{"id":"ec1d7d30-2540-4f98-8e34-e13418eb73d3","arxiv_id":"2505.12695","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"A pseudo-likelihood ratio screening procedure is introduced to select both self-related and network-related features for network-involved preference classification, with consistency guarantees and a Sina Weibo application.","lead":"This paper proposes a feature screening method for ultra-high-dimensional categorical tags in social networks, using a pseudo-likelihood ratio that accounts for both a user's own tags and the network structure. The method aims to identify features that directly predict preferences as well as features that shape who connects to whom.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The literal definition of Λ_j in Eqs. (5)–(7) is not a log-likelihood ratio: the product over all response levels yields a per-node sum of R log-ratios that can be negative for a strongly self-related feature, so Theorem 2 is not about the stated statistic.","rationale":"The reader's REJECT verdict is justified, but by a more direct route than the reader's stated weakest assumption. The weakest assumption as written emphasizes possible misspecification of the edge-generating model; the sharper, load-bearing problem is internal: the statistic defined in Section 2.4 is not a likelihood ratio even when the assumed conditional-independence structure holds exactly. The product over all response levels per node changes the self effect into a sum over R categories, makes the claimed PMLE frequency estimators incorrect, and can assign negative values to strongly predictive self-related features. Since Theorem 2, Corollary 3, and Proposition 6 all concern this statistic, the central claim as written is unsupported. The simulations and real-data analysis may match an intended corrected definition, but the manuscript does not state that correction, and the real-data comparison also confounds screening with the downstream classifier. A literal implementation of Eqs. (5)–(7) on the simple binary example above would settle whether the authors' code matches the text; if it does not, the paper needs a major revision defining and analyzing the corrected statistic. Because the reader already reached REJECT and our analysis supports that conclusion, no verdict adjustment is needed.","tokens_in":22147,"tokens_out":12123,"duration_ms":129206,"concrete_test":"Run a minimal implementation of the literal definition: n=1000, p=2, R=K=2, A=0, X1~Bernoulli(0.5), P(Y=1|X1=1)=0.9, P(Y=1|X1=0)=0.1, X2 independent. Compute L0 and L1 exactly as products over all i and r in Eqs. (5)–(6). If bΛ_1 is negative (≈−0.98) while bΛ_2≈0, the stated screening rule bS={j:bΛ_j>c*} cannot recover X1, contradicting Theorem 2. Then inspect the authors' code: if bΛ_j is instead computed as n^{-1}∑_i log(ℓ^*_{i,Y_i}/ℓ_{i,Y_i}), the paper's theorems apply to an unstated corrected statistic rather than to the one defined in Section 2.4.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section 2.4, L0 and Lj are defined as products over every node i1 and every response level r1: L0=∏_{i1,r1}ℓ_{i1 r1}, Lj=∏_{i1,r1}ℓ^*_{i1 r1}, and (7) sets Λ_j=n^{-1}(log Lj−log L0). Because the product is over all r rather than only the observed Y_i, the self component of Λ_j is n^{-1}∑_i∑_r log(π^{r|X_{ij}}_{y|j}/π^r_y), plus network terms that cancel under the null. This is not the log-likelihood-ratio statistic n^{-1}∑_i log(π^{Y_i|X_{ij}}_{y|j}/π^{Y_i}_y) that would justify the PMLE frequency estimators, Condition (C3), or Proposition 6's chi-square limits. The sum over r can even be negative for a relevant feature: with R=K=2, P(Y=1|X=1)=0.9, P(Y=1|X=0)=0.1, P(Y=1)=0.5, each node contributes log(1.8)+log(0.2)≈−0.98, so a perfectly predictive self-related feature has Λ_j<0 and cannot be selected by any threshold c*>0. Moreover, the claim that the PMLEs are observed frequencies fails under the literal definition: maximizing the self part n∑_r log π^r_y subject to ∑_r π^r_y=1 gives π^r_y=1/R, not n_r/n. The subsequent decomposition into Λ_self^j and Λ_network^j inherits the same defect, and no supplementary proof can repair the definition as written. The simulations must be using the corrected product over observed levels, but the paper never states this correction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes PLR-SIS, a marginal feature-screening procedure for ultra-high-dimensional categorical features when the response and network edges are interdependent. It introduces self-related features, which directly affect the response, and network-related features, which affect edge formation, and constructs a log pseudo-likelihood ratio Lambda_j comparing a pseudo-likelihood without features with one that includes feature X_j. The main theoretical claims are strong screening consistency (Theorem 2), ranking consistency (Corollary 3), an improved dimension-growth rate when all true features are network-related (Corollary 4), interaction screening (Theorem 5), and chi-square null distributions for the self and network components (Proposition 6). The numerical evaluation includes nine simulation examples and a Sina Weibo application, reporting that PLR-SIS outperforms PC-SIS in feature recovery and prediction accuracy.","tokens_in":22459,"tokens_out":10589,"duration_ms":104214,"significance":"Network-aware feature screening for categorical data is a relevant and underdeveloped problem, and the conceptual separation of features into self-related and network-related components is a useful contribution. If the intended statistic were correctly defined, the PLR-SIS idea would give a principled marginal screening procedure with a clean self/network decomposition and a natural chi-square calibration, extending PC-SIS to network data. The paper also reports substantial prediction gains over PC-SIS on a real Weibo dataset. However, none of these strengths can be credited to the manuscript as written, because the displayed statistic is not the one analyzed in the theorems or, evidently, the one used in the simulations.","major_comments":[{"comment":"The literal definition of L0 and Lj as products over every node i1 and every response level r1 makes Lambda_j = n^{-1} sum_{i1} sum_{r1} log(ell*_{i1 r1}/ell_{i1 r1}). For a self-related feature with no network effect, this reduces to n^{-1} sum_i sum_r log(pi^{r|X_{ij}}_{y|j}/pi^r_y), which is not the likelihood-ratio statistic n^{-1} sum_i log(pi^{Y_i|X_{ij}}_{y|j}/pi^{Y_i}_y). The displayed quantity can be negative for informative features: with K=R=2, P(Y=1|X=1)=0.9, P(Y=1|X=0)=0.1, and P(Y=1)=0.5, every node contributes log(1.8)+log(0.2)=-1.02, so a perfectly predictive self-related feature has Lambda_j<0 and is never selected by the rule bS={j: bLambda_j>c*} with c*>0. Theorem 2 and Corollary 3 are therefore not theorems about the statistic that is defined and computed in the paper, and the simulation results in Table 3 cannot be reproducing the stated procedure unless a correction is made and reported.","section":"Section 2.4, Eq. (7), and Algorithm 1"},{"comment":"The statement that 'the PMLEs can be proved to be the observation frequencies' is inconsistent with the displayed pseudo-likelihood. Maximizing the self-part n sum_r log pi^r_y subject to sum_r pi^r_y = 1 gives pi^r_y = 1/R for all r, not n^r_y/n; the observed frequencies are the maximizers only for the product over observed response levels, product_i ell_{i,Y_i}. Similarly, for each level k of X_j, the factor n_k sum_r log pi^{r|k}_{y|j} is maximized by the uniform distribution over r, not by the observed conditional frequencies n^{rk}_{yj}/n^k_j. Thus the plug-in estimators used in Algorithm 1 are not the PMLEs for the objective defined in Eq. (7).","section":"Section 2.5"},{"comment":"Because Algorithm 1 as written computes the product over all response levels, the reported coverage probabilities, such as CP(X1)=1.00 and CP(X2)=0.99 in Example 1, cannot be reproduced from the procedure described in the text. The real-data decomposition of bLambda_self_j and bLambda_network_j is likewise not attributable to Eq. (7). The manuscript must state the statistic actually used in the numerical work and, after correcting the definition, re-run the simulations and the real-data analysis; without this, the empirical claims are not tied to the proposed method.","section":"Section 3, Table 3, and Section 4"},{"comment":"The claimed asymptotic distributions also fail under the displayed definition. For the self component, 2 bLambda_self_j is not the usual likelihood-ratio chi-square statistic for independence, because the product over r changes both the sign and the scaling; the example in the first comment gives a negative value for a relevant feature, so it cannot converge in distribution to a chi-square random variable. The degrees of freedom (R-1)(K-1) and R^2(K^2-1) correspond to the corrected observed-level statistic, not to Eq. (7).","section":"Section 2.6, Proposition 6"}],"minor_comments":[{"comment":"The word 'summerized' should be 'summarized'.","section":"Section 1.3"},{"comment":"The definition of Y_{(-i)} contains a typographical double comma: 'i1 not equal to i,, 1 <= i1 <= n'.","section":"Section 2.2"},{"comment":"The term 'model-free' is overstated, since the statistic is constructed under explicit conditional independence and Bernoulli edge-generation assumptions; this should be qualified in the introduction and abstract.","section":"Section 2.4"},{"comment":"The referenced tables D1-D3 in Appendix D are not included in the arXiv submission; please ensure the supplementary material is complete and available in any resubmission.","section":"Section 3.2"},{"comment":"The notation summary in Figure 3 is not fully explained in the text; the caption should define the tables and their row/column sums more explicitly.","section":"Section 2 and Figure 3"},{"comment":"The