Exact Recovery for a Family of Community-Detection Generative Models

Corinzia, Luca; Penna, Paolo; Luca, Mondada,; Buhmann, Joachim M.

doi:10.1109/isit.2019.8849311

Cited by 7 publications

(8 citation statements)

References 20 publications

(31 reference statements)

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“…To the best of our knowledge the approach is novel for hypergraph models. There have also been some works taking some more conventional approaches, for example, information-theoretic bounds in densest subhypergraphs [Buhmann et al] and hypergraph SBMs [Corinzia et al, 2019], as well as detection (i.e., determining whether there exists certain planted structures) in hypergraph SBMs [Angelini et al, 2015] and hypergraph planted cliques [Zhang and Xia, 2018]. These could be a direction in our future works.…”

Section: Discussionmentioning

confidence: 99%

Exact Partitioning of High-order Planted Models with a Tensor Nuclear Norm Constraint

Ke¹,

Honorio²

2020

Preprint

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We study the problem of efficient exact partitioning of the hypergraphs generated by highorder planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing hyperedges among nodes. Example models include the disjoint hypercliques, the densest subhypergraphs, and the hypergraph stochastic block models. We show that exact partitioning of high-order planted models (a NP-hard problem in general) is achievable through solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint. Our analysis provides the conditions for our approach to succeed on recovering the true underlying cluster structures, with high probability. IntroductionOn a higher level, a planted model simulates interactions among various groups of entities in a network. Typical planted models assume that nodes are grouped into a number of clusters, and each pair of nodes is connected randomly with some probability related to the cluster membership. The generative and non-deterministic nature makes planted models of both theoretical and practical interests in the field of community detection, data mining, engineering, biology, among others. Various classical planted models have been studied extensively in recent years. This includes, for instance, the stochastic block models (SBMs) [

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Section: Discussionmentioning

confidence: 99%

Exact Partitioning of High-order Planted Models with a Tensor Nuclear Norm Constraint

Ke¹,

Honorio²

2020

Preprint

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“…• FEMNIST (image) [8]: It includes images of handwritten characters with 62 labels and is divided into 3,400 sub-datasets by writers. FEMNIST Writer [7], [9], [12], [13], [25], [28], [31], [32], [37], [38] Random [28] Class [32] Shakespeare Role [27], [37], [39], [38], [32], [13] Office-Home Domain [49] Sent140 User [12], [32] Vehicle Sensors Network Sensor [31], [48], [13] Human Activity Recognition Smartphone [48], [13] GLEAM Smart glass [48] FLICKR-AES Worker [4] MNIST Random [45], [39], [15], [5], [13] Class [46], [24], [50], [39], [9] , [7], [15], [32], [19], [34] Dirichlet dist.…”

Section: A Datasetsmentioning

confidence: 99%

Benchmark for Personalized Federated Learning

Matsuda,

Sasaki,

Xiao

et al. 2024

IEEE Open J. Comput. Soc.

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Federated learning is a distributed machine learning approach that allows a single server to collaboratively build machine learning models with multiple clients without sharing datasets. Since data distributions may differ across clients, data heterogeneity is a challenging issue in federated learning. To address this issue, numerous federated learning methods have been proposed to build personalized models for clients, referred to as personalized federated learning. Nevertheless, no studies comprehensively investigate the performance of personalized federated learning methods in various settings such as datasets and client settings. Therefore, in this article, we aim to benchmark the performance of existing personalized federated learning methods in various settings. We first investigate the experimental settings in existing studies. We then benchmark the performance of existing methods through comprehensive experiments to reveal their characteristics in computer vision and natural language processing tasks which are the most popular tasks based on our survey. Our experimental study shows that (i) large data heterogeneity often leads to highly accurate predictions and (ii) standard federated learning methods (e.g. FedAvg) with fine-tuning often outperform personalized federated learning methods.

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“…However, to the best of our knowledge, only a few other works studied how the same AoN phenomenon extends to other estimators. Examples include [17], [18], where non-matching upper and lower bounds are provided for the transition of the vectorial-MLE in the sparse planted hypergraph problem (equivalent to sparse tensor-PCA up to a reparameterization of the dimensionality of the problem), and [19] where the AoN is proved in the sparse linear regression model for the vectorial-MLE estimator.…”

Section: B Related Workmentioning

confidence: 99%

“…Lemma 13 (equivalent to Theorem 1 in [17]). For the model defined in Equation (1), the MLE estimator reads:…”

Section: Appendix C Useful Lemmasmentioning

confidence: 99%

On maximum-likelihood estimation in the all-or-nothing regime

Corinzia¹,

Penna²,

Szpankowski³

et al. 2021

Preprint

Self Cite

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We study the problem of estimating a rank-1 additive deformation of a Gaussian tensor according to the maximumlikelihood estimator (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support that scales sublinearly with the total number of dimensions. We show that for Bernoulli distributed signals, the MLE undergoes an all-or-nothing (AoN) phase transition, already established for the minimum mean-square-error estimator (MMSE) in the same problem. The result follows from two main technical points: (i) the connection established between the MLE and the MMSE, using the first and second-moment methods in the constrained signal space, (ii) a recovery regime for the MMSE stricter than the simple error vanishing characterization given in the standard AoN, that is here proved as a general result.

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Exact Recovery for a Family of Community-Detection Generative Models

Cited by 7 publications

References 20 publications

Exact Partitioning of High-order Planted Models with a Tensor Nuclear Norm Constraint

Exact Partitioning of High-order Planted Models with a Tensor Nuclear Norm Constraint

Benchmark for Personalized Federated Learning

On maximum-likelihood estimation in the all-or-nothing regime

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