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REVIEW 4 major objections 4 minor 87 references

CHIP: A Hawkes Process Model for Continuous-time Networks with Scalable and Consistent Estimation

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Spectral clustering on aggregated event counts is a consistent community detector as node count and observation time grow.

desk verdict Useful, scalable Hawkes block model with a real proof gap in the spectral clustering guarantee; worth serious refereeing but the headline consistency claim needs an honest fix. read the letter →

arxiv 1908.06940 v3 pith:2HWCENLP submitted 2019-08-19 cs.SI cs.LGphysics.soc-phstat.MEstat.ML

Makan Arastuie , Subhadeep Paul , Kevin S. Xu This is my paper · ORCID
classification cs.SIcs.LGphysics.soc-phstat.MEstat.ML MSC 60G5562F1262H30
keywords CHIPmodelHawkesprocesscontinuous-timenetworkcommunitydetectionspectralclusteringstochasticblockmomentestimatorconsistency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper introduces the Community Hawkes Independent Pairs (CHIP) model for networks whose edges are timestamped relational events, such as messages, emails, or financial transactions. The central claim is that a two-stage estimation recipe—aggregate events between each pair of nodes into a count matrix, run spectral clustering to recover communities, then estimate Hawkes process parameters from per-block-pair count means and variances—recovers both communities and model parameters consistently as the number of nodes and the observation time grow. The misclustering rate is bounded by a $k^2/(nT)$-type term, so longer observation windows can compensate for smaller networks. Because each node pair is modeled by an independent Hawkes process with shared block-pair parameters, the analysis is tractable and the estimator scales to networks with tens of thousands of nodes. The paper also reports that CHIP fits several real event datasets better than existing continuous-time network models.

What carries the argument

The load-bearing construction is independence between node pairs: for each block pair $(a,b)$, every ordered node pair $(i,j)$ with $c_i=a$, $c_j=b$ generates events as an independent univariate exponential Hawkes process with shared intensity parameters $\mu_{ab}$, $\alpha_{ab}$, $\beta_{ab}$. This makes the aggregated count matrix $N$ a matrix of independent entries whose per-entry mean and variance are the Hawkes asymptotic moments $\nu_{ab}=\mu_{ab}T/(1-\alpha_{ab}/\beta_{ab})$ and $\sigma_{ab}^2=\mu_{ab}T/(1-\alpha_{ab}/\beta_{ab})^3$. The argument then uses three standard pieces: the ratio of sample mean to sample variance identifies $m=\alpha/\beta$ and $\mu$; a sharp nonasymptotic bound on the spectral norm of a random matrix with independent entries controls $\|N-\mathbb{E}[N]\|$; and a standard eigenvector-perturbation argument converts that control into a bound on the spectral-clustering misclustering rate. To recover $\alpha$ and $\beta$ separately, $\hat{m}$ is plugged into the exponential-Hawkes log-likelihood, leaving a scalar line search over $\beta$.

What would settle it

Simulate the simplified CHIP model with known parameters at moderate $T$ and $\mu \asymp \log(n)/(nT)$, then compare spectral-clustering adjusted Rand scores to the $k^2/(nT)$ rate and compare sample count means to $\mu T/(1-\alpha/\beta)$. A systematic negative bias equal to the finite-time correction $-\mu\alpha(1-e^{-(\beta-\alpha)T})/(\beta-\alpha)^2$, or a misclustering rate that does not shrink as predicted, would show the asymptotic assumptions are not met in that regime.

Watch

Extended reading notes

Core claim

The paper claims that for the CHIP model, spectral clustering applied to the weighted adjacency matrix $N$—the matrix of pairwise event counts—is a consistent estimator of community membership. In the simplified equal-size two-parameter version, the misclustering rate satisfies $r \lesssim \frac{k^2}{nT}\frac{\sigma_1^2}{(\nu_1-\nu_2)^2}$ as $n$ and $T$ grow, where $\nu=\mu T/(1-\alpha/\beta)$ and $\sigma^2=\mu T/(1-\alpha/\beta)^3$ are the asymptotic Hawkes count mean and variance. The paper further establishes that the moment estimators $\hat{m}=1-\sqrt{\bar{N}/S^2}$ and $\hat{\mu}=\frac{1}{T}\sqrt{\bar{N}^3/S^2}$ are consistent and asymptotically normal at rate $\sqrt{n_{ab}}$, and gives an end-to-end mean-squared-error bound for estimating block-pair mean counts when communities are themselves estimated. In practice, the procedure is reported to fit a Facebook wall-post network with over 40,000 nodes and 800,000 events and to give better held-out-event log-likelihoods than prior models.

