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International audience; Background: In the framework of network sampling, random walk (RW) based estimation techniques provide many pragmatic solutions while uncovering the unknown network as little as possible. Despite several theoretical advances in this area, RW based sampling techniques usually make a strong assumption that the samples are in stationary regime, and hence are impelled to leave out the samples collected during the burn-in period. Methods: This work proposes two sampling schemes without burn-in time constraint to estimate the average of an arbitrary function defined on the network nodes, for example, the average age of users in a social network. The central idea of the algorithms lies in exploiting regeneration of RWs at revisits to an aggregated super-node or to a set of nodes, and in strategies to enhance the frequency of such regenerations either by contracting the graph or by making the hitting set larger. Our first algorithm, which is based on reinforcement learning (RL), uses stochastic approximation to derive an estimator. This method can be seen as intermediate between purely stochastic Markov chain Monte Carlo iterations and deterministic relative value iterations. The