## Section: New Results

### Online Social Networks (OSN)

Community detection; bandit algorithms; privacy preservation; reward mechanisms

#### Community detection

Participants : Laurent Massoulié, Marc Lelarge, Charles Bordenave.

We have progressed in the design of spectral methods for community detection and in the corresponding analysis, in particular by proving the so-called spectral redemption conjecture. This has been published in IEEE FOCS'15. The abstract of the paper is as follows. A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The nonbacktracking matrix of a graph is indexed by its directed edges and can be used to count non-backtracking walks of a given length. It has been used recently in the context of community detection and has appeared previously in connection with the Ihara zeta function and in some generalizations of Ramanujan graphs. In this work, we study the largest eigenvalues of the non-backtracking matrix of the Erdős-Rényi random graph and of the Stochastic Block Model in the regime where the number ´ of edges is proportional to the number of vertices. Our results confirm the “spectral redemption conjecture” that community detection can be made on the basis of the leading eigenvectors above the feasibility threshold.

#### Bandit algorithms for active learning of content type at low spam cost

Participants : Laurent Massoulié, Mesrob Ohanessian, Alexandre Proutière.

Progress on “bandit algorithms” for targeted news dissemination. We developed a framework in which to cast the problem, and the so-called “greedy Bayes” algorithm to determine which user to expose to a given content. We proved corresponding optimality properties, and observed that “greedy Bayes” beats the so-called Thompson sampling approach, that is the state-of the-art method in bandit problems. This work was published at ACM Sigmetrics’15.

#### Clustering and Inference From Pairwise Comparisons

Participants : Rui Wu, Jiaming Xu, Srikant Rayadurgam, Marc Lelarge, Laurent Massoulié, Bruce Hajek.

In a short publication at ACM Sigmetrics'15, we do the following. Given a set of pairwise comparisons, the classical ranking problem computes a single ranking that best represents the preferences of all users. In this paper, we study the problem of inferring individual preferences, arising in the context of making personalized recommendations. In particular, we assume users form clusters; users of the same cluster provide similar pairwise comparisons for the items according to the Bradley-Terry model. We propose an efficient algorithm to estimate the preference for each user: first, compute the net-win vector for each user using the comparisons; second, cluster the users based on the net-win vectors; third, estimate a single preference for each cluster separately. We show that the net-win vectors are much less noisy than the high dimensional vectors of pairwise comparisons, therefore our algorithm can cluster the users reliably. Moreover, we show that, when a cluster is only approximately correct, the maximum likelihood estimation for the Bradley-Terry model is still close to the true preference.