Load-bearing premise

The load-bearing premise is that, once $T$ is large, each pairwise event count is approximately Gaussian with mean $\mu T/(1-\alpha/\beta)$ and variance $\mu T/(1-\alpha/\beta)^3$; if observation time is too short or counts are too sparse, the dropped finite-time corrections become non-negligible and both the community-detection bound and the estimator consistency can fail.

Editorial extensions

If this is right

  • As $T$ grows with $n$ and $k$ fixed, the misclustering rate bound falls like $1/T$, so observing the same network for longer yields the same accuracy gain as adding more nodes.
  • In sparse settings with $\mu \asymp \log(n)/(nT)$, consistent recovery holds when the number of communities satisfies $k=o(\sqrt{\log n}\,|c_1-c_2|)$.
  • The count matrix alone—without timestamps—suffices to estimate $\mu$ and the branching ratio $m=\alpha/\beta$ with $\sqrt{n_{ab}}$-consistent, asymptotically normal estimators, enabling closed-form confidence intervals.
  • With communities estimated by spectral clustering, the average mean-squared error for estimating block-pair mean counts decays at least linearly in $n/k$, not quadratically as it would with known communities.
  • Fitting the model to a 43,953-node, 852,833-event Facebook wall-post network takes about 141 seconds for $k=10$ blocks and yields better held-out log-likelihoods than the compared models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The moment estimators need only the count matrix, so they could serve as fast initialization or as inference when event timestamps are missing or too expensive to process—an application the paper does not itself propose.
  • Because the model assumes independent node pairs, reciprocity is captured only indirectly through symmetric block-pair parameters; adding an explicit reciprocity term would be a natural testable extension, which the paper's limitations discussion hints at.
  • The finite-time correction to the count mean quoted in the supplement implies a simple diagnostic: at moderate $T$, if sample means systematically fall below $\mu T/(1-\alpha/\beta)$, the asymptotic regime behind the consistency theorems has not been reached.
  • The supplement's comparison of weighted versus unweighted adjacency matrices suggests a hybrid clustering rule—use the unweighted matrix when only $\mu$ separates communities and the weighted matrix when burstiness carries the signal—that could outperform either alone in sparse networks.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper introduces CHIP, a continuous-time network generative model in which each directed node pair follows an independent univariate exponential Hawkes process whose parameters depend only on the pair's communities. Estimation proceeds by spectral clustering on the aggregated count matrix N, followed by closed-form method-of-moments estimators for m = alpha/beta and mu, and a line search for beta. The main theoretical claims are that spectral clustering consistently recovers communities as n and T grow, with the misclustering rate bounded by k^2/(nT) in a simplified two-parameter setting, and that the estimators for m and mu are consistent and asymptotically normal. The paper also presents simulation experiments and comparisons on three real timestamped networks, emphasizing scalability to tens of thousands of nodes.

Significance. If the theoretical results were fully rigorous, this would be a notable contribution: it proposes a tractable Hawkes-based block model for timestamped relational data, gives the first consistency guarantees for community detection and parameter estimation in such a model, and provides a scalable implementation with reproducible code, simulation studies, and real-data comparisons against BHM and REM. The empirical scalability to the Facebook wall-post network is a clear strength. However, the core proofs have substantial gaps, so the guarantees as currently written are not established.

major comments (4)
  1. [Supplementary B.1.3, proof of Lemma B.1 and Theorem B.1]
  2. [Section 4.2, Theorem 2 and Supplementary B.2.2]
  3. [Abstract, Section 3.2, Section 5.2]
  4. [Supplementary B.2.2, proof of Theorem 3]
minor comments (4)
  1. [Supplementary B.1, Lemma B.1]
  2. [Supplementary B.1, finite-time correction]
  3. [Section 4.1, Theorem 1]
  4. [Section 5.2, Figure 2]

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central consistency proofs are self-contained, and self-citations are not load-bearing.

