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Note de lecture de *Bipartite Stochastic Block Models with Tiny Clusters* de Stefan Neumann. | ../these_ref.bib |
::: {.callout-note title="Synthèse"}
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FirstAuthor:: Neumann, Stefan
Title:: Bipartite Stochastic Block Models with Tiny Clusters
Year:: 2018
Citekey:: neumannBipartiteStochasticBlock2018
itemType:: conferencePaper
Volume:: 31
Publisher:: Curran Associates, Inc.
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::: {.callout-note title="Pièces-jointes"}
- Full Text PDF. :::
::: {.callout-note title="Abstract"}
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Prise de notes
{{< include local_macros.tex.md >}}
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Vaguement en lien avec notre sujet de papier.
Propose une méthode pour détecter des petits clusters du "côté droit" du graphe (les noeuds j \in V). Avec des tailles de clusters de l'ordre de n_{2}^{\varepsilon} où \varepsilon>0
La preuve de la proposition 4 sur la récupération des clusters de V est intéressante.
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Annotations importées
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Importées : 2026-05-22 3:23 pm
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For V there are clusters V1, … , Vk with Vi ⊆ V ; we do not assume that the Vj are disjoint or that their union equals V
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Fix two probabilities p > q ≥ 0. For any two vertices u ∈ Ui and v ∈ Vi, insert an edge with probability p; for u ∈ Ui and v 6∈ Vi, insert an edge with probability q
Importées : 2026-05-22 3:31 pm
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We make the decision for the parameter based on the likelihood of observing Zv edges incident upon v. Parameter p is more likely if: |Ui 1 −
1 − q |Ui|−
Ui Zv pZv (1 − p)|Ui|−Z
q Zv 1 −
1 − q
≥
|U
qZv (1 − q)|Ui|−
v Solving this inequality for Zv gives that one should decide for parameter p if Zv ≥ θ|Ui|, where θ
as in Equation
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%% Import Date: 2026-05-22T15:31:44.079+02:00 %%