{"id":"90b16f5b-eec7-46b9-9638-3ddc4e2ee4b1","arxiv_id":"2506.22963","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"CN-SBM jointly clusters samples and genomic bins using categorical copy number states, decomposes profiles into primary and residual variation, and reports better held-out likelihood than existing CNV co-clustering methods.","lead":"The paper introduces CN-SBM, a categorical block model that clusters tumor samples and genomic regions from integer copy number calls, then separates the calls into broad primary patterns and finer residual deviations. On TCGA low-grade glioma, the resulting clusters plus age reach a survival concordance index of 0.855.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The benchmark scoring is asymmetric: PoissonSBM and Blockcluster are scored under empirical categorical block distributions (B.2) rather than their own fitted predictive distributions, so Table 1's 'improved model fit' may reflect scoring protocol rather than model quality.","rationale":"I read the paper as a serious contribution: the categorical SBM and the two-stage primary/residual decomposition are sensible, and the released code is a concrete asset. The reader's first concern about LGG in-sample selection is real, but I think the more load-bearing issue is B.2's asymmetric scoring: it underlies every quantitative benchmark claim in Table 1, not just one application. The baseline comparison is not intrinsically unfair if the question is 'which method produces partitions that are more useful under a categorical model,' but the paper's wording ('model fit') and the reported held-out log-likelihood and ICL are then not a comparison of fitted models. A symmetric rerun is feasible and would settle it. The clinical C-index concern is important but secondary; even if validated, the benchmark claim needs the correction. Since the reader already identified this B.2 issue (as a second premise), I partially agree with their weighting; I would keep the CONDITIONAL verdict.","tokens_in":19663,"tokens_out":5916,"duration_ms":70378,"concrete_test":"Using the released code, rerun the Table 1 benchmark with symmetric model scoring: score PoissonSBM under its fitted Poisson block model's posterior predictive on the 1% held-out entries, score Blockcluster under its own fitted categorical block distributions, and score CN-SBM under its variational posterior predictive; compute ICL with each method's own integrated likelihood and with the actual number of row and column clusters used by that method in the penalty. If CN-SBM still wins on a majority of datasets, the model-fit claim stands; if not, the claim must be weakened to 'better under a categorical post-hoc scoring'.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 and Table 1 are the backbone of the model-fit claim, but the comparison is not apples-to-apples. The text states that for PoissonSBM and Blockcluster, held-out log-likelihood and ICL are computed from empirical categorical block distributions estimated from the hard partitions, explicitly not from the probability distributions those methods infer. For PoissonSBM, the own-model Poisson likelihood is much lower by construction (B.2, Table 3); for Blockcluster, the package's own categorical outputs were so unstable that package-specific metrics are reported only in Table 3. Scoring every baseline under a categorical block likelihood estimated after the fact measures the clustering partition, not the fitted generative model, while CN-SBM is credited with its own variational predictive distribution. The ICL comparison is also muddied because PoissonSBM does not fix row and column cluster counts (it averaged 25 row clusters on BRCA despite K=10), yet the ICL penalty in B.1 is written in terms of a single K and L. Thus the strongest quantitative support for 'highest held-out log-likelihood across most datasets' and 'highest ICL across all datasets' rests on a scoring choice that favours the categorical model by construction. This is not a claim that the method is wrong, only that the headline comparison has not yet been fairly demonstrated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes CN-SBM, a bipartite categorical stochastic block model for integer copy-number states, with Dirichlet priors and mean-field variational inference, including missing-data weighting and a stochastic variational extension. A two-stage procedure fits the model, constructs a main-variation matrix from posterior modes, subtracts it from the data, and refits the model on the categorical residuals. The manuscript evaluates held-out log-likelihood, ICL, accuracy, and entropy against PoissonSBM, Blockcluster, k-means, and spectral biclustering on simulated data, single-cell PDX data, and TCGA bulk cohorts, and applies the two-stage decomposition to TCGA low-grade glioma survival analysis. The headline claims are that CN-SBM achieves the highest held-out log-likelihood across most datasets and the highest ICL across all datasets, and that residual clusters add independent prognostic information.","tokens_in":19891,"tokens_out":6008,"duration_ms":62626,"significance":"If the claims hold, CN-SBM would be a useful addition to CNV analysis: it respects the discrete and multimodal nature of copy-number states, scales through CAVI and SVI, and provides an interpretable primary/residual decomposition. The paper ships public code, gives a closed-form ELBO derivation in Appendix A.1, and evaluates on multiple real datasets with a held-out missingness protocol, which