full rationale

The CHIP paper does not exhibit a derivation that reduces to its own inputs. The moment estimators (2) are explicit inverses of the standard Hawkes mean and variance relations (3); this is parameter estimation by method of moments, not a fitted quantity being relabeled as a prediction. The spectral-clustering theorems for the weighted count matrix use external concentration results (Bandeira–van Handel) and SBM eigen-structure arguments (Rohe et al., Lei–Rinaldo), with the misclustering bound in Theorem 1 following algebraically from lambda_min(E[N]) = (n/k)(nu1-nu2)T and the norm bound on N - E[N]. The paper does cite prior work by its own authors (BHM [9], Xu [12,13], Han et al. [33], Paul and Chen [59]), but none of these citations is the load-bearing step: BHM is a modeling inspiration and empirical comparison baseline, and the spectral-clustering framework comes from external literature. The finite-time mean correction from Da Fonseca and Zaatour is explicitly dropped as asymptotically negligible, which is a quantitative approximation rather than a circular argument. The main legitimate concern raised by the skeptic is that Lemma B.1 replaces Hawkes counts with i.i.d. Gaussian entries without a joint approximation error bound; that is a rigor gap in the proof of Theorem 1 in the sparse regime, not a circularity, because no stated theorem or estimator is defined in terms of the conclusion it is used to prove. Simulations use the same generative model as the theory, which is ordinary model checking rather than circular inference. Overall, the paper's claims are supported by an independent derivation chain, with no step equivalent to its own input by construction.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The model parameters mu, alpha, beta, and pi are the estimation targets of the paper, not ad hoc tuning constants introduced to force a result. The ledger therefore lists only the user-selected input k and the mathematical or modeling assumptions that the proof relies on.

free parameters (1)
  • Number of communities k = k=10 for Facebook (eigengap), k=2 for Enron (singular value gap)
    The consistency theorems assume k is fixed and known, while applications select k from singular value gaps or held-out log-likelihood. Results depend on the chosen k, so it functions as a user-selected input rather than a parameter estimated inside the model.
assumptions (5)
  • domain assumption Asymptotic count moments for stationary exponential Hawkes processes: E[N]=mu*T/(1-m), Var[N]=mu*T/(1-m)^3 (Eq. 3).
    Used in Section 4.1 and Section 4.2 to derive the moment estimators and Theorem 2; taken from Hawkes-Oakes and Lewis.
  • domain assumption Pairwise independence of Hawkes processes given community assignments.
    This is the defining generative assumption of CHIP in Section 3, and it enables the matrix concentration and CLT arguments.
  • domain assumption Stationarity condition alpha<beta for each exponential Hawkes process.
    Assumed in Section 2.1 to ensure finite stationary moments and non-explosive processes.
  • ad hoc to paper Simplified special-case model in Theorem 1: equal community sizes, common within/between parameters, nu_1>nu_2, nu_1 approximately nu_2, sigma_1 approximately sigma_2.
    Imposed in Section 4.1 to get a clean closed-form misclustering bound; the general theorem in Section B.1 does not use all of these conditions.
  • standard math Matrix concentration bounds (Bandeira-van Handel) and eigenvector perturbation bounds (Davis-Kahan, Lei-Rinaldo) for random matrices with independent entries.
    Used in the proofs of Theorems B.1, B.2, and 1 to control the spectral norm of N-E[N] and the eigenvector error.

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Cite this review

Pith. "Pith review of CHIP: A Hawkes Process Model for Continuous-time Networks with Scalable and Consistent Estimation." pith.science (2026). https://pith.science/paper/2HWCENLP

@misc{pith2026190806940,
  author       = {Pith},
  title        = {Pith review of: CHIP: A Hawkes Process Model for Continuous-time Networks with Scalable and Consistent Estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2HWCENLP}},
  note         = {Machine review of arXiv:1908.06940}
}
read the original abstract

In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data consist of timestamped relational events, which form a continuous-time network. We propose the Community Hawkes Independent Pairs (CHIP) generative model for such networks. We show that applying spectral clustering to an aggregated adjacency matrix constructed from the CHIP model provides consistent community detection for a growing number of nodes and time duration. We also develop consistent and computationally efficient estimators for the model parameters. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits than existing continuous-time network models on several real networks.

Figures

Figures reproduced from arXiv: 1908.06940 by the authors.

Figure 1
Figure 1. Heat map of adjusted Rand score of spectral clustering on weighted adjacency matrix, with [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Mean-squared errors (MSEs) of CHIP’s Hawkes parameter estimators averaged over 100 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. CHIP’s fitting runtime on the Facebook data on a log-log scale with increasing k. In addition to the improved predictive ability of CHIP compared to the BHM, the computational demand is also significantly de￾creased. Fitting the CHIP model for each value of k took on average 0.15 s and 0.3 s on the Reality Mining and Enron datasets, respectively, while the BHM took on average 250 s and 30 m, mostly due to the time-c… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Inferred CHIP parameters on the largest connected component of the Facebook Wall Posts [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

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Works this paper leans on

87 extracted references · 74 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    Modeling relational events via latent classes

