining bound delta_FS(n) using Massart's lemma and Dudley's integral, and an asymptotic approximation delta_asy(n) via a Donsker theorem showing sqrt{n} psi-hat converges to a Generalized Brownian Bridge. These correction factors are what make the adaptive threshold in Algorithm 1 work.","core_discovery":"The central claim is that the effect of random label noise on marginal conformal coverage is fully captured by a scalar function $\\Delta$(t) = F(t) - F(tilde-F)(t), the difference between the CDF of non-conformity scores evaluated at the true label and at the observed noisy label. Under the assumption that the label transition matrix T is known and invertible, this function can be written as a linear combination of estimable quantities, and its empirical estimate can be used to correct the conformal threshold. The paper proves that Algorithm 1, run with any correction factor delta(n) at least as large as the expected supremum of a certain zero-mean empirical process, yields prediction sets with P[Y_{n+1} in hat{C}(X_{n+1})] >= 1 - $\\alpha$. It then constructs two concrete such factors: delta_FS(n) from a chaining bound that scales as 1/$\\sqrt$(n) independent of the number of classes, and delta_asy(n) from a Generalized Brownian Bridge limit whose expectation is estimated by Monte Carlo. Under additional smoothness and accuracy assumptions, coverage is also bounded above by 1 - $\\alpha$ + delta(n) + o(1), so the sets are asymptotically tight.","pith_inferences":["A natural extension the authors leave implicit is to treat T as uncertain and replace the point estimate by a confidence set, which would convert the empirical robustness on real data into a rigorous coverage guarantee under model misspecification.","The same Delta(t) correction strategy could be adapted to regression by defining non-conformity scores on continuous labels and modeling label noise through a known corruption density, though the empirical process analysis would need reworking.","The Generalized Brownian Bridge approximation suggests a direct bootstrap alternative: resample calibration scores to estimate the expected supremum of psi-hat empirically, which could avoid the discretization and extrapolation steps and work for small n.","Because the correction is marginal rather than label-conditional, the method implicitly trades per-class guarantees for overall efficiency; users with rare but safety-critical classes should combine it with a separate check on those classes."],"forward_implications":["If the central claim holds, practitioners can apply conformal prediction to data sets with noisy labels and obtain marginal coverage at the nominal level with prediction sets that shrink toward the noise-free size as n grows.","The 1/sqrt(n) scaling of the finite-sample correction, independent of the number of classes K, implies the method remains informative in many-class or highly imbalanced problems where label-conditional conformal methods produce impractically large sets.","The asymptotic correction delta_asy(n), although not theoretically guaranteed to be conservative in finite samples, performs well in experiments and offers a computationally feasible alternative for large calibration sets.","The method can be applied with an estimated transition matrix T, as demonstrated on real data, suggesting that clean labels may be needed only to estimate T once, not for every calibration set.","The decomposition of coverage inflation via Delta(t) provides a template for adapting conformal inference to other structured deviations from exchangeability that can be modeled as a known invertible transformation."],"supporting_citations":[{"why":"Provides the noisy-label conformal inference framework and the optimistic adaptive idea that this paper extends from label-conditional to marginal coverage.","marker":"Sesia et al. (2024)"},{"why":"Defines the generalized inverse quantile non-conformity scores and prediction functions used in the empirical demonstrations.","marker":"Romano et al. (2020)"},{"why":"Establishes the general framework for conformal prediction beyond exchangeability, motivating the relaxation studied here.","marker":"Barber et al. (2023)"},{"why":"Identifies conditions under which standard conformal methods are conservative under label noise, a premise the paper builds on.","marker":"Einbinder et al. (2024)"},{"why":"Supplies the concentration inequality used in the finite-sample bound on the empirical process.","marker":"Massart (2000)"},{"why":"Provides the chaining and Dudley entropy integral machinery used to derive the finite-sample correction factor.","marker":"Wainwright (2019)"},{"why":"Supplies Donsker's theorem and empirical process theory used to establish the asymptotic Gaussian limit.","marker":"Van der Vaart (2000)"}],"fun_headline_variants":["Noise-adaptive conformal keeps coverage tight with 1/√n fix","Conformal prediction adapts to noisy labels, preserving marginal coverage","1/√n correction gives tight conformal sets even with corrupted labels","Adaptive conformal method maintains coverage under random label noise","Survive label noise: conformal sets stay valid via new correction"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The finite-sample coverage guarantee requires that the label transition matrix T is known exactly and invertible, so the inverse W used in the correction is correct; if T is estimated, the theoretical guarantee no longer applies and the method rests on empirical evidence of robustness.","fun_headline_variants_meta":{"raw":{"variants":["Noise-adaptive conformal keeps coverage tight with 1/√n fix","Conformal prediction adapts to noisy labels, preserving marginal coverage","1/√n correction gives tight conformal sets even with corrupted labels","Adaptive conformal method maintains coverage under random label noise","Survive label noise: conformal sets stay valid via new correction"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000235,"raw_usage":{"total_tokens":1481,"prompt_tokens":909,"completion_tokens":572,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":525,"completion_tokens_details":{"reasoning_tokens":479}},"tokens_in":525,"tokens_out":572,"duration_ms":6738,"temperature":1.0,"reasoning_tokens":479,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T00:51:16.907065+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate data with two classes under a two-level randomized response model with known T, run Algorithm 1 with the finite-sample correction delta_FS(n) for n = 1000, 5000, 20000, and verify empirically that marginal coverage stays at or above 1 - alpha. Then repeat the same simulation with a deliberately biased estimate of T (e.g., misspecified noise rate plus 0.05) and check that coverage drops below 1 - alpha by more than Monte Carlo error as n grows; if it does not drop, the method is more robust than the theory claims, while if it drops, the theory's reliance on exact T is confirmed.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the noisy-label conformal inference framework and the optimistic adaptive idea that this paper extends from label-conditional to marginal coverage."},{"cited_title":"Sesia, and E","cited_arxiv_id":null,"evidence_quote":"Defines the generalized inverse quantile non-conformity scores and prediction functions used in the empirical demonstrations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the general framework for conformal prediction beyond exchangeability, motivating the relaxation studied here."},{"cited_title":"Feldman, S","cited_arxiv_id":null,"evidence_quote":"Identifies conditions under which standard conformal methods are conservative under label noise, a premise the paper builds on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the concentration inequality used in the finite-sample bound on the empirical process."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the chaining and Dudley entropy integral machinery used to derive the finite-sample correction factor."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies Donsker's theorem and empirical process theory used to establish the asymptotic Gaussian limit."}],"review_version":1}