{"id":"c6653f1b-5770-4395-bf4b-97fa50200eba","arxiv_id":"2506.00379","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A new label-shift robust utility, LR-FFS, is proposed for federated feature screening, with a unifying framework, distributed estimation, and FDR control.","lead":"This paper introduces LR-FFS, a federated feature screening method for high-dimensional classification that stays accurate when different clients have different class proportions. It also unifies several existing screening methods in one framework and provides a false discovery rate control procedure for federated screening.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The federated estimator's probability limit is a client-mixture of class-proportion-dependent utilities, not the pooled utility, so Theorem 11's sure-screening claim needs an unstated common-target assumption.","rationale":"The reader's weakest assumption identifies the same load-bearing issue: the LR-FFS utility is defined through client-specific mixtures of the other R−1 classes, and Condition C1 does not ensure these mixtures match the pooled mixture. This is the most central threat to the paper's headline claim because the sure-screening property in Theorem 11 is proven for a single population γ_{j,r}, but under general label shift no such single quantity is defined by S2. The bias-correction in Eq. (5) only aligns the variance-type terms π(1−π), not the full mixture weights, so the aggregated estimator's limit is a weighted average of client-specific targets. The simulations in the paper do not surface this because their design (often a single shifted class per feature) makes the max-utility component insensitive to the relative proportions of the remaining classes; this is a special case, not the general claim. The FDR control concern raised by the reader is secondary: Theorem 14 is imported from Tong et al. (2023) without verifying the marginal symmetry condition under label shift, but the central screening-effectiveness claim is already conditional on the common-target gap. I do not recommend changing the verdict because the issue is addressable by either adding the common-target condition to S2/C1 or reformulating the claim as convergence to the client-mixture target and showing this still yields comparable screening in the settings of interest. The paper has useful independent support: a unified framework, reproducible code, and extensive simulations; these do not resolve the theoretical target mismatch but they support the method's practical promise. Thus the verdict remains conditional.","tokens_in":51619,"tokens_out":8548,"duration_ms":78123,"concrete_test":"Simulate a 3-class problem with two clients: client 1 has Y∈{1,2} and client 2 has Y∈{1,3}, each with equal class proportions, and class-conditional densities X|Y=1 ~ N(0,1), X|Y=2 ~ N(2,1), X|Y=3 ~ N(-2,1) for one relevant feature, plus an irrelevant feature with identical densities across all classes. Run Algorithm 1 with n_l=200 per client over 1000 replications, and compare the federated LR-FFS utility for the relevant feature with the pooled-data utility from the combined sample. If the federated estimate does not converge to the pooled utility, or if the relevant/irrelevant feature ranking differs from the centralized ranking, the common-target assumption is violated and Theorem 11 does not establish the advertised equivalence to centralized screening.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that LR-FFS 'maintains screening effectiveness comparable to centralized processing' requires the federated estimator to converge to the pooled utility ω_j = max_r |E_{Y=y_r}(F_{Y≠y_r}^{pool}(X_j)) − 1/2|. Under S2, P(X|Y) is common but each client l has its own γ_{j,r}^{(l)} = E_{Y=y_r}(F_{Y≠y_r}^{(l)}(X_j)), where F_{Y≠y_r}^{(l)} = Σ_{y≠r} (π_{l,y}/(1−π_{l,r})) P(X|Y=y). This depends on the relative proportions of the other R−1 classes, which S2 allows to vary. Equation (5) only matches the weighted average of π_{l,r}(1−π_{l,r}); it does not match the mixture weights. Hence E(\\bar U_{j,r}) = (Σ h_l π_{l,r}(1−π_{l,r}) γ_{j,r}^{(l)})/Σ h_l, which equals U_{j,r}^{pool} only if γ_{j,r}^{(l)} is constant across l. The proofs of Lemma 20 and Theorem 11 use a single γ_{j,r} for all clients; Condition C1 does not rule out, e.g., client 1 with classes {1,2} and client 2 with classes {1,3} when P(X|Y=2)≠P(X|Y=3). In that case the federated limit is a mixture of client-specific targets, not the pooled target, so the sure-screening bound in Theorem 11 is for a different quantity than the centralized one. The 'comparable to centralized processing' claim therefore rests on an unstated assumption stronger than S2.