paired t-test p-values in Table 5 should be interpreted cautiously because the 50 replications use overlapping random 70/30 splits, so the effective sample size is smaller than 50; please state whether any correction for overlapping samples was applied.","section":"Section 4, Table 5"}],"recommendation":"reject","confidential_remarks":"The definitional inconsistency is decisive. The paper's central statistic, as displayed in Eq. (7) and Algorithm 1, is not the statistic used in the theorems or, evidently, in the experiments. A correction would change the definition, the PMLE claim, the theoretical statements, and the numerical evaluation, so the current submission does not support its central claims. If the authors resubmit after a major rewrite that reconciles the definition, the proofs, and the simulations, the underlying idea may warrant renewed consideration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know before reading further: the paper's central statistic, as defined in (5)–(7), is not the log-likelihood ratio the authors think it is, and the theory doesn't cover the written definition. The product over all response levels for every node makes the self-part a sum of log-odds over all categories, which can be negative for a strongly predictive feature. The claimed PMLEs are not the MLEs under that product; they'd be uniform. So the main theorem, the ranking corollary, and the chi-square limits are about a different statistic than the one defined.\n\nThe problem is real and timely. The split between self-related and network-related features gives a clean vocabulary, and using a pseudo-likelihood ratio to capture both marginal self-association and edge-generation association is a sensible idea. The simulation studies are fairly extensive (nine settings, varying levels, interactions, mismeasured networks), and the Sina Weibo application is appropriate. The writing is clear.\n\nThe definitional problem is not a typo at the margin—it breaks the paper. The stress-test arithmetic is correct: with binary Y and X, if P(Y=1|X=1)=0.9, P(Y=1|X=0)=0.1, P(Y=1)=0.5, each node contributes log(1.8)+log(0.2)<0 to the self part, so a perfect feature gets a negative Λ_j. No c*>0 would select it. Worse, the PMLE argument cannot produce observed frequencies from ∏_r π^r; the maximizer is uniform. The authors must have intended the product over observed responses only, and the simulations likely use that corrected version, but it is not written. That is an internal contradiction that a supplementary proof cannot repair. Also, the real-data comparison mixes the screening method with the downstream classifier type (Type-I for PC-SIS, Type-II/III for PLR-SIS), so the AUC gains may reflect the classifier rather than the screening. No code or data are provided, and the appendices are not in the arXiv posting.\n\nIf you need to know whether to cite or trust the results: don't yet. The idea deserves scrutiny and the fix looks feasible, but as it stands the central claim is unsupported. I'd tell the editor to send it out, but it will require major revision before it is publishable.","headline":"The central statistic as defined in (5)-(7) is not a log-likelihood ratio and the theory does not apply to it, so the paper's main claims are unsupported in the current form, though the underlying screening idea is worth developing.","tokens_in":23040,"tokens_out":3243,"would_cite":false,"duration_ms":33272,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F12","62H12","62H30"],"pacs":[],"model":"deepseek-v4-flash","headline":"A pseudo-likelihood ratio statistic can screen ultra-high-dimensional categorical tag data and recover exactly the features that drive both responses and network connections.","keywords":["feature screening","pseudo-likelihood ratio","network data","sure independence screening","strong screening consistency","ultra-high-dimensional categorical data","self-related features","network-related features"],"falsifier":"Generate $n=500$ nodes with $p=1000$ binary tags, draw $Y$ independent of all tags, and draw edges with probability $\\text{Sigmoid}(c \\cdot I(X_{i1}=X_{i2}=1))$ for two interacting tags while all other tags have zero edge effect; under the paper's (C3)-type signal condition no single tag changes the edge-generation probability marginally, so if PLR-SIS fails to select the interacting pair the claim that it recovers exactly $S_T$ in this regime is falsified.","tokens_in":21860,"feed_emoji":"🔗","tokens_out":8109,"duration_ms":76172,"temperature":0.7,"pith_summary":"This paper tackles feature screening for ultra-high-dimensional categorical tag data observed together with a social network, where the response (a user's preference) may be driven both by the user's own tags and by tags that shape who connects to whom. The central claim is that a single marginal statistic, the log pseudo-likelihood ratio $\\Lambda_j = n^{-1}(\\log L_j - \\log L_0)$ comparing a network