are genuine strengths. The main weaknesses are the asymmetric benchmark scoring in Table 1 and the in-sample survival model selection in Section 4; both bear directly on the paper's central claims and need to be addressed before the conclusions can be accepted at face value.","major_comments":[{"comment":"The headline benchmark comparison is asymmetric. The main text states that for PoissonSBM and Blockcluster, held-out log-likelihood and ICL in Table 1 are computed from empirical categorical block distributions estimated from the hard partitions, 'as the inferred probability distributions from their implementations generally yielded poorer results.' CN-SBM, by contrast, is scored under its own variational predictive distribution. Consequently, Table 1 does not compare fitted generative models: it compares CN-SBM's model-based prediction against a post-hoc categorical plug-in applied to the baselines' partitions. The finding that a categorical plug-in beats a Poisson plug-in is partly by construction, because the Poisson likelihood assigns much lower probability to individual copy-number values (Appendix B.2, Table 3). To support 'improved model fit,' the authors should report each method's own-model held-out log-likelihood and ICL under comparable model-selection settings, or explicitly reframe Table 1 as a comparison of hard-partition quality under a common empirical categorical scoring rule and move accuracy and entropy (Table 2) to the primary claim.","section":"Section 4 and Appendix B.3"},{"comment":"The prognostic claim is based on in-sample model selection. The final Cox model was obtained by inspecting p-values in the same LGG cohort, merging main clusters 1 and 2 after observing their similarity and refitting without the X chromosome, and adding residual clusters 3 and 8 because of their hazard-ratio significance. The reported C-index of 0.855 (SE = 0.019) is then computed on the same data used for selection, with no cross-validation, bootstrap correction, or external validation. This protocol is known to inflate discrimination, so the claim that residual variation 'provides complementary and independently prognostic information' is not yet supported. The authors should provide internal validation (e.g., cross-validated C-index or optimism-corrected bootstrap) or an independent cohort, and otherwise describe the analysis as exploratory.","section":"Section 3 and Appendix B.1"},{"comment":"The ICL comparison is not well-defined for baselines whose model size is not fixed. The ICL penalty in B.1 is written for a single K and L, but the text reports that PoissonSBM 'averaging 25 row clusters in BRCA despite K = 10' and Blockcluster also selects its own number of clusters; Table 1 still reports ICL for these methods under the empirical block distributions. The authors need to specify which K and L were used in the ICL penalty for each fitted model, and adjust the penalty if the final number of clusters differs from the requested K and L. Without this, the 'highest ICL across all datasets' claim is not comparable across methods.","section":"Section 3 and Appendix B.1"}],"minor_comments":[{"comment":"Algorithm 1: the global update for γh is written as αh + Σ_{j=1}^N φ^h_{j,·}, but the column index runs to M; the same N/M slip appears in the local-update notation in Algorithm 2. The text defines N cells and M bins, so the column update should use M.","section":"Algorithm 1"},{"comment":"Section 4 states N = 490 for LGG, but Figure 3A caption says N = 484 after excluding six outlier samples; make the cohort sizes consistent at each stage of the analysis.","section":"Section 4 and Figure 3"},{"comment":"Appendix B.3 refers to 'the final model shown in Fig. 3D', but Figure 3 has panels A through C only; the reference should be to Figure 4A or the figure should be re-labelled.","section":"Appendix B.3"},{"comment":"Appendix B.2 contains a typo: 'perfomrance' should be 'performance'.","section":"Appendix B.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is competently written and the method itself is reasonable and well motivated. The main risk is the asymmetric benchmark scoring in the central model-fit comparison; I would send the paper back for major revision. If the authors rescore or reframe the benchmarks and add validation for the survival analysis, the paper could become acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a legitimate methods paper — a categorical SBM for integer copy-number states with a two-stage primary/residual split — and the LGG analysis is suggestive. But the main benchmark claim, \"highest held-out log-likelihood and ICL,\" rests on a scoring protocol that favors the categorical model, and the survival numbers are in-sample with data-driven cluster merging. Neither kills the paper; both need to be fixed or reframed.\n\nWhat's new and useful: previous co-clustering for CNV has used Gaussian or Poisson emissions; a categorical emission is the natural distribution for integer CNV calls, so the model choice is well-motivated. The variational inference is standard but competently derived, with an SVI extension and missing-data weighting, and code is released. The two-stage idea — fit an SBM for dominant patterns, then fit a second SBM to the residuals — is simple and interpretable. The LGG results (e.g., residual clusters adding survival separation within main clusters) are a nice illustration, not proof.