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On model selection for dense stochastic block models

Part of: Sufficiency and information Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 January 2022

Ilkka Norros Open the ORCID record for Ilkka Norros [Opens in a new window] ,
Hannu Reittu Open the ORCID record for Hannu Reittu [Opens in a new window]  and
Fülöp Bazsó
Ilkka Norros*
Affiliation:
University of Helsinki
Hannu Reittu*
Affiliation:
VTT Technical Research Centre of Finland
Fülöp Bazsó*
Affiliation:
Wigner Research Centre for Physics
*
*Postal address: Department of Mathematics and Statistics, P.O. Box 64, FI-00014 University of Helsinki, Finland. Email address: ilkka.norros@elisanet.fi
**Postal address: VTT Technical Research Centre of Finland, Espoo, 02044 VTT, Finland. Email address: hannu.reittu@vtt.fi
***Postal address: Department of Computational Sciences, Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary. Email address: bazso.fulop@wigner.hu
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Abstract

This paper studies estimation of stochastic block models with Rissanen’s minimum description length (MDL) principle in the dense graph asymptotics. We focus on the problem of model specification, i.e., identification of the number of blocks. Refinements of the true partition always decrease the code part corresponding to the edge placement, and thus a respective increase of the code part specifying the model should overweight that gain in order to yield a minimum at the true partition. The balance between these effects turns out to be delicate. We show that the MDL principle identifies the true partition among models whose relative block sizes are bounded away from zero. The results are extended to models with Poisson-distributed edge weights.

Keywords

Minimum description length principlerandom graphSzemerédi’s regularity lemmaregular decomposition

MSC classification

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see )
Secondary: 62B10: Information-theoretic topics
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 1 , March 2022 , pp. 202 - 226
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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