pseudo-likelihood without features to one with feature $j$, detects both 'self-related' and 'network-related' features at once. The paper proves strong screening consistency: under conditions (C1)-(C3), the selected set equals the true union of the two types with probability tending to one, with faster convergence when all signal flows through edge formation. If correct, this turns the network structure from a complication into a source of selection signal, and gives practitioners a model-free way to shrink thousands of tags to a handful before downstream classification.","feed_headline":"Network structure becomes signal in tag feature screening","feed_subtitle":"PLR-SIS recovers both the tags that shape a user's choice and the tags that shape their ties, with probability approaching one.","key_machinery":"The central object is the log pseudo-likelihood ratio statistic $\\Lambda_j = n^{-1}(\\log L_j - \\log L_0)$, where $L_0$ and $L_j$ are products over nodes and response levels of posterior factors derived under two working models: edges are conditionally independent given the responses (Case 1), or given the responses and the single candidate feature $X_j$ (Case 2). The statistic carries the argument because it separates into a self-related component and a network-related component, and because the screening theorem shows that the population version $\\Lambda_j$ is exactly zero for irrelevant features while remaining positive for every feature in $S_T$. The conditional-independence working model is the engine that makes the statistic computable from observed frequencies, gives it tractable null chi-square asymptotics, and lets the same construction handle interactions by treating pairs of features as candidate items.","core_discovery":"The paper's discovery is that feature relevance in network-involved classification can be defined by two separate mechanisms, directly changing the response distribution and changing the edge-generation probability, and that both mechanisms are picked up by one pseudo-likelihood ratio statistic. For each candidate feature $j$, the statistic $\\Lambda_j = n^{-1}(\\log L_j - \\log L_0)$ is built from plug-in frequency estimators of $\\pi^{r_1r_2}_y$ and $\\pi^{r_1r_2k_1k_2}_{yj}$, and it decomposes as $\\Lambda_j = n^{-1}(\\Lambda_j^{\\text{self}} + \\Lambda_j^{\\text{network}})$. Self-related features register in the first term through the difference between $\\pi^{r|k}_{y|j}$ and $\\pi^r_y$; network-related features register in the second through the relative change in edge probabilities. The paper establishes that $\\Lambda_j = 0$ for irrelevant features and is bounded away from zero for every $j$ in $S_T$, yielding $P(\\hat{S} = S_T) = 1 - \\eta\\exp(\\log p - \\mu n) \\to 1$ under (C4), ranking consistency, a stronger $n^2$ rate when $S_Y \\subset S_A$, interaction screening over $O(p^2)$ pairs, and null chi-square limits for the two components.","pith_inferences":["An implicit consequence is that PLR-SIS can be read as a collection of conditional-independence screens: if one trusts the working model, $\\Lambda_j$ is a test statistic for whether $Y$ or $A$ depends on $X_j$, so the method doubles as an exploratory tool for classifying each tag's role as self-related, network-related, or both.","A natural stress test beyond the paper's simulations is to let edge formation depend on a low-dimensional latent community variable that correlates with many tags; the paper's conditions do not cover unobserved confounders, and one would expect the screening guarantee to degrade gracefully or fail.","The binomial edge assumption could be relaxed to a logistic degree-corrected model; the same pseudo-likelihood ratio construction should remain consistent if the correction is known or estimated at a fast enough rate, though the paper does not prove this.","Because the statistic separates self and network contributions, one could build a two-stage pipeline that screens with $\\Lambda_j$ and then fits a downstream network classifier using only the selected features; the paper's Type-II/III classifier comparison suggests the gain should persist for other network-aware classifiers."],"forward_implications":["PLR-SIS gives a model-free screening step for network classification: no model for $P(X,Y)$ or $P(A|X,Y)$ needs to be specified before selecting features.","When all true signals are network-related, exact feature recovery requires less data: the failure probability drops to $\\eta\\exp(\\log p - \\mu n^2)$, not $\\eta\\exp(\\log p - \\mu n)$.","Interactions among features can be screened in the same pass, so the procedure extends naturally from main-effect sets to sets that include pair products.","The null distributions of the self and network components are approximately chi-square, so threshold choices can be informed by p-values rather than by arbitrary cut-offs.","On the Sina Weibo data, the procedure selects 9 features instead of the 77 selected