Algorithmic detectability threshold of the stochastic block model

Physical Review. E
Tatsuro Kawamoto

Abstract

The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation-maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold. Our analysis is not restricted to the community structure but includes general modular structures. Because the algorithm cannot always learn the planted model parameters correctly, the algorithmic detectability threshold is qualitatively different from the one with the Nishimori condition.

References

Jan 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jun-ichi Inoue, Kazuyuki Tanaka
Sep 4, 2008·Physical Review Letters·Jörg Reichardt, Michele Leone
Nov 26, 2009·Proceedings of the National Academy of Sciences of the United States of America·Peter J Bickel, Aiyou Chen
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Brian Karrer, M E J Newman
Sep 10, 2011·Physical Review Letters·Aurelien DecelleLenka Zdeborová
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Brian BallM E J Newman
Feb 7, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aurelien DecelleLenka Zdeborová
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dandan HuZohar Nussinov
Jun 19, 2013·Scientific Reports·Núria Rovira-AsenjoRoger Guimerà
Nov 28, 2013·Proceedings of the National Academy of Sciences of the United States of America·Florent KrzakalaPan Zhang
Dec 18, 2013·PLoS Computational Biology·Roger Guimerà, Marta Sales-Pardo
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tiago P Peixoto
Aug 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel B LarremoreAbigail Z Jacobs
Dec 10, 2014·Proceedings of the National Academy of Sciences of the United States of America·Pan Zhang, Cristopher Moore
Dec 11, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pan ZhangLenka Zdeborová
Apr 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xiao ZhangM E J Newman
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tatsuro Kawamoto, Yoshiyuki Kabashima
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tiago P Peixoto
Mar 24, 2016·Proceedings of the National Academy of Sciences of the United States of America·Adel JavanmardFederico Ricci-Tersenghi
Jun 17, 2016·Nature Communications·M E J Newman, Aaron Clauset
Aug 27, 2016·Physical Review Letters·M E J Newman, Gesine Reinert
Dec 8, 2016·Physical Review Letters·Izaak Neri, Fernando Lucas Metz
Feb 18, 2017·Physical Review. E·Tatsuro Kawamoto, Yoshiyuki Kabashima
Jul 16, 2017·Physical Review. E·Jean-Gabriel YoungLouis J Dubé

❮ Previous
Next ❯

Citations

Jul 18, 2018·Physical Review. E·Toni Vallès-CatalàRoger Guimerà
Feb 13, 2021·Physical Review Letters·Fernando Lucas Metz, Izaak Neri

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E
Tatsuro Kawamoto, Yoshiyuki Kabashima
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Aurelien DecelleLenka Zdeborová
Journal of Emergency Nursing : JEN : Official Publication of the Emergency Department Nurses Association
Monica CatesKimberly Kendall
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Xiao ZhangM E J Newman
© 2022 Meta ULC. All rights reserved