How many asymmetric communities are there in multi-layer directed networks?

• URL: http://arxiv.org/abs/2602.21569v1
• Date: Wed, 25 Feb 2026 04:46:10 GMT
• Title: How many asymmetric communities are there in multi-layer directed networks?
• Authors: Huan Qing,
• Abstract summary: Estimating the asymmetric numbers of communities in multi-layer directed networks is a challenging problem.<n>We develop a sequential testing procedure that searches through candidate pairs of sender and receiver community numbers in a lexicographic order.<n>For robustness, we also propose a ratio-based algorithm, which detects sharp changes in the sequence of test statistics.
• Score: 4.314956204483074
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimating the asymmetric numbers of communities in multi-layer directed networks is a challenging problem due to the multi-layer structures and inherent directional asymmetry, leading to possibly different numbers of sender and receiver communities. This work addresses this issue under the multi-layer stochastic co-block model, a model for multi-layer directed networks with distinct community structures in sending and receiving sides, by proposing a novel goodness-of-fit test. The test statistic relies on the deviation of the largest singular value of an aggregated normalized residual matrix from the constant 2. The test statistic exhibits a sharp dichotomy: Under the null hypothesis of correct model specification, its upper bound converges to zero with high probability; under underfitting, the test statistic itself diverges to infinity. With this property, we develop a sequential testing procedure that searches through candidate pairs of sender and receiver community numbers in a lexicographic order. The process stops at the smallest such pair where the test statistic drops below a decaying threshold. For robustness, we also propose a ratio-based variant algorithm, which detects sharp changes in the sequence of test statistics by comparing consecutive candidates. Both methods are proven to consistently determine the true numbers of sender and receiver communities under the multi-layer stochastic co-block model.

Related papers

• Don't Throw Away Your Beams: Improving Consistency-based Uncertainties in LLMs via Beam Search [111.6996614063716]
  We introduce a new family of methods that employ beam search to generate candidates for consistency-based uncertainty estimates.<n>We empirically evaluate our approach on six QA datasets and find that its consistent improvements over multinomial sampling lead to state-of-the-art UQ performance.
  arXiv  Detail & Related papers  (2025-12-10T11:24:29Z)
• Size-adaptive Hypothesis Testing for Fairness [8.315080617799445]
  We introduce a unified, size-adaptive, hypothesis-testing framework that turns fairness assessment into an evidence-based statistical decision.<n>We prove a Central-Limit result for the statistical parity difference, leading to analytic confidence intervals and a Wald test whose type-I (false positive) error is guaranteed at level $alpha$.<n>For the long tail of small intersectional groups, we derive a fully Bayesian Dirichlet-multinomial estimator.
  arXiv  Detail & Related papers  (2025-06-12T11:22:09Z)
• A Scalable Nyström-Based Kernel Two-Sample Test with Permutations [9.849635250118912]
  Two-sample hypothesis testing is a fundamental problem in statistics and machine learning.<n>In this work, we use a Nystr"om approximation of the maximum mean discrepancy (MMD) to design a computationally efficient and practical testing algorithm.
  arXiv  Detail & Related papers  (2025-02-19T09:22:48Z)
• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• Bootstrapped Edge Count Tests for Nonparametric Two-Sample Inference Under Heterogeneity [5.8010446129208155]
  We develop a new nonparametric testing procedure that accurately detects differences between the two samples. A comprehensive simulation study and an application to detecting user behaviors in online games demonstrates the excellent non-asymptotic performance of the proposed test.
  arXiv  Detail & Related papers  (2023-04-26T22:25:44Z)
• Testing randomness of series generated in Bell's experiment [62.997667081978825]
  We use a toy fiber optic based setup to generate binary series, and evaluate their level of randomness according to Ville principle. Series are tested with a battery of standard statistical indicators, Hurst, Kolmogorov complexity, minimum entropy, Takensarity dimension of embedding, and Augmented Dickey Fuller and Kwiatkowski Phillips Schmidt Shin to check station exponent. The level of randomness of series obtained by applying Toeplitz extractor to rejected series is found to be indistinguishable from the level of non-rejected raw ones.
  arXiv  Detail & Related papers  (2022-08-31T17:39:29Z)
• Statistical and Computational Phase Transitions in Group Testing [73.55361918807883]
  We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease. We consider two different simple random procedures for assigning individuals tests.
  arXiv  Detail & Related papers  (2022-06-15T16:38:50Z)
• Optimal Clustering with Bandit Feedback [57.672609011609886]
  This paper considers the problem of online clustering with bandit feedback. It includes a novel stopping rule for sequential testing that circumvents the need to solve any NP-hard weighted clustering problem as its subroutines. We show through extensive simulations on synthetic and real-world datasets that BOC's performance matches the lower boundally, and significantly outperforms a non-adaptive baseline algorithm.
  arXiv  Detail & Related papers  (2022-02-09T06:05:05Z)
• A Statistical Analysis of Summarization Evaluation Metrics using Resampling Methods [60.04142561088524]
  We find that the confidence intervals are rather wide, demonstrating high uncertainty in how reliable automatic metrics truly are. Although many metrics fail to show statistical improvements over ROUGE, two recent works, QAEval and BERTScore, do in some evaluation settings.
  arXiv  Detail & Related papers  (2021-03-31T18:28:14Z)
• Significance tests of feature relevance for a blackbox learner [6.72450543613463]
  We derive two consistent tests for the feature relevance of a blackbox learner. The first evaluates a loss difference with perturbation on an inference sample. The second splits the inference sample into two but does not require data perturbation.
  arXiv  Detail & Related papers  (2021-03-02T00:59:19Z)
• Adjusted chi-square test for degree-corrected block models [13.122543280692641]
  We propose a goodness-of-fit test for degree-corrected block models (DCSBM) We show that a simple adjustment allows the statistic to converge in distribution, under null, as long as the harmonic mean of $d_i$ grows to infinity. Our distributional results are nonasymptotic, with explicit constants, providing finite-sample bounds on the Kolmogorov-Smirnov distance to the target distribution.
  arXiv  Detail & Related papers  (2020-12-30T05:20:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.