Optimality of variational inference for stochastic block model with missing links

Solenne Gaucher; Olga Klopp

Optimality of variational inference for stochastic block model with missing links

Solenne Gaucher
, Olga Klopp

Université Paris-Saclay
ESSEC Business School

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the stochastic block model. In the present work, we consider the case of networks with missing links that is important in application and show that the variational approximation to the maximum likelihood estimator converges at the minimax rate. This provides the first minimax optimal and tractable estimator for the problem of parameter estimation for the stochastic block model with missing links. We complement our results with numerical studies of simulated and real networks, which confirm the advantages of this estimator over current methods.

langue originale	Anglais
titre	Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
rédacteurs en chef	Marc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
Editeur	Neural information processing systems foundation
Pages	19947-19959
Nombre de pages	13
ISBN (Electronique)	9781713845393
état	Publié - 1 janv. 2021
Modification externe	Oui
Evénement	35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online Durée: 6 déc. 2021 → 14 déc. 2021

Série de publications

Nom	Advances in Neural Information Processing Systems
Volume	24
ISSN (imprimé)	1049-5258

Une conférence

Une conférence	35th Conference on Neural Information Processing Systems, NeurIPS 2021
La ville	Virtual, Online
période	6/12/21 → 14/12/21

Contient cette citation

Gaucher, S., & Klopp, O. (2021). Optimality of variational inference for stochastic block model with missing links. Dans MA. Ranzato, A. Beygelzimer, Y. Dauphin, P. S. Liang, & J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021 (p. 19947-19959). (Advances in Neural Information Processing Systems; Vol 24). Neural information processing systems foundation.

Gaucher, Solenne ; Klopp, Olga. / Optimality of variational inference for stochastic block model with missing links. Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021. Editeur / Marc'Aurelio Ranzato ; Alina Beygelzimer ; Yann Dauphin ; Percy S. Liang ; Jenn Wortman Vaughan. Neural information processing systems foundation, 2021. p. 19947-19959 (Advances in Neural Information Processing Systems).

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title = "Optimality of variational inference for stochastic block model with missing links",

abstract = "Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the stochastic block model. In the present work, we consider the case of networks with missing links that is important in application and show that the variational approximation to the maximum likelihood estimator converges at the minimax rate. This provides the first minimax optimal and tractable estimator for the problem of parameter estimation for the stochastic block model with missing links. We complement our results with numerical studies of simulated and real networks, which confirm the advantages of this estimator over current methods.",

author = "Solenne Gaucher and Olga Klopp",

note = "Publisher Copyright: {\textcopyright} 2021 Neural information processing systems foundation. All rights reserved.; 35th Conference on Neural Information Processing Systems, NeurIPS 2021 ; Conference date: 06-12-2021 Through 14-12-2021",

year = "2021",

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series = "Advances in Neural Information Processing Systems",

publisher = "Neural information processing systems foundation",

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editor = "Marc'Aurelio Ranzato and Alina Beygelzimer and Yann Dauphin and Liang, \{Percy S.\} and \{Wortman Vaughan\}, Jenn",

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Gaucher, S & Klopp, O 2021, Optimality of variational inference for stochastic block model with missing links. Dans MA Ranzato, A Beygelzimer, Y Dauphin, PS Liang & J Wortman Vaughan (eds), Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021. Advances in Neural Information Processing Systems, VOL. 24, Neural information processing systems foundation, p. 19947-19959, 35th Conference on Neural Information Processing Systems, NeurIPS 2021, Virtual, Online, 6/12/21.

Optimality of variational inference for stochastic block model with missing links. / Gaucher, Solenne; Klopp, Olga.
Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021. Ed. / Marc'Aurelio Ranzato; Alina Beygelzimer; Yann Dauphin; Percy S. Liang; Jenn Wortman Vaughan. Neural information processing systems foundation, 2021. p. 19947-19959 (Advances in Neural Information Processing Systems; Vol 24).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

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N2 - Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the stochastic block model. In the present work, we consider the case of networks with missing links that is important in application and show that the variational approximation to the maximum likelihood estimator converges at the minimax rate. This provides the first minimax optimal and tractable estimator for the problem of parameter estimation for the stochastic block model with missing links. We complement our results with numerical studies of simulated and real networks, which confirm the advantages of this estimator over current methods.

AB - Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the stochastic block model. In the present work, we consider the case of networks with missing links that is important in application and show that the variational approximation to the maximum likelihood estimator converges at the minimax rate. This provides the first minimax optimal and tractable estimator for the problem of parameter estimation for the stochastic block model with missing links. We complement our results with numerical studies of simulated and real networks, which confirm the advantages of this estimator over current methods.

M3 - Conference contribution

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Gaucher S, Klopp O. Optimality of variational inference for stochastic block model with missing links. Dans Ranzato MA, Beygelzimer A, Dauphin Y, Liang PS, Wortman Vaughan J, rédacteurs en chef, Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021. Neural information processing systems foundation. 2021. p. 19947-19959. (Advances in Neural Information Processing Systems).

Optimality of variational inference for stochastic block model with missing links

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Série de publications

Une conférence

Empreinte digitale

Contient cette citation