    Christopher DuBois and Padhraic Smyth. Modeling relational events via latent classes . In Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 803--812, 2010

    2010

  3. [3]

    Charles Blundell, Jeff Beck, and Katherine A. Heller. Modelling reciprocating relationships with Hawkes processes. In Advances in Neural Information Processing Systems 25, pages 2600--2608, 2012

    2012

  4. [4]

    Butts, and Padhraic Smyth

    Christopher DuBois, Carter T. Butts, and Padhraic Smyth. Stochastic blockmodeling of relational event dynamics . In Proceedings of the 16th International Conference on Artificial Intelligence and Statistics, pages 238--246, 2013

    2013

  5. [5]

    A continuous-time stochastic block model for basketball networks

    Lu Xin, Mu Zhu, and Hugh Chipman. A continuous-time stochastic block model for basketball networks. The Annals of Applied Statistics, 11 0 (2): 0 553--597, 2017

    2017

  6. [6]

    A semiparametric extension of the stochastic block model for longitudinal networks

    Catherine Matias, Tabea Rebafka, and Fanny Villers. A semiparametric extension of the stochastic block model for longitudinal networks . Biometrika, 105 0 (3): 0 665--680, 2018

    2018

  7. [7]

    Decoupling Homophily and Reciprocity with Latent Space Network Models

    Jiasen Yang, Vinayak Rao, and Jennifer Neville. Decoupling Homophily and Reciprocity with Latent Space Network Models . In Proceedings of the Conference on Uncertainty in Artificial Intelligence, 2017

    2017

  8. [8]

    Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data

    Xenia Miscouridou, Fran c ois Caron, and Yee Whye Teh. Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data. In Advances in Neural Information Processing Systems, pages 2343--2352, 2018

    work page 2018

Show all 87 references
  1. [9]

    Junuthula, Maysam Haghdan, Kevin S

    Ruthwik R. Junuthula, Maysam Haghdan, Kevin S. Xu, and Vijay K. Devabhaktuni. The Block Point Process Model for continuous-time event-based dynamic networks . In Proceedings of the World Wide Web Conference, pages 829--839, 2019

    2019

  2. [10]

    Xing, Wenjie Fu, and Le Song

    Eric P. Xing, Wenjie Fu, and Le Song. A state-space mixed membership blockmodel for dynamic network tomography . The Annals of Applied Statistics, 4: 0 535--566, 2010

    2010

  3. [11]

    Detecting communities and their evolutions in dynamic social networks---a Bayesian approach

    Tianbao Yang, Yun Chi, Shenghuo Zhu, Yihong Gong, and Rong Jin. Detecting communities and their evolutions in dynamic social networks---a Bayesian approach . Machine Learning, 82 0 (2): 0 157--189, 2011

    2011

  4. [12]

    Xu and Alfred O

    Kevin S. Xu and Alfred O. Hero III . Dynamic stochastic blockmodels for time-evolving social networks . IEEE Journal of Selected Topics in Signal Processing, 8 0 (4): 0 552--562, 2014

    2014

  5. [13]

    Kevin S. Xu. Stochastic block transition models for dynamic networks . In Proceedings of the 18th International Conference on Artificial Intelligence and Statistics, pages 1079--1087, 2015

    2015

  6. [14]

    Statistical clustering of temporal networks through a dynamic stochastic block model

    Catherine Matias and Vincent Miele. Statistical clustering of temporal networks through a dynamic stochastic block model . Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79 0 (4): 0 1119--1141, 2017

    2017

  7. [15]

    Consistent estimation of dynamic and multi-layer block models

    Qiuyi Han, Kevin Xu, and Edoardo Airoldi. Consistent estimation of dynamic and multi-layer block models. In International Conference on Machine Learning, pages 1511--1520, 2015

    2015

  8. [16]

    Detectability thresholds and optimal algorithms for community structure in dynamic networks

    Amir Ghasemian, Pan Zhang, Aaron Clauset, Cristopher Moore, and Leto Peel. Detectability thresholds and optimal algorithms for community structure in dynamic networks. Physical Review X, 6 0 (3): 0 031005, 2016

    2016

  9. [17]

    Spectral clustering for multiple sparse networks: I

    Sharmodeep Bhattacharyya and Shirshendu Chatterjee. Spectral clustering for multiple sparse networks: I. arXiv preprint arXiv:1805.10594, 2018

    2018 arXiv

  10. [18]

    Spectral clustering in the dynamic stochastic block model

    Marianna Pensky, Teng Zhang, et al. Spectral clustering in the dynamic stochastic block model. Electronic Journal of Statistics, 13 0 (1): 0 678--709, 2019