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a federated feature screening framework for high-dimensional classification under label shift. It proposes a new utility, LR-FFS, defined as the maximum over classes of |E_{Y=y_r}(F_{Y≠y_r}(X_j)) − 1/2|, and estimates it with client-level U-statistics, one-shot aggregation, and a bias correction based on a parameter π* defined through Eq. (5). The paper proves uniform consistency, sure screening, ranking consistency, and FDR control for this estimator, embeds CRU, MV-SIS, and CAVS as special cases of a general framework, and reports extensive simulations plus a TCGA breast-cancer application.","tokens_in":52016,"tokens_out":11610,"duration_ms":117329,"significance":"The framework is elegant and the one-shot communication scheme is practically attractive. If the target-identification issue is resolved, this would be a useful contribution: it unifies several existing screening methods, gives explicit concentration bounds that match centralized rates, demonstrates robustness to heavy tails and outliers, and releases code. The numerical study is extensive and the computational cost claims are plausible. However, the central claim of screening effectiveness 'comparable to centralized processing' is not supported as stated, because under the paper's label-shift assumption the federated estimator's probability limit is not generally the pooled utility.","major_comments":[{"comment":"The target γ_{j,r} is not identified under S2. On client l, γ_{j,r}^{(l)} = E_{Y=y_r}(F_{Y≠y_r}^{(l)}(X_j)) with F_{Y≠y_r}^{(l)}(x) = Σ_{y≠y_r}(π_l^y/(1−π_l^r)) F_{Y=y}(x); this depends on the relative proportions of the other R−1 classes, which S2 allows to vary arbitrarily across clients. Eq. (5) matches only the weighted average of π_l^r(1−π_l^r), so E(\\bar U_{j,r}) = (Σ_l h_l π_l^r(1−π_l^r) γ_{j,r}^{(l)})/(Σ_l h_l), which equals the pooled U_{j,r} only if γ_{j,r}^{(l)} is constant in l. Lemma 20 and Theorem 11 use a single γ_{j,r}; Condition C1 does not rule out, for example, client 1 with classes {1,2} and client 2 with classes {1,3} when P(X|Y=2)≠P(X|Y=3). Proposition 3 itself only covers the case where the ratios among the remaining R−1 classes are fixed, and that assumption is not stated in S2. The authors should either add an explicit common-relative-mixture assumption to the setup or redefine the target as the client-weighted mixture and prove the sure-screening and ranking-consistency properties for that target.","section":""},{"comment":"The relevant set A is defined through F(Y|X), but under S2 there is no single conditional distribution of Y given X: P_l(Y|X) differs across clients because P_l(Y) varies while P(X|Y) is common. The paper should define A directly in terms of the common class-conditional distributions P(X|Y), for instance A={j: P(X_j|Y=y) depends on X_j for some y}, or should specify a pooled prior distribution for Y. Without this, the active set in Theorem 11 is ambiguous.","section":""},{"comment":"The proof of Theorem 13 conditions on max_j |\\barω_j−ω_j| ≥ cN^{-κ} to bound |\\hat A|, but the stated bound follows from small estimation error. On the event max_j |\\barω_j−ω_j| ≤ cN^{-κ}/2, every selected feature satisfies ω_j ≥ cN^{-κ}/2, so |\\hat A| ≤ (c/2)^{-1}N^κ Σ_j ω_j; the complementary event gives the stated probability. As written, the displayed inequality has the wrong direction and the proof needs correction.","section":""},{"comment":"The proof of Theorem 14 consists of a sentence referring to Tong et al. after asserting that the estimates have the same efficiency. The conditions Eϕ*_j = 0.5+o(c_n^{-1}) and c_n/p→0 are not verified for the federated permutation estimator of ϕ_j. Since this theorem is stated as a new FDR guarantee, the proof should either verify these conditions under the paper's assumptions or state them as additional assumptions.","section":""}],"minor_comments":[{"comment":"","section":"Section 2.4, Proposition 6"},{"comment":"The identity E_{Y=y_r}(F_{Y=y_r}(X_j)) = 1/2 presumes that X_j is continuous; please state this regularity condition explicitly.","section":"Section 2.3"},{"comment":"The text and caption describe the plotted symbols inconsistently (red triangles versus red circles, blue circles versus blue dots); please align them.","section":"Figure 1"}],"recommendation":"major_revision","confidential_remarks":"The main concern is the identification gap between S2 and the theoretical target in Theorems 9–14. I do not see a novelty disclosure problem; the paper appropriately builds on Li and Xu (2024). The paper is within the journal's scope. If the authors can fix the target definition, correct the proof of Theorem 13, and provide a real proof for Theorem 14, the paper would be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: worth reading, method probably useful, but the central theory overreaches. The LR-FFS utility — max over classes of |E_{Y=y_r}(F_{Y≠y_r}(X_j)) − 1/2| — is a sensible model-free screening statistic, and the unifying framework in Eq. (1) that recovers CRU, MV-SIS, and CAVS as special cases is a real contribution. The bias-corrected aggregation via π* is clever, the simulations are extensive, and code is provided. I take the empirics as supporting practical value.