{"id":"45b2a724-55d7-4b47-b103-db111996b91e","arxiv_id":"2502.08567","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper derives p-values for signed co-occurrence in bipartite networks and uses false discovery rate control to build validated signed projections.","lead":"This paper introduces an unsupervised, statistically validated method to project bipartite signed networks, linking nodes with significantly many shared agreements or disagreements. It assigns signed edges based on p-values from null models and tests it on synthetic and real voting and rating data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The FDR step is not actually error-controlled: BH is invoked 'irrespectively of independence' and |H| is set to sum V_ij rather than the number of tested pairs, so the claim of statistical validation is unsupported until both issues are fixed.","rationale":"The reader's weakest assumption matches the concern I would put at the centre: error-rate accounting. I agree rather than partially because both components of that assumption, dependence robustness and the |H| count, are load-bearing. The algebraic derivation of the Poisson-binomial nulls (Eqs. 33, 40, and appendices) is internally coherent, and the released SIMONA code is a genuine point in the authors' favour; I have no substantive objection to the maximum-entropy benchmarks themselves. The strongest reason for not rejecting outright is that the flaw is localised in the multiple-testing step and is checkable: if the Monte Carlo test controls FDP, the conditional verdict may be lifted; if it does not, recalibration or a dependence-robust correction is necessary. I therefore leave the reader's CONDITIONAL verdict unchanged.","tokens_in":32465,"tokens_out":10117,"duration_ms":115703,"concrete_test":"Simulate R=1000 null realizations of each real network under each fitted benchmark (fixed-topology BiSRGM-FT and BiSCM-FT with fitted p+_iα; free-topology BiSRGM and BiSCM with fitted probabilities). For every realization, compute the full matrix of two-sided p-values via Eq. 41 and apply the paper's FDR rule using (a) |H| = sum V_ij as in Appendix C, (b) |H| = number of tested node pairs, and (c) Benjamini-Yekutieli. Under the global null, estimate the realized FDP among rejected pairs. If the average FDP under (a) or (b) exceeds the nominal 0.05, or if (a) and (b) yield materially different edge sets, the FDR claim fails and the projection must be recalibrated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the edge set produced in Step 3 have a controlled false-discovery rate. That requirement is not met as stated. Section IV.H invokes Benjamini-Hochberg as controlling FDR 'irrespectively of the independence of the hypotheses tested'. This is not true of the BH procedure: BH controls FDR under independence or positive regression dependence (PRDS), not under arbitrary dependence. The p-values for different node pairs are dependent because they are functions of the same signed entries b_iα, e.g. S_ij and S_ik both involve b_iα for a shared item α, and no PRDS proof or dependence-robust correction is supplied. Separately, Appendix C sets the zero-deflated number of hypotheses to |H| = sum_{i<j} V_ij, although the algorithm computes one p-value per node pair. BH requires |H| to be the number of p-values in the sorted list; using sum V_ij changes the critical values p_th = i*t/|H| and makes the stated procedure inconsistent with the p-value matrix actually produced. Consequently the validated projection may include more false-positive edges than the nominal level, so the abstract's 'statistically validated' edges and the inferred 'genuine traces of self-organisation' are not supported as stated. The issues are fixable by correcting |H| and either proving PRDS for these p-values or applying a dependence-robust FDR method, but they are load-bearing.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a method for obtaining statistically validated signed projections of binary undirected bipartite signed networks. Two schemes are defined: a zero-deflated scheme that ignores motifs involving missing ties and a zero-inflated scheme that treats missing ties as agreeing/disagreeing evidence. For each node pair, a signature S_ij is compared with its distribution under maximum-entropy benchmarks (global and local, fixed- and free-topology variants, namely BiSRGM-FT, BiSCM-FT, BiSRGM, BiSCM), yielding a two-sided p-value from a binomial or Poisson-binomial distribution. The p-value matrix is thresholded with the Benjamini-Hochberg FDR procedure to produce positive/negative/zero edges in the projection. The method is tested on synthetic BiSSBM configurations and applied to FilmTrust, U.S. Senate, and U.S. House of Representatives data, where the authors claim to detect non-trivial mesoscopic structures that reveal 'genuine traces of self-organisation'.","tokens_in":32782,"tokens_out":7101,"duration_ms":82552,"significance":"The paper addresses a genuine gap: statistically validated projections for signed bipartite networks are much less developed than for unsigned networks. The derivations in Appendices A and B are careful and internally consistent, the synthetic tests based on a fully controllable