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arxiv: 2301.07386 · v4 · submitted 2023-01-18 · 🧬 q-bio.NC · stat.AP

Hierarchical Bayesian inference for community detection and connectivity of functional brain networks

Lingbin Bian , Nizhuan Wang , Leonardo Novelli , Jonathan Keith , Adeel Razi This is my paper

Pith reviewed 2026-05-24 09:45 UTC · model grok-4.3

classification 🧬 q-bio.NC stat.AP
keywords community detectionfunctional brain networksBayesian inferencelatent block modelfMRImultilayer networksnetwork connectivity
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The pith

A Bayesian latent block model detects community structures in functional brain networks at both individual and group levels while preserving subject variability.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a multilayer community detection method using Bayesian latent block model to estimate hierarchically organized functional brain networks from fMRI data. Unlike most existing methods, it accounts for variability between subjects at both individual and group levels with an unknown number of communities. A new community structure-based multivariate Gaussian generative model is proposed to simulate synthetic signals for validation. Simulation studies confirm that estimated community memberships match predefined labels, and tests on Human Connectome Project data show better accuracy and reliability than modularity models.

Core claim

The central claim is that the proposed hierarchical Bayesian method based on the latent block model can robustly detect the community structure of weighted functional networks with an unknown number of communities at both individual and group levels, retaining individual network variability, and is more accurate than commonly used modularity models as shown in synthetic and real fMRI data analyses.

What carries the argument

Bayesian latent block model (LBM) applied hierarchically for multilayer community detection in weighted networks.

If this is right

  • The method handles unknown number of communities without prior specification.
  • Individual subject variability is preserved in the estimates.
  • Consistency with predefined communities in simulated data based on the generative model.
  • Improved split-half reproducibility in task fMRI data from 100 subjects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach could enable better tracking of cognitive and behavioral changes through more reliable network estimates across subjects.
  • The generative model offers a way to benchmark other community detection algorithms for fMRI signals.
  • Direct inclusion of connectivity parameters in the model might link detected communities to integration properties of brain networks.

Load-bearing premise

The community structure-based multivariate Gaussian generative model accurately represents the statistical properties of real fMRI signals.

What would settle it

If applying the method to synthetic data generated from the model fails to recover the exact predefined community memberships, or if split-half reproducibility on real data is not superior to modularity methods.

Figures

Figures reproduced from arXiv: 2301.07386 by Adeel Razi, Jonathan Keith, Leonardo Novelli, Lingbin Bian, Nizhuan Wang.

Figure 1
Figure 1. Figure 1: Multilayer community detection for functional brain networks. a Individual-level modelling. For real data analysis, the BOLD time series are extracted from brain regions of interest for each subject. For synthetic data analysis, the time series are simulated from generative models with known community structures. The FC (a weighted adjacency matrix) is computed via Pearson’s correlation from the regional t… view at source ↗
Figure 2
Figure 2. Figure 2: Validation of group-level community memberships and connectivity estimates using syn￾thetic data with SNR of 10dB. Three episodes with different communities are generated for each subject to simulate three states of networks (State 1 in a, State 2 in b, and State 3 in c). The latent labels are first inferred separately for each subject and shown with different colors (top left most matrices). The labels of… view at source ↗
Figure 3
Figure 3. Figure 3: The results of community detection and connectivity using working memory task fMRI data. We show the results of 2-back a, 0-back b, and fixation c. The matrix at the top left in each panel is the estimation of community memberships at individual level. Different colors represent community memberships of functional brain networks for 100 unrelated healthy subjects. The rows correspond to the nodes and the c… view at source ↗
Figure 4
Figure 4. Figure 4: This figure is in the same format as Fig.2 in the main text only that it is the experimental result with SNR of 5dB. The Jaccard similarity coefficient J = 1 in State 1, J = 0.9 in State 2, and J = 1 in State 3 respectively. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: This figure is in the same format as Fig.2 in the main text only that it is the experimental result with SNR of 0dB.The Jaccard similarity coefficient J = 1 in State 1, J = 0.8182 in State 2, and J = 0.8 in State 3 respectively. 32 [PITH_FULL_IMAGE:figures/full_fig_p032_5.png] view at source ↗
read the original abstract

Most functional magnetic resonance imaging studies rely on estimates of hierarchically organized functional brain networks whose segregation and integration reflect the cognitive and behavioral changes in humans. However, most existing methods for estimating the community structure of networks from both individual and group-level analysis methods do not account for the variability between subjects. In this paper, we develop a new multilayer community detection method based on Bayesian latent block model (LBM). The method can robustly detect the community structure of weighted functional networks with an unknown number of communities at both individual and group levels and retain the variability of the individual networks. For validation, we propose a new community structure-based multivariate Gaussian generative model to simulate synthetic signal. Our simulation study shows that the community memberships estimated by hierarchical Bayesian inference are consistent with the predefined node labels in the generative model. The method is also tested via split-half reproducibility using working memory task fMRI data of 100 unrelated healthy subjects from the Human Connectome Project. Analyses using both synthetic and real data show that our proposed method is more accurate and reliable compared with the commonly used (multilayer) modularity models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript introduces a hierarchical Bayesian latent block model (LBM) for multilayer community detection in weighted functional brain networks from fMRI data. The method detects community structure at individual and group levels with unknown numbers of communities while retaining inter-subject variability. Validation uses a newly proposed community structure-based multivariate Gaussian generative model showing consistency of estimated memberships with predefined labels, plus split-half reproducibility on HCP working memory task data from 100 subjects; the authors claim superior accuracy and reliability versus (multilayer) modularity models.