    2019

  11. [19]

    Stochastic blockmodels: First steps

    Paul W Holland, Kathryn Blackmond Laskey, and Samuel Leinhardt. Stochastic blockmodels: First steps. Social networks, 5 0 (2): 0 109--137, 1983

    1983

  12. [20]

    Spectra of some self-exciting and mutually exciting point processes

    Alan G Hawkes. Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58 0 (1): 0 83--90, 1971 a

    1971

  13. [21]

    Extending earthquakes' reach through cascading

    David Marsan and Olivier Lengline. Extending earthquakes' reach through cascading. Science, 319 0 (5866): 0 1076--1079, 2008

    2008

  14. [22]

    Multivariate hawkes processes: an application to financial data

    Paul Embrechts, Thomas Liniger, and Lu Lin. Multivariate hawkes processes: an application to financial data. Journal of Applied Probability, 48 0 (A): 0 367--378, 2011

    2011

  15. [23]

    Hawkes processes in finance

    Emmanuel Bacry, Iacopo Mastromatteo, and Jean-Fran c ois Muzy. Hawkes processes in finance. Market Microstructure and Liquidity, 1 0 (01): 0 1550005, 2015

    2015

  16. [24]

    Learning triggering kernels for multi-dimensional hawkes processes

    Ke Zhou, Hongyuan Zha, and Le Song. Learning triggering kernels for multi-dimensional hawkes processes. In International Conference on Machine Learning, pages 1301--1309, 2013 a

    2013

  17. [25]

    Modelling dyadic interaction with hawkes processes

    Peter F Halpin and Paul De Boeck. Modelling dyadic interaction with hawkes processes. Psychometrika, 78 0 (4): 0 793--814, 2013

    2013

  18. [26]

    Self-exciting point process modeling of conversation event sequences

    Naoki Masuda, Taro Takaguchi, Nobuo Sato, and Kazuo Yano. Self-exciting point process modeling of conversation event sequences. In Temporal Networks, pages 245--264. Springer, 2013

    2013

  19. [27]

    Seismic: A self-exciting point process model for predicting tweet popularity

    Qingyuan Zhao, Murat A Erdogdu, Hera Y He, Anand Rajaraman, and Jure Leskovec. Seismic: A self-exciting point process model for predicting tweet popularity. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 1513--1522....

    2015

  20. [28]

    A survey of statistical network models

    Anna Goldenberg, Alice X Zheng, Stephen E Fienberg, Edoardo M Airoldi, et al. A survey of statistical network models. Foundations and Trends in Machine Learning, 2 0 (2): 0 129--233, 2010

    2010

  21. [29]

    A tutorial on spectral clustering

    Ulrike Von Luxburg. A tutorial on spectral clustering. Statistics and computing, 17 0 (4): 0 395--416, 2007

    2007

  22. [30]

    Spectral clustering of graphs with general degrees in the extended planted partition model

    Kamalika Chaudhuri, Fan Chung, and Alexander Tsiatas. Spectral clustering of graphs with general degrees in the extended planted partition model. In Conference on Learning Theory, pages 35--1, 2012

    2012

  23. [31]

    Pseudo-likelihood methods for community detection in large sparse networks

    Arash A Amini, Aiyou Chen, Peter J Bickel, Elizaveta Levina, et al. Pseudo-likelihood methods for community detection in large sparse networks. The Annals of Statistics, 41 0 (4): 0 2097--2122, 2013

    2013

  24. [32]

    K. Rohe, S. Chatterjee, and B. Yu. Spectral clustering and the high-dimensional stochastic blockmodel. Ann. Statist, 39 0 (4): 0 1878--1915, 2011

    1915

  25. [33]

    Sussman, Minh Tang, Donniell E

    Daniel L. Sussman, Minh Tang, Donniell E. Fishkind, and Carey E. Priebe. A consistent adjacency spectral embedding for stochastic blockmodel graphs . Journal of the American Statistical Association, 107 0 (499): 0 1119--1128, 2012

    2012

  26. [34]

    Regularized spectral clustering under the degree-corrected stochastic blockmodel

    Tai Qin and Karl Rohe. Regularized spectral clustering under the degree-corrected stochastic blockmodel . In Advances in Neural Information Processing Systems 26, pages 3120--3128, 2013

    2013

  27. [35]

    Consistency of spectral clustering in stochastic block models

    Jing Lei and Alessandro Rinaldo. Consistency of spectral clustering in stochastic block models. The Annals of Statistics, 43 0 (1): 0 215--237, 2015