generative model are appropriate, and the authors release their code. If the multiple-testing step is correctly calibrated, the proposed tool would be a useful contribution to the statistical validation of signed bipartite projections. However, the current FDR implementation contains two load-bearing problems, so the 'statistically validated' claim in the abstract is not yet supported as written.","major_comments":[{"comment":"The definition of |H| in Appendix C is inconsistent with the procedure that actually generates the p-values. Step B of Section IV.E computes one p-value per node pair, yet Appendix C sets |H| = sum_{i<j} V_ij within the zero-deflated scheme. The BH procedure requires |H| to be the number of p-values in the sorted list; if the actual list has length m, the critical value for the i-th sorted p-value is i*t/m. Using sum_{i<j} V_ij instead of m (or instead of the number of pairs with V_ij>0, if zero-common-neighbour pairs are excluded) changes the rejection threshold and invalidates the claimed FDR control. Depending on the data, sum_{i<j} V_ij can be larger or smaller than the number of tested pairs, so the miscalibration can be either conservative or anti-conservative. Please correct |H| to the actual number of tested hypotheses and explicitly state how pairs with V_ij=0 are handled.","section":"Appendix C and Section IV.H"},{"comment":"The statement that FDR controls errors 'irrespectively of the independence of the hypotheses tested' is not correct for the Benjamini-Hochberg procedure. BH controls FDR under independence or under positive regression dependence (PRDS), but not under arbitrary dependence. The p-values produced here are dependent: S_ij and S_ik are functions of the same signed entries b_iα for common items α, and the manuscript supplies no PRDS proof and no dependence-robust correction. A concrete fix is to prove the required dependence property for these p-values, to replace BH with a dependence-robust method (e.g., Benjamini-Yekutieli), or to calibrate the procedure by simulation under the null model.","section":"Section IV.H"},{"comment":"The real-world mesoscopic conclusions, including the claim of 'genuine traces of self-organisation', are drawn from the edge sets produced by the FDR step. These conclusions therefore inherit the FDR calibration problems described above. Once the multiple-testing step is corrected, the corresponding claims about modular structures, negative/positive modules, and balance-theory alignment should be re-examined, since the validated edge set may change.","section":"Section II.B.2-3"}],"minor_comments":[{"comment":"The update equation for y_i has a typo: the numerator should be w_alpha^{(n-1)}, not z_alpha^{(n-1)}, to match the derivative with respect to y_i. The same typo appears in the displayed iterative form.","section":"Appendix E, Eq. (E2)"},{"comment":"The fourth row is labelled 'Zero-deflated projection - nai¨ve' but, based on its values and the surrounding rows, it should be labelled 'Zero-inflated projection - nai¨ve'. In addition, the entry '1.135.278' appears to be a malformed number.","section":"Table I"},{"comment":"The definition of MRE uses expressions such as |k^-_i(B*)⟨k^-_i⟩| / k^-_i(B*), which are missing the subtraction operator; it should read |k^-_i(B*) - ⟨k^-_i⟩| / k^-_i(B*), and analogously for the h^-_alpha term.","section":"Appendix E, Eq. (E8)"},{"comment":"The text 'see Sections IV I 1, IV I 1' contains a duplicated cross-reference; one of the two references appears to be intended for the local-constraint model and the other for the global-constraint model.","section":"Section IV.G.1"}],"recommendation":"major_revision","confidential_remarks":"The FDR issues are substantive but local: the underlying distributional derivations and the synthetic validation are sound, and the problems can be fixed by correcting |H| and either proving the required dependence property or using a dependence-robust FDR procedure. I would not reject the paper on the current evidence, but the revision should address the multiple-testing step before the statistical-validation claims can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper does something genuinely useful—extends the statistically validated projection framework to signed bipartite networks, with four benchmarks, two missing-tie treatments, and a released code package. The derivations in Appendices A and B are careful, and the synthetic tests are appropriate. If you work on signed bipartite data, this is worth reading.\n\nThe soft spot is the multiple-testing step, and it is load-bearing. Section IV.H says FDR controls errors 'irrespectively of the independence of the hypotheses tested.' That is not true of Benjamini-Hochberg; it needs at least positive regression dependence. The p-values here are dependent because they are functions of the same signed entries. No PRDS proof is given. Separately, Appendix C sets the zero-deflated number of hypotheses to |H| = sum of V_ij, but the algorithm produces one p-value per node pair. That miscalibrates the BH critical values. Both issues are fixable, but as written the 'statistically validated' edges are not actually error-controlled, and the 'genuine self-organisation' conclusions inherit that weakness.