Moez Draief

Victor M. Preciado, Moez Draief, Ali Jadbabaie

We study how the behavior of viral spreading processes is influenced by local structural properties of the network over which they propagate. For a wide variety of spreading processes, the largest eigenvalue of the adjacency matrix of the network plays a key role on their global dynamical behavior. For many real-world large-scale networks, it is unfeasible to exactly retrieve the complete network structure to compute its largest eigenvalue. Instead, one usually have access to myopic, egocentric views of the network structure, also called egonets. In this paper, we propose a mathematical framework, based on algebraic graph theory and convex optimization, to study how local structural properties of the network constrain the interval of possible values in which the largest eigenvalue must lie. Based on this framework, we present a computationally efficient approach to find this interval from a collection of egonets. Our numerical simulations show that, for several social and communication networks, local structural properties of the network strongly constrain the location of the largest eigenvalue and the resulting spreading dynamics. From a practical point of view, our results can be used to dictate immunization strategies to tame the spreading of a virus, or to design network topologies that facilitate the spreading of information virally.

Symeon Chouvardas, Moez Draief

This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively minimize a cost function by employing a diffusion based Kernel Least Mean Squares (KLMS). The algorithm follows the Adapt Then Combine mode of cooperation. Moreover, the theoretical properties of the algorithm are studied and it is proved that under certain assumptions the algorithm suffers a no regret bound. Finally, comparative experiments verify that the proposed scheme outperforms other variants of the LMS.

Geovani Rizk, Igor Colin, Albert Thomas et al.

Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a different criterion: mean square error, robustness, \emph{etc}. Computing such designs is generally an NP-hard problem and one can instead rely on a convex relaxation that considers probability distributions over the samples. Although greedy strategies and rounding procedures have received a lot of attention, straightforward sampling from the optimal distribution has hardly been investigated. In this paper, we propose theoretical guarantees for randomized strategies on E and G-optimal design. To this end, we develop a new concentration inequality for the eigenvalues of random matrices using a refined version of the intrinsic dimension that enables us to quantify the performance of such randomized strategies. Finally, we evidence the validity of our analysis through experiments, with particular attention on the G-optimal design applied to the best arm identification problem for linear bandits.

Igor Colin, Albert Thomas, Moez Draief

As cellular networks become denser, a scalable and dynamic tuning of wireless base station parameters can only be achieved through automated optimization. Although the contextual bandit framework arises as a natural candidate for such a task, its extension to a parallel setting is not straightforward: one needs to carefully adapt existing methods to fully leverage the multi-agent structure of this problem. We propose two approaches: one derived from a deterministic UCB-like method and the other relying on Thompson sampling. Thanks to its bayesian nature, the latter is intuited to better preserve the exploration-exploitation balance in the bandit batch. This is verified on toy experiments, where Thompson sampling shows robustness to the variability of the contexts. Finally, we apply both methods on a real base station network dataset and evidence that Thompson sampling outperforms both manual tuning and contextual UCB.

Moez Draief, Konstantin Kutzkov, Kevin Scaman et al.

We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where edges are created over time, which induces an order. Combining convolutional subgraph kernels and string kernels, we design new scalable algorithms for generation of explicit graph feature maps using sketching techniques. We obtain precise bounds for the approximation accuracy and computational complexity of the proposed approaches and demonstrate their applicability on real datasets. In particular, our experiments demonstrate that neighborhood ordering results in more informative features. For the special case of general graphs, i.e. graphs without ordered neighborhoods, the new graph kernels yield efficient and simple algorithms for the comparison of label distributions between graphs.

Mohammed Amin Abdullah, Aldo Pacchiano, Moez Draief

We describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between the distribution of mappings of trajectories of a policy into some metric space, and some other fixed distribution (which may, for example, come from another policy). Different policies induce different distributions, so given an underlying metric, the Wasserstein distance quantifies how different policies are. This can be used to learn multiple polices which are different in terms of such Wasserstein distances by using a Wasserstein regulariser. Changing the sign of the regularisation parameter, one can learn a policy for which its trajectory mapping distribution is attracted to a given fixed distribution.