    2015

  28. [36]

    Stochastic block model and community detection in sparse graphs: A spectral algorithm with optimal rate of recovery

    Peter Chin, Anup Rao, and Van Vu. Stochastic block model and community detection in sparse graphs: A spectral algorithm with optimal rate of recovery. In COLT, pages 391--423, 2015

    2015

  29. [37]

    Impact of regularization on spectral clustering

    Antony Joseph, Bin Yu, et al. Impact of regularization on spectral clustering. The Annals of Statistics, 44 0 (4): 0 1765--1791, 2016

    2016

  30. [38]

    Achieving optimal misclassification proportion in stochastic block models

    Chao Gao, Zongming Ma, Anderson Y Zhang, and Harrison H Zhou. Achieving optimal misclassification proportion in stochastic block models. The Journal of Machine Learning Research, 18 0 (1): 0 1980--2024, 2017

    1980

  31. [39]

    A simple svd algorithm for finding hidden partitions

    Van Vu. A simple svd algorithm for finding hidden partitions. Combinatorics, Probability and Computing, 27 0 (1): 0 124--140, 2018

    2018

  32. [40]

    Understanding regularized spectral clustering via graph conductance

    Yilin Zhang and Karl Rohe. Understanding regularized spectral clustering via graph conductance. In Advances in Neural Information Processing Systems, pages 10631--10640, 2018

    2018

  33. [41]

    Structure of growing social networks

    Emily M Jin, Michelle Girvan, and Mark EJ Newman. Structure of growing social networks. Physical review E, 64 0 (4): 0 046132, 2001

    2001

  34. [42]

    Tie-decay temporal networks in continuous time and eigenvector-based centralities

    Walid Ahmad, Mason A Porter, and Mariano Beguerisse-D \' az. Tie-decay temporal networks in continuous time and eigenvector-based centralities. arXiv preprint arXiv:1805.00193, 2018

    2018 arXiv

  35. [43]

    Models of continuous-time networks with tie decay, diffusion, and convection

    Xinzhe Zuo and Mason A Porter. Models of continuous-time networks with tie decay, diffusion, and convection. arXiv preprint arXiv:1906.09394, 2019

    1906 arXiv

  36. [44]

    Linderman and Ryan P

    Scott W. Linderman and Ryan P. Adams. Discovering latent network structure in point process data . In Proceedings of the 31st International Conference on Machine Learning, pages 1413--1421, 2014

    2014

  37. [45]

    Linderman and Ryan P

    Scott W. Linderman and Ryan P. Adams. Scalable Bayesian inference for excitatory point process networks. arXiv preprint arXiv:1507.03228, 2015. URL https://arxiv.org/abs/1507.03228

    2015 arXiv

  38. [46]

    COEVOLVE: A joint point process model for information diffusion and network co-evolution

    Mehrdad Farajtabar, Yichen Wang, Manuel Gomez Rodriguez, Shuang Li, Hongyuan Zha, and Le Song. COEVOLVE: A joint point process model for information diffusion and network co-evolution . In Advances in Neural Information Processing Systems 28, pages 1945--1953, 2015

    1945

  39. [47]

    NetCodec: Community detection from individual activities

    Long Tran, Mehrdad Farajtabar, Le Song, and Hongyuan Zha. NetCodec: Community detection from individual activities . In Proceedings of the SIAM International Conference on Data Mining, pages 91--99, 2015

    2015

  40. [48]

    HawkesTopic: A joint model for network inference and topic modeling from text-based cascades

    Xinran He, Theodoros Rekatsinas, James Foulds, Lise Getoor, and Yan Liu. HawkesTopic: A joint model for network inference and topic modeling from text-based cascades . In Proceedings of the 32nd International Conference on Machine Learning, pages 871--880, 2015

    2015

  41. [49]

    Hall and Rebecca M

    Eric C. Hall and Rebecca M. Willett. Tracking dynamic point processes on networks . IEEE Transactions on Information Theory, 62 0 (7): 0 4327--4346, 2016

    2016

  42. [50]

    P. D. Hoff, A. E. Raftery, and M. S. Handcock. Latent space approaches to social network analysis. J. Amer. Statist. Assoc., 97: 0 1090--1098, 2002

    2002

  43. [51]

    Learning social infectivity in sparse low-rank networks using multi-dimensional hawkes processes

    Ke Zhou, Hongyuan Zha, and Le Song. Learning social infectivity in sparse low-rank networks using multi-dimensional hawkes processes. In Artificial Intelligence and Statistics, pages 641--649, 2013 b

    2013

  44. [52]