by a tag-only categorical screening method and gives higher prediction AUC, consistent with the claim that network-related features add predictive signal."],"supporting_citations":[{"why":"Establishes the sure independence screening paradigm and supplies the $[n/\\log n]$ and $n-1$ hard cut-off choices PLR-SIS adopts.","marker":"(Fan and Lv, 2008)"},{"why":"Provides the categorical PC-SIS baseline and the maximum-ratio soft cut-off rule used in Algorithm 1.","marker":"(Huang, Li and Wang, 2014)"},{"why":"Defines the network naive Bayes model that serves as simulation generation model and as motivation for response dependence on neighbors.","marker":"(Huang et al., 2018)"},{"why":"Supplies the network logistic regression model and the logistic edge-generation specification used in simulations and real-data estimation.","marker":"(Zhang et al., 2020)"},{"why":"Gives the flexible generative framework $P(A|X,Y)$ that underlies the paper's data-generation assumptions and the sufficiency decomposition.","marker":"(Ma et al., 2019)"},{"why":"Supports the assumption that only a few nodal covariates drive edge formation, which motivates condition (C3) for network-related features.","marker":"(Yan et al., 2019)"},{"why":"Provides the model-free screening framework and marginal-probability conditions similar to (C1).","marker":"(Cui, Li and Zhong, 2015)"},{"why":"Introduces network linear discriminant analysis and the form of edge-probability sparsity conditions the paper invokes.","marker":"(Cai et al., 2018)"},{"why":"Supplies network-dependence limit theory that supports the conditional-independence working model for edges.","marker":"(Kojevnikov, Marmer and Song, 2021)"}],"fun_headline_variants":["One statistic catches both direct and network-driven tag effects","Pseudo-likelihood ratio screens tags for user choice and ties","Tag screening goes beyond self-effects to network structure","Two relevance pathways, one pseudo-likelihood ratio statistic"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a feature's full relevance is captured by the marginal pseudo-likelihood that conditions on at most the response and that one feature; if edge formation or response actually depends on combinations of features or on unobserved confounders, the screening consistency proof does not apply.","fun_headline_variants_meta":{"raw":{"variants":["One statistic catches both direct and network-driven tag effects","Pseudo-likelihood ratio screens tags for user choice and ties","Tag screening goes beyond self-effects to network structure","Two relevance pathways, one pseudo-likelihood ratio statistic"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000221,"raw_usage":{"total_tokens":1467,"prompt_tokens":980,"completion_tokens":487,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":596,"completion_tokens_details":{"reasoning_tokens":421}},"tokens_in":596,"tokens_out":487,"duration_ms":4711,"temperature":1.0,"reasoning_tokens":421,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:32:00.799022+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate $n=500$ nodes with $p=1000$ binary tags, draw $Y$ independent of all tags, and draw edges with probability $\\text{Sigmoid}(c \\cdot I(X_{i1}=X_{i2}=1))$ for two interacting tags while all other tags have zero edge effect; under the paper's (C3)-type signal condition no single tag changes the edge-generation probability marginally, so if PLR-SIS fails to select the interacting pair the claim that it recovers exactly $S_T$ in this regime is falsified.","supporting_citations":[{"cited_title":", Li , Runze R","cited_arxiv_id":null,"evidence_quote":"Provides the categorical PC-SIS baseline and the maximum-ratio soft cut-off rule used in Algorithm 1."},{"cited_title":", Guan , Guoyu G","cited_arxiv_id":null,"evidence_quote":"Defines the network naive Bayes model that serves as simulation generation model and as motivation for response dependence on neighbors."},{"cited_title":", Pan , Rui R","cited_arxiv_id":null,"evidence_quote":"Supplies the network logistic regression model and the logistic edge-generation specification used in simulations and real-data estimation."},{"cited_title":", Jiang , Binyan B","cited_arxiv_id":null,"evidence_quote":"Supports the assumption that only a few nodal covariates drive edge formation, which motivates condition (C3) for network-related features."},{"cited_title":", Li , Runze R","cited_arxiv_id":null,"evidence_quote":"Provides the model-free screening framework and marginal-probability conditions similar to (C1)."},{"cited_title":", Guan , Guoyu G","cited_arxiv_id":null,"evidence_quote":"Introduces network linear discriminant analysis and the form of edge-probability sparsity conditions the paper invokes."},{"cited_title":", Marmer , Vadim V","cited_arxiv_id":null,"evidence_quote":"Supplies network-dependence limit theory that supports the conditional-independence working model for edges."}],"review_version":1}