\n\nSoft spots: (1) Table 1's head-to-head is not clean. For PoissonSBM and Blockcluster, held-out log-likelihood and ICL are computed using empirical categorical block distributions estimated from hard partitions, not the distributions those models infer. That turns the metric into a measure of partition purity under categorical emission, while CN-SBM is credited with its own variational predictive distribution. The gap can be partly an artifact of scoring. You disclose this in B.2 and give Table 3 with package-specific metrics, which is honest, but the abstract and Section 3's \"highest ICL across all datasets\" overstate what the comparison actually shows. The ICL penalty is also written for a single K and L, while PoissonSBM varies row cluster count. (2) The survival analysis is entirely in-sample: clusters merged based on p-values, residual clusters kept based on significance, no validation cohort. The 0.855 C-index should be labeled exploratory. (3) The CNAsim simulation has known ground truth but no clustering-recovery metric (e.g., ARI); reporting that would be much stronger than likelihood alone. (4) The IPW missing-data scheme is presented as a contribution but isn't empirically tested.\n\nIs the central method sound? Yes, circularity isn't an issue. I'd send this to peer review, but ask for a cleaner benchmark or reframed claims, a validation split for the survival model, and a ground-truth simulation result.","headline":"A sensible categorical SBM for CNV with a useful two-stage decomposition, but the headline fit comparison is scored under a rule that favors it, and the survival claim is exploratory.","tokens_in":20482,"tokens_out":3331,"would_cite":true,"duration_ms":38351,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62H30","62F15"],"pacs":[],"model":"deepseek-v4-flash","headline":"CN-SBM, a bipartite categorical stochastic block model, jointly clusters tumor samples and genomic bins by copy-number state and then re-models the leftover variation, which carries independent survival signal.","keywords":["copy number variation","stochastic block model","categorical data","co-clustering","variational inference","tumor heterogeneity","survival analysis","low-grade glioma"],"falsifier":"Re-run the survival analysis on a separate low-grade glioma cohort with the residual-cluster inclusion rule fixed in advance rather than selected by p-values; if the C-index falls back toward the age-only 0.741, the claim that residual variation adds independent prognostic information fails.","tokens_in":19430,"feed_emoji":"🧬","tokens_out":6405,"duration_ms":61355,"temperature":0.7,"pith_summary":"Copy-number profiles are integer-valued and multimodal, so modeling them as Gaussian or Poisson can blur the very structure that defines tumor subgroups. The paper introduces CN-SBM, a bipartite stochastic block model in which each cell (or sample) and each genomic bin gets a latent cluster, and every cluster pair has its own categorical distribution over copy-number states. Because the model respects discreteness, it can be fit in two stages: the first stage captures dominant, large-scale alterations, and the second stage re-models the residual deviations that remain after subtracting the dominant pattern. On simulated and real cancer datasets the model reports the highest held-out log-likelihood on most benchmarks and the highest integrated completed likelihood on all of them, and in low-grade glioma the residual layer adds survival discrimination beyond the primary clusters. The care-worthy point is that structured signal can survive in the part of the data that is usually thrown away as noise.","feed_headline":"Block model splits copy-number data into two signal layers","feed_subtitle":"The leftover variation beyond dominant copy-number patterns still separates patient outcomes.","key_machinery":"The carrying object is the bipartite categorical stochastic block model: latent cluster assignments $g_i$ for rows (cells or samples), $h_j$ for columns (genomic bins), and per-cluster-pair categorical distributions $\\pi_{(k,l)}$ over the discrete copy-number alphabet, with Dirichlet priors. Inference is mean-field coordinate-ascent variational inference, whose updates use digamma expectations of log block probabilities; the two-stage analysis works by assigning each entry its block's modal category to form a main matrix, subtracting that from the observed matrix to form residuals, then refitting the same model to the residual matrix.","core_discovery":"The paper claims that copy-number variation is better described by a categorical bipartite block model than by count or continuous co-clustering models, and that the fitted model yields a natural decomposition into primary and residual layers. The central discovery is empirical: once the dominant block pattern is subtracted from each cell-bin pair, the leftover residual matrix is not noise but contains structured, reproducible patterns—focal losses, gains, and widespread deletions—and in low-grade glioma data these residual clusters improve a Cox survival model from a C-index of 0.741 with age alone to 0.855 with age, main clusters, and residual clusters. The paper also claims that mean-field variational inference with empty-cluster support and a stochastic extension makes the fit efficient enough for cohorts of roughly a thousand samples at 500 kb resolution, with model selection handled automatically.","pith_inferences":["If the residual prognostic signal replicates in an independent cohort, the same two-stage recipe could be applied directly to any integer-valued copy-number calling output, turning