    Mean-field inference of hawkes point processes

    Emmanuel Bacry, St \'e phane Ga \" ffas, Iacopo Mastromatteo, and Jean-Fran c ois Muzy. Mean-field inference of hawkes point processes. Journal of Physics A: Mathematical and Theoretical, 49 0 (17): 0 174006, 2016

    2016

  45. [53]

    Tick: a python library for statistical learning, with an emphasis on hawkes processes and time-dependent models

    Emmanuel Bacry, Martin Bompaire, Philip Deegan, St \'e phane Ga \" ffas, and S ren V Poulsen. Tick: a python library for statistical learning, with an emphasis on hawkes processes and time-dependent models. The Journal of Machine Learning Research, 18 0 (1): 0 7937--7941, 2017

    2017

  46. [54]

    A cluster process representation of a self-exciting process

    Alan G Hawkes and David Oakes. A cluster process representation of a self-exciting process. Journal of Applied Probability, 11 0 (3): 0 493--503, 1974

    1974

  47. [55]

    Point spectra of some mutually exciting point processes

    Alan G Hawkes. Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society. Series B (Methodological), pages 438--443, 1971 b

    1971

  48. [56]

    Asymptotic properties and equilibrium conditions for branching poisson processes

    P.A.W Lewis. Asymptotic properties and equilibrium conditions for branching poisson processes. Journal of Applied Probability, 6 0 (2): 0 355--371, 1969

    1969

  49. [57]

    Spectral and matrix factorization methods for consistent community detection in multi-layer networks

    Subhadeep Paul, Yuguo Chen, et al. Spectral and matrix factorization methods for consistent community detection in multi-layer networks. The Annals of Statistics, 48 0 (1): 0 230--250, 2020

    2020

  50. [58]

    Community detection in general stochastic block models: Fundamental limits and efficient algorithms for recovery

    Emmanuel Abbe and Colin Sandon. Community detection in general stochastic block models: Fundamental limits and efficient algorithms for recovery. In IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pages 670--688. IEEE, 2015

    2015

  51. [59]

    Community detection and stochastic block models: recent developments

    Emmanuel Abbe. Community detection and stochastic block models: recent developments. The Journal of Machine Learning Research, 18 0 (1): 0 6446--6531, 2017

    2017

  52. [60]

    Comparing partitions

    Lawrence Hubert and Phipps Arabie. Comparing partitions . Journal of Classification, 2: 0 193--218, 1985

    1985

  53. [61]

    Inferring friendship network structure by using mobile phone data

    Nathan Eagle, Alex Sandy Pentland, and David Lazer. Inferring friendship network structure by using mobile phone data. Proceedings of the national academy of sciences, 106 0 (36): 0 15274--15278, 2009

    2009

  54. [62]

    The enron corpus: A new dataset for email classification research

    Bryan Klimt and Yiming Yang. The enron corpus: A new dataset for email classification research. In European Conference on Machine Learning, pages 217--226. Springer, 2004

    2004

  55. [63]

    On the evolution of user interaction in facebook

    Bimal Viswanath, Alan Mislove, Meeyoung Cha, and Krishna P Gummadi. On the evolution of user interaction in facebook. In Proceedings of the 2nd ACM workshop on Online social networks, pages 37--42. ACM, 2009

    2009

  56. [64]

    Codebook for the dyadic militarized interstate incident data, version 3.10

    Faten Ghosn and Scott Bennett. Codebook for the dyadic militarized interstate incident data, version 3.10. Online: http://correlatesofwar.org, 2003

    2003

  57. [65]

    Murder by structure: Dominance relations and the social structure of gang homicide

    Andrew V Papachristos. Murder by structure: Dominance relations and the social structure of gang homicide. American journal of sociology, 115 0 (1): 0 74--128, 2009

    2009

  58. [66]

    Randomized controlled field trials of predictive policing

    George O Mohler, Martin B Short, Sean Malinowski, Mark Johnson, George E Tita, Andrea L Bertozzi, and P Jeffrey Brantingham. Randomized controlled field trials of predictive policing. Journal of the American statistical association, 110 0 (512): 0 1399--1411, 2015

    2015

  59. [67]

    Does predictive policing lead to biased arrests? results from a randomized controlled trial

    P Jeffrey Brantingham, Matthew Valasik, and George O Mohler. Does predictive policing lead to biased arrests? results from a randomized controlled trial. Statistics and Public Policy, 5 0 (1): 0 1--6, 2018

    2018

  60. [68]

