91 lines
2.3 KiB
Markdown
91 lines
2.3 KiB
Markdown
---
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categories: [literature note, ]
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title: Note de lecture de *Bipartite Stochastic Block Models with Tiny Clusters* de
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Stefan Neumann.
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bibliography: ../these_ref.bib
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---
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::: {.callout-note title="Synthèse"}
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**Contribution**::
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**Related**::
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:::
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::: {.callout-note title="Markdown"}
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**FirstAuthor**:: Neumann, Stefan
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**Title**:: Bipartite Stochastic Block Models with Tiny Clusters
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**Year**:: 2018
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**Citekey**:: neumannBipartiteStochasticBlock2018
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**itemType**:: conferencePaper
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**Volume**:: 31
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**Publisher**:: Curran Associates, Inc.
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:::
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::: {.callout-note title="Pièces-jointes"}
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- [Full Text PDF](file:///home/louis/snap/zotero-snap/common/Zotero/storage/NNDNV2GV/Neumann%20-%202018%20-%20Bipartite%20Stochastic%20Block%20Models%20with%20Tiny%20Clusters.pdf).
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:::
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::: {.callout-note title="Abstract"}
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::::
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# Prise de notes
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{{< include local_macros.tex.md >}}
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![[local_macros.tex]]
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%% begin user_notes %%
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Vaguement en lien avec notre sujet de papier.
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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 $\varepsilon>0$
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La preuve de la proposition 4 sur la récupération des clusters de $V$ est intéressante.
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%% end user_notes %%
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# Annotations importées
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%% begin annotations %%
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## Importées : 2026-05-22 3:23 pm
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<mark style="background-color: #ffd400">Quote</mark>
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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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<mark style="background-color: #ff6666">Quote</mark>
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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
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## Importées : 2026-05-22 3:31 pm
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<mark style="background-color: #5fb236">Quote</mark>
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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
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1 −
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1 − q |Ui|−
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Ui
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Zv pZv (1 − p)|Ui|−Z
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q Zv 1 −
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1 − q
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≥
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|U
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qZv (1 − q)|Ui|−
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v Solving this inequality for Zv gives that one should decide for parameter p if Zv ≥ θ|Ui|, where θ
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as in Equation
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%% end annotations %%
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%% Import Date: 2026-05-22T15:31:44.079+02:00 %%
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