a standard preprocessing artifact into a stratification feature without new assays.","The categorical block model could be lifted to other discrete genomic readouts, such as allele-specific copy states, mutation multiplicity, or binarized methylation, where the same Gaussian or Poisson mismatch occurs.","The subtraction-based residual construction is post hoc; a generative two-layer model that treats primary modes and residual deviations as separate latent variables would let the decomposition be scored by likelihood and would make the main-residual split a testable hypothesis rather than an algorithmic step."],"forward_implications":["Across simulated and real datasets, CN-SBM reports the highest integrated completed likelihood on all seven benchmarks and the highest held-out log-likelihood on most, so categorical modeling outperforms Poisson and empirical-block baselines on the paper's comparisons.","The two-stage decomposition turns copy-number data into interpretable layers: large-scale recurrent events in the main stage, and focal or sample-specific aberrations in the residual stage.","In low-grade glioma, patients sharing a primary copy-number cluster split into residual clusters with distinct survival trajectories, so residual variation is a candidate stratification feature.","The variational updates tolerate empty clusters, giving an implicit automated way to choose the number of cell and bin clusters, and the stochastic variant scales to large cohorts and finer bin resolutions."],"supporting_citations":[{"why":"Supplies the categorical latent block model that CN-SBM builds on.","marker":"Keribin et al., 2015"},{"why":"Provides the single-cell PDX datasets and motivates separating primary from residual variation.","marker":"Funnell et al., 2022"},{"why":"Supplies the simulator used to generate the simulated benchmark.","marker":"Weiner and Bansal, 2023"},{"why":"Supplies the allele-specific copy-number calls used for bulk tumor cohort inputs.","marker":"Van Loo et al., 2010"},{"why":"Defines the Poisson bipartite stochastic block model used as a baseline.","marker":"Bar-Hen et al., 2022"},{"why":"Provides the SBM implementation used for the PoissonSBM baseline.","marker":"Chiquet et al., 2024"},{"why":"Provides the Blockcluster categorical co-clustering baseline.","marker":"Bhatia et al., 2017"},{"why":"Defines the integrated completed likelihood criterion used to compare models.","marker":"Biernacki et al., 2000"},{"why":"Supplies the stochastic variational inference procedure that underpins the scalability claim.","marker":"Hoffman et al., 2013"}],"fun_headline_variants":["Residual copy-number signals predict glioma survival","CN-SBM splits copy-number into primary and residual layers","Discrete block model reveals structured residual CNV patterns","Cancer copy-number model captures two signal layers","CNV co-clustering improves survival prediction beyond age"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The survival claim rests on the assumption that choosing which main and residual clusters to enter the Cox model after seeing their p-values did not inflate the concordance index; the paper reports no independent validation cohort.","fun_headline_variants_meta":{"raw":{"variants":["Residual copy-number signals predict glioma survival","CN-SBM splits copy-number into primary and residual layers","Discrete block model reveals structured residual CNV patterns","Cancer copy-number model captures two signal layers","CNV co-clustering improves survival prediction beyond age"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000746,"raw_usage":{"total_tokens":3290,"prompt_tokens":878,"completion_tokens":2412,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":494,"completion_tokens_details":{"reasoning_tokens":2339}},"tokens_in":494,"tokens_out":2412,"duration_ms":62990,"temperature":1.0,"reasoning_tokens":2339,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:54:13.434871+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the survival analysis on a separate low-grade glioma cohort with the residual-cluster inclusion rule fixed in advance rather than selected by p-values; if the C-index falls back toward the age-only 0.741, the claim that residual variation adds independent prognostic information fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the categorical latent block model that CN-SBM builds on."},{"cited_title":"H., Williams, M","cited_arxiv_id":null,"evidence_quote":"Provides the single-cell PDX datasets and motivates separating primary from residual variation."},{"cited_title":"and Bansal, M","cited_arxiv_id":null,"evidence_quote":"Supplies the simulator used to generate the simulated benchmark."},{"cited_title":"H., Lingj rde, O","cited_arxiv_id":null,"evidence_quote":"Supplies the allele-specific copy-number calls used for bulk tumor cohort inputs."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Poisson bipartite stochastic block model used as a baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the SBM implementation used for the PoissonSBM baseline."},{"cited_title":"S., Iovleff, S., and Govaert, G","cited_arxiv_id":null,"evidence_quote":"Provides the Blockcluster categorical co-clustering baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the integrated completed likelihood criterion used to compare models."},{"cited_title":"D., Blei, D","cited_arxiv_id":null,"evidence_quote":"Supplies the stochastic variational inference procedure that underpins the scalability claim."}],"review_version":1}