    S., Van Handel, R., et al

    Bandeira, A. S., Van Handel, R., et al. Sharp nonasymptotic bounds on the norm of random matrices with independent entries. The Annals of Probability, 44 0 (4): 0 2479--2506, 2016

    2016

  61. [69]

    Blundell, C., Beck, J., and Heller, K. A. Modelling reciprocating relationships with Hawkes processes. In Advances in Neural Information Processing Systems 25, pp.\ 2600--2608, 2012

    2012

  62. [70]

    and Kahan, W

    Davis, C. and Kahan, W. M. The rotation of eigenvectors by a perturbation. iii. SIAM Journal on Numerical Analysis, 7 0 (1): 0 1--46, 1970

    1970

  63. [71]

    and Smyth, P

    DuBois, C. and Smyth, P. Modeling relational events via latent classes . In Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp.\ 803--812, 2010

    2010

  64. [72]

    T., and Smyth, P

    DuBois, C., Butts, C. T., and Smyth, P. Stochastic blockmodeling of relational event dynamics . In Proceedings of the 16th International Conference on Artificial Intelligence and Statistics, pp.\ 238--246, 2013

    2013

  65. [73]

    S., and Lazer, D

    Eagle, N., Pentland, A. S., and Lazer, D. Inferring friendship network structure by using mobile phone data. Proceedings of the national academy of sciences, 106 0 (36): 0 15274--15278, 2009

    2009

  66. [74]

    Hawkes, A. G. and Oakes, D. A cluster process representation of a self-exciting process. Journal of Applied Probability, 11 0 (3): 0 493--503, 1974

    1974

  67. [75]

    R., Haghdan, M., Xu, K

    Junuthula, R. R., Haghdan, M., Xu, K. S., and Devabhaktuni, V. K. The Block Point Process Model for continuous-time event-based dynamic networks . In Proceedings of the World Wide Web Conference, pp.\ 829--839, 2019

    2019

  68. [76]

    and Yang, Y

    Klimt, B. and Yang, Y. The enron corpus: A new dataset for email classification research. In European Conference on Machine Learning, pp.\ 217--226. Springer, 2004

    2004

  69. [77]

    J., Taimre, T., and Pollett, P

    Laub, P. J., Taimre, T., and Pollett, P. K. Hawkes processes. arXiv preprint arXiv:1507.02822, 2015

    2015 arXiv

  70. [78]

    Lehmann, E. L. Elements of large-sample theory. Springer Science & Business Media, 2004

    2004

  71. [79]

    and Rinaldo, A

    Lei, J. and Rinaldo, A. Consistency of spectral clustering in stochastic block models. The Annals of Statistics, 43 0 (1): 0 215--237, 2015

    2015

  72. [80]

    A semiparametric extension of the stochastic block model for longitudinal networks

    Matias, C., Rebafka, T., and Villers, F. A semiparametric extension of the stochastic block model for longitudinal networks . Biometrika, 105 0 (3): 0 665--680, 2018

    2018

  73. [81]

    and Wright, S

    Nocedal, J. and Wright, S. Numerical optimization. Springer Science & Business Media, 2006

    2006

  74. [82]

    Maximum likelihood estimation of hawkes' self-exciting point processes

    Ozaki, T. Maximum likelihood estimation of hawkes' self-exciting point processes. Annals of the Institute of Statistical Mathematics, 31 0 (1): 0 145--155, 1979

    1979

  75. [83]

    Spectral clustering in the dynamic stochastic block model

    Pensky, M., Zhang, T., et al. Spectral clustering in the dynamic stochastic block model. Electronic Journal of Statistics, 13 0 (1): 0 678--709, 2019

    2019

  76. [84]

    Spectral clustering and the high-dimensional stochastic blockmodel

    Rohe, K., Chatterjee, S., and Yu, B. Spectral clustering and the high-dimensional stochastic blockmodel. Ann. Statist, 39 0 (4): 0 1878--1915, 2011

    1915

  77. [85]

    Stewart, G. W. and Sun, J.-G. Matrix Perturbation Theory. Academic Press, Boston, MA., 1990

    1990

  78. [86]

    Viswanath, B., Mislove, A., Cha, M., and Gummadi, K. P. On the evolution of user interaction in facebook. In Proceedings of the 2nd ACM workshop on Online social networks, pp.\ 37--42. ACM, 2009

    2009

  79. [87]

    A continuous-time stochastic block model for basketball networks

    Xin, L., Zhu, M., and Chipman, H. A continuous-time stochastic block model for basketball networks. The Annals of Applied Statistics, 11 0 (2): 0 553--597, 2017

    2017

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.