Le Pouvoir d'Information Supplementaire en Detection des Sousgraphes

In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erd\H{o}s-R\'enyi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of two kinds of side-information. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when an effective signal-to-noise ratio (SNR) parameter falls below a threshold. In contrast, in the presence of non-trivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of the SNR parameter. We validate our results through simulations on synthetic datasets as well as on a few real world networks

Almost exact recovery in noisy semi-supervised learning

This paper investigates noisy graph-based semi-supervised learning or community detection. We consider the Stochastic Block Model (SBM), where, in addition to the graph observation, an oracle gives a non-perfect information about some nodes' cluster assignment. We derive the Maximum A Priori (MAP) estimator, and show that a continuous relaxation of the MAP performs almost exact recovery under non-restrictive conditions on the average degree and amount of oracle noise. In particular, this method avoids some pitfalls of several graph-based semi-supervised learning methods such as the flatness of the classification functions, appearing in the problems with a very large amount of unlabeled data

The Power of Side-Information in Subgraph Detection

International audienceIn this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erdos-Renyi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of twokinds of side-information. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when a so-called effective signal-to-noise ratio (SNR) parameter falls below a threshold. In contrast, in the presence of non-trivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of a suitably defined phase-transition parameter. We validate our results on synthetic datasets and a few real world networks