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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
Editors	Marc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
Publisher	Neural information processing systems foundation
Pages	19947-19959
Number of pages	13
ISBN (Electronic)	9781713845393
Publication status	Published - 1 Jan 2021
Externally published	Yes
Event	35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online Duration: 6 Dec 2021 → 14 Dec 2021

Publication series

Name	Advances in Neural Information Processing Systems
Volume	24
ISSN (Print)	1049-5258

Conference

Conference	35th Conference on Neural Information Processing Systems, NeurIPS 2021
City	Virtual, Online
Period	6/12/21 → 14/12/21

Cite this

Gaucher, S., & Klopp, O. (2021). Optimality of variational inference for stochastic block model with missing links. In 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 (pp. 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. editor / Marc'Aurelio Ranzato ; Alina Beygelzimer ; Yann Dauphin ; Percy S. Liang ; Jenn Wortman Vaughan. Neural information processing systems foundation, 2021. pp. 19947-19959 (Advances in Neural Information Processing Systems).

@inproceedings{aeb00ae94a474c12b920400d980c4eec,

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",

month = jan,

day = "1",

language = "English",

series = "Advances in Neural Information Processing Systems",

publisher = "Neural information processing systems foundation",

pages = "19947--19959",

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

booktitle = "Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021",

}

Gaucher, S & Klopp, O 2021, Optimality of variational inference for stochastic block model with missing links. in 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, pp. 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).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Klopp, Olga

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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.

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M3 - Conference contribution

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T3 - Advances in Neural Information Processing Systems

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BT - Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021

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Gaucher S, Klopp O. Optimality of variational inference for stochastic block model with missing links. In Ranzato MA, Beygelzimer A, Dauphin Y, Liang PS, Wortman Vaughan J, editors, 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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