---
categories: [literature note, ]
title: Note de lecture de *Bipartite Stochastic Block Models with Tiny Clusters* de
 Stefan Neumann.
bibliography: ../these_ref.bib
---

::: {.callout-note title="Synthèse"}

**Contribution**::

**Related**:: 

:::

::: {.callout-note title="Markdown"}

**FirstAuthor**:: Neumann, Stefan  

**Title**:: Bipartite Stochastic Block Models with Tiny Clusters

**Year**:: 2018

**Citekey**:: neumannBipartiteStochasticBlock2018 

**itemType**:: conferencePaper

**Volume**:: 31  
**Publisher**:: Curran Associates, Inc.    
:::

::: {.callout-note title="Pièces-jointes"} 

 - [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).
:::

::: {.callout-note title="Abstract"}

::::

# Prise de notes

{{< include local_macros.tex.md >}}

![[local_macros.tex]]

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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

<mark style="background-color: #ffd400">Quote</mark>

 > 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

<mark style="background-color: #ff6666">Quote</mark>

 > 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

<mark style="background-color: #5fb236">Quote</mark>

 > 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 %%