\n\nThe circularity concern does not land. Fitting the null model to the same network is calibration, not circularity; the synthetic tests are generated independently.\n\nNet: a sound framework with a broken error-rate accounting. I would not desk-reject it: the method is useful and the fixes are straightforward. Send it out to a referee who knows multiple-testing theory, and ask for a correction or a dependence-robust FDR procedure.","headline":"A useful signed-network projection method whose FDR step is miscalibrated as written—fixable but load-bearing.","tokens_in":33303,"tokens_out":1820,"would_cite":true,"duration_ms":18583,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["89.75.Fb","02.50.Tt"],"model":"deepseek-v4-flash","headline":"Statistically validated projections of bipartite signed networks are obtained by turning significant concordance into positive edges and significant discordance into negative edges.","keywords":["signed bipartite networks","statistically validated projection","p-value matrix","maximum-entropy null models","false discovery rate","balance theory","mesoscale structure","Poisson-binomial distribution"],"falsifier":"Generate signed bipartite networks from a null model with no community or block structure, run the full pipeline many times, and count the fraction of validated positive and negative edges; if that fraction consistently exceeds the 0.05 false-discovery-rate level, the p-value construction in Eqs. (33), (40), and (41) is miscalibrated.","tokens_in":32239,"feed_emoji":"🔗","tokens_out":9922,"duration_ms":87482,"temperature":0.7,"pith_summary":"Signed bipartite networks—votes on bills, ratings of movies—leave the interesting question open: which two legislators or users genuinely agree or disagree, rather than merely sharing many items by chance? This paper argues that the answer is a signed projection in which a positive edge connects any pair of nodes sharing a statistically significant number of concordant relationships and a negative edge connects any pair sharing a statistically significant number of discordant relationships. Significance is judged against four maximum-entropy benchmarks that randomize signs (and, in the free-topology variants, missing links) while preserving global or local degree constraints, and the resulting p-values are filtered with the false discovery rate. Applied to U.S. Congress voting and FilmTrust ratings, the method produces sparse projections whose mesoscale structure aligns better with relaxed balance theory—which permits negative links within communities and positive links between them—than with traditional balance theory.","feed_headline":"A p-value picks out genuine agreements in signed networks","feed_subtitle":"Shared likes become positive links and shared dislikes negative links, once chance is filtered out by a maximum-entropy benchmark.","key_machinery":"The load-bearing object is the signature $S_{ij}=C_{ij}-D_{ij}$, where $C_{ij}$ counts concordant dyadic motifs ($++$, $--$, and in the zero-inflated scheme also $00$) and $D_{ij}$ counts discordant motifs ($+-$, $-+$, and the partial motifs $0+$, $+0$, $0-$, $-0$). Under the maximum-entropy null models, each motif is a Bernoulli variable, making $S_{ij}$ Poisson-binomial for local constraints (BiSCM, BiSCM-FT) and binomial for global constraints (BiSRGM, BiSRGM-FT); the two-sided p-value follows from the cumulative distribution, and the false-discovery-rate procedure [58] converts the p-value matrix into a validated edge set. The zero-deflated schemes fix the bipartite topology and randomize only signs; the zero-inflated schemes leave topology free and count missing ties as part of concordance or discordance.","core_discovery":"The paper's central claim is that a statistically validated projection of any binary undirected bipartite signed network can be obtained by defining, for each pair of nodes in the layer of interest, the signature $S_{ij}=C_{ij}-D_{ij}$, the difference between concordant and discordant shared motifs, and retaining a positive (negative) edge exactly when the empirical signature is so far from the benchmark expectation that the two-sided p-value $p_{ij}=2\\min\\{F(S^*_{ij}),1-F(S^*_{ij})\\}$ falls below the FDR threshold. This is an unsupervised, white-box rule: no hand-tuned threshold is needed, and the output is a matrix of link-specific p-values from which the projection follows. The authors test the algorithm on synthetic block-model configurations and on U.S. Senate, U.S. House, and FilmTrust data, finding modules that survive validation and are not explained by the constraints encoded in the benchmarks.","pith_inferences":["Setting the FDR denominator to $|H|=\\sum_{i<j} V_{ij}$ in the zero-deflated scheme, rather than to the number of tested node pairs $N(N-1)/2$, may make the threshold less conservative; recomputing the Senate and House projections with the full denominator would show whether the detected modules survive.","The zero-inflated treatment of a $00$ motif as concordance encodes a substantive assumption about missingness; an analysis that instead treats missing ties as neutral would test how much of the \"self-organisation\" reading