\n\nThe problem is Theorem 11. Under the paper's heterogeneity setting S2, clients share P(X|Y) but differ in P(Y). The quantity γ_{j,r} = E_{Y=y_r}(F_{Y≠y_r}(X_j)) is not client-invariant: F_{Y≠y_r} is a mixture of the other R−1 class-conditional distributions with local class proportions as weights. If those proportions vary across clients, each client's γ differs. After bias correction, the federated estimator converges to a weighted average of client-specific γ's, not the pooled γ. Lemma 20 and the proof of Theorem 11 use a single γ for all clients — an unstated assumption stronger than S2. It may hold if all other classes have identical conditional distributions, but that is not stated or checked.\n\nFor instance, a client with only classes {1,2} and another with only classes {1,3} have different F_{Y≠1}, so the estimator of ω_1 is a mixture of two different targets. The sure-screening bound is for that mixture, but 'comparable to centralized processing' requires that mixture to equal the pooled utility. Generally it does not.\n\nThis is load-bearing for the theory, but not fatal for the method. The authors could add a condition (e.g., relative proportions of the other classes constant across clients) or redefine the target as the client-mixture limit and prove screening for that. I would send this to peer review; the idea is solid and the flaw is fixable. Referees should ask for the target parameter to be explicitly defined and the assumption stated.\n\nThe FDR control result is imported from Tong et al. (2023) without verifying the conditions; that is minor and also fixable.","headline":"A genuinely new screening utility and a clean federated estimator, but the sure-screening theorem is proved for a target that under arbitrary label shift differs from the pooled utility.","tokens_in":52538,"tokens_out":5540,"would_cite":false,"duration_ms":47956,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper introduces LR-FFS, a federated feature screening utility whose class-proportion-free estimator matches centralized sure screening rates under label shift.","keywords":["federated learning","feature screening","label shift","high-dimensional classification","Mann-Whitney statistic","sure screening","false discovery rate","model-free screening"],"falsifier":"Run a three-client, three-class simulation with identical $P(X\\mid Y)$ and fixed share of class 1, but make client A see only class 2 as 'not class 1' and client B see only class 3 as 'not class 1', then compare the federated LR-FFS estimate of $\\omega_j$ for a feature that separates classes 2 and 3 with the same statistic computed on the pooled data; a material gap shows the invariance claim does not extend to arbitrary label shift.","tokens_in":51441,"feed_emoji":"📊","tokens_out":9207,"duration_ms":82050,"temperature":0.7,"pith_summary":"This paper tries to settle a specific failure mode in distributed high-dimensional classification: when the same features predict the same classes but class prevalence differs across clients (label shift), existing screening utilities estimate different quantities on different clients and drift from the pooled ranking. The authors propose LR-FFS, a utility defined as the largest, over classes $y_r$, of the deviation $|E_{Y=y_r}(F_{Y\\neq y_r}(X_j))-1/2|$, a Mann-Whitney comparison of class $y_r$ against all other classes. They give a one-shot federated estimator that corrects class-proportion bias through a global $\\pi_r^*$ equation, then aggregates per-client Mann-Whitney estimates. The main theoretical result is the sure screening property: with probability at least $1-6sR\\exp(-c_5N^{1-2\\kappa-4\\xi})$ the estimated active set contains all $s$ relevant features, at the same rate as centralized screening. If correct, federated systems can screen features before modeling, with no raw data leaving clients and no extra communication or local computation relative to existing baselines.","feed_headline":"Label shift no longer breaks federated feature screening","feed_subtitle":"A class-proportion-free utility keeps every client scoring the same features and matches single-machine screening rates.","key_machinery":"The load-bearing object is the class-conditional Mann-Whitney identity $\\gamma_{j,r}=E_{Y=y_r}(F_{Y\\neq y_r}(X_j))=P(X_{j,i_1}