Significance. If validated independently, the approach could improve estimation of hierarchically organized functional networks by explicitly modeling subject variability and unknown community counts via Bayesian inference. The split-half test on real HCP data supplies external grounding for reliability, and the method's ability to operate on weighted networks is a potential strength over standard modularity.

major comments (3)
  1. [Abstract] Abstract: the central accuracy claim rests on synthetic experiments generated from the authors' own community structure-based multivariate Gaussian model, which explicitly encodes the block/community structure that the LBM is designed to recover; this creates circularity and does not constitute an independent stress test against modularity baselines that optimize a different objective.
  2. [Abstract] Abstract: the simulation reports only qualitative consistency with predefined labels and provides no quantitative metrics (accuracy, error rates, or statistical comparisons) against the modularity baselines, preventing assessment of the claimed superiority.
  3. [Abstract] Abstract / generative model description: the manuscript does not report validation of the proposed multivariate Gaussian generative model against empirical fMRI statistics (heavy tails, temporal autocorrelation, non-Gaussianity), which is required before using it to benchmark detection performance.
minor comments (1)
  1. The split-half reproducibility test on HCP data is a positive external check, but the manuscript should clarify how community labels are aligned across halves and subjects for quantitative comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central accuracy claim rests on synthetic experiments generated from the authors' own community structure-based multivariate Gaussian model, which explicitly encodes the block/community structure that the LBM is designed to recover; this creates circularity and does not constitute an independent stress test against modularity baselines that optimize a different objective.

    Authors: The synthetic experiments are designed to test recovery of known structure under the model's assumptions, which is a standard validation approach for inference methods. The primary comparison to modularity relies on the independent split-half reproducibility analysis of real HCP data. We will revise the abstract and discussion to clarify the distinct roles of the two evaluations and reduce emphasis on synthetic accuracy claims relative to modularity. revision: partial

  2. Referee: [Abstract] Abstract: the simulation reports only qualitative consistency with predefined labels and provides no quantitative metrics (accuracy, error rates, or statistical comparisons) against the modularity baselines, preventing assessment of the claimed superiority.

    Authors: We agree that quantitative metrics are needed to support the superiority claim on synthetic data. In the revision we will add accuracy, adjusted Rand index, and statistical comparisons against the modularity baselines. revision: yes

  3. Referee: [Abstract] Abstract / generative model description: the manuscript does not report validation of the proposed multivariate Gaussian generative model against empirical fMRI statistics (heavy tails, temporal autocorrelation, non-Gaussianity), which is required before using it to benchmark detection performance.

    Authors: The generative model serves as a controlled simulation tool rather than a full statistical model of fMRI time series. We will add an explicit limitations paragraph discussing its simplifying assumptions, but a comprehensive match to all empirical fMRI properties lies outside the scope of the current work focused on the detection method. revision: partial

Circularity Check

1 steps flagged

Synthetic validation circular: data generated from author-proposed model whose block structure matches LBM by construction

specific steps
  1. self definitional [Abstract]
    "For validation, we propose a new community structure-based multivariate Gaussian generative model to simulate synthetic signal. Our simulation study shows that the community memberships estimated by hierarchical Bayesian inference are consistent with the predefined node labels in the generative model."

    The generative model is defined to contain the exact community structure that the hierarchical Bayesian LBM is designed to recover; therefore the reported consistency is true by construction of the simulation rather than an independent verification of the method's superiority.

full rationale

The paper's accuracy claim against modularity baselines rests primarily on synthetic recovery experiments. The authors introduce both the LBM inference method and a 'community structure-based multivariate Gaussian generative model' whose node labels are then recovered by the LBM. Because the generative process explicitly encodes the same community/block structure the LBM is built to infer, successful recovery is guaranteed under the model's own assumptions and does not constitute an independent test. The real-data split-half test addresses only reproducibility, not accuracy. No external validation of the generative model's match to empirical fMRI statistics is provided in the abstract or described validation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Review based on abstract only; full details on model assumptions, priors, and implementation are unavailable, limiting the ledger to elements explicitly named in the provided text.

free parameters (1)
  • number of communities
    The method infers an unknown number of communities from data, but the mechanism and any associated hyperparameters are not specified in the abstract.
axioms (1)
  • domain assumption Functional brain networks can be represented as weighted graphs whose community structure follows the assumptions of a latent block model.
    This is the foundational modeling choice for the Bayesian inference method described.
invented entities (1)
  • community structure-based multivariate Gaussian generative model no independent evidence
    purpose: To generate synthetic fMRI signals with known community labels for validating the detection method.
    A new simulation tool proposed specifically for testing the Bayesian LBM approach.

pith-pipeline@v0.9.0 · 5731 in / 1392 out tokens · 33146 ms · 2026-05-24T09:45:49.819436+00:00 · methodology

discussion (0)

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Reference graph

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