depends on that choice.","The same p-value machinery could be applied to temporal signed bipartite data to ask whether validated agreement/disagreement networks become more balanced over time, a prediction the paper's cross-sectional results hint at but do not test."],"forward_implications":["Validated projections are sparser than naive ones: the local filters cut more edges than the global filter on all three real-world datasets, and both filters reveal more BIC-detected modules than the naive projections.","The surviving structures favor relaxed balance theory: negative links appear inside modules and positive links between modules in several projections, a pattern traditional balance theory rules out.","The algorithm doubles as a sign-prediction rule: pairs with significantly concordant motifs get +1, significantly discordant pairs get -1, and non-significant pairs are left unlinked.","Because the output is a p-value matrix, any multiple-hypothesis procedure can be swapped in place of the FDR filter without changing the earlier steps."],"supporting_citations":[{"why":"Supplies the unsigned statistically validated projection algorithm that this paper extends to signed networks.","marker":"[36]"},{"why":"Introduces the free-topology Bipartite Signed Random Graph and Configuration Models used as benchmarks.","marker":"[13]"},{"why":"Provides the false-discovery-rate procedure that turns the p-value matrix into a validated edge set.","marker":"[58]"},{"why":"Supplies the U.S. Senate and U.S. House signed bipartite datasets and their Congress-vote encoding.","marker":"[21]"},{"why":"Supplies the FilmTrust rating dataset, binarized into positive and negative user-movie links.","marker":"[45]"},{"why":"Provides the fixed-point numerical recipe used to fit the local-constraint benchmarks BiSCM and BiSCM-FT.","marker":"[66]"},{"why":"Defines relaxed balance theory and the BIC-based module detection used to interpret the projections.","marker":"[8]"}],"fun_headline_variants":["p-values expose genuine signed links in bipartite projections","Statistical validation for signed bipartite network projections","Chance-filtered projection reveals true signed relationships","Unsupervised algorithm validates signed bipartite projections","Signed projections now statistically grounded via p-values"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that each sign and each missing link can be treated as an independent random variable once its probability is fitted from the data, and that the false-discovery-rate correction still controls errors when the pairwise tests are correlated and the number of tested hypotheses is counted through shared motifs rather than through node pairs.","fun_headline_variants_meta":{"raw":{"variants":["p-values expose genuine signed links in bipartite projections","Statistical validation for signed bipartite network projections","Chance-filtered projection reveals true signed relationships","Unsupervised algorithm validates signed bipartite projections","Signed projections now statistically grounded via p-values"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000208,"raw_usage":{"total_tokens":1377,"prompt_tokens":891,"completion_tokens":486,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":416}},"tokens_in":507,"tokens_out":486,"duration_ms":5640,"temperature":1.0,"reasoning_tokens":416,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T04:37:56.382772+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate signed bipartite networks from a null model with no community or block structure, run the full pipeline many times, and count the fraction of validated positive and negative edges; if that fraction consistently exceeds the 0.05 false-discovery-rate level, the p-value construction in Eqs. (33), (40), and (41) is miscalibrated.","supporting_citations":[{"cited_title":"Latapy, C","cited_arxiv_id":null,"evidence_quote":"Supplies the unsigned statistically validated projection algorithm that this paper extends to signed networks."},{"cited_title":"Zaslavsky, The Electronic Journal of Combinatorics , DS8 (2012)","cited_arxiv_id":null,"evidence_quote":"Introduces the free-topology Bipartite Signed Random Graph and Configuration Models used as benchmarks."},{"cited_title":"Andres, G","cited_arxiv_id":null,"evidence_quote":"Provides the false-discovery-rate procedure that turns the p-value matrix into a validated edge set."},{"cited_title":"Iorio, M","cited_arxiv_id":null,"evidence_quote":"Supplies the U.S. Senate and U.S. House signed bipartite datasets and their Congress-vote encoding."},{"cited_title":"Gualdi, G","cited_arxiv_id":null,"evidence_quote":"Supplies the FilmTrust rating dataset, binarized into positive and negative user-movie links."},{"cited_title":"Schoch, The Journal of Mathematical Sociology 45, 37 (2021)","cited_arxiv_id":null,"evidence_quote":"Provides the fixed-point numerical recipe used to fit the local-constraint benchmarks BiSCM and BiSCM-FT."},{"cited_title":"In what follows we will focus on Sij but the same considerations hold true for Sij","cited_arxiv_id":null,"evidence_quote":"Defines relaxed balance theory and the BIC-based module detection used to interpret the projections."}],"review_version":1}