# Decoding from Pooled Data: Phase Transitions of Message Passing

Abstract : We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the random dense setting where each observed histogram involves a random subset of entries of size proportional to n. We characterize the performance of the algorithm in the asymptotic regime where the number of observations $m$ tends to infinity proportionally to n, by deriving the corresponding State Evolution (SE) equations and studying their dynamics. We initiate the analysis of the multi-dimensional SE dynamics by proving their convergence to a fixed point, along with some further properties of the iterates. The analysis reveals sharp phase transition phenomena where the behavior of AMP changes from exact recovery to weak correlation with the signal as m/n crosses a threshold. We derive formulae for the threshold in some special cases and show that they accurately match experimental behavior.
Type de document :
Pré-publication, Document de travail
t17/109. 2017
Domaine :
Liste complète des métadonnées

Littérature citée [2 références]

https://hal-cea.archives-ouvertes.fr/cea-01553606
Contributeur : Emmanuelle De Laborderie <>
Soumis le : lundi 3 juillet 2017 - 16:12:24
Dernière modification le : mardi 24 avril 2018 - 17:20:04
Document(s) archivé(s) le : vendredi 15 décembre 2017 - 00:03:16

### Fichier

1702.02279.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : cea-01553606, version 1
• ARXIV : 1702.02279

### Citation

Ahmed El Alaoui, Aaditya Ramdas, Florent Krzakala, Lenka Zdeborova, Michael I. Jordan. Decoding from Pooled Data: Phase Transitions of Message Passing. t17/109. 2017. 〈cea-01553606〉

### Métriques

Consultations de la notice

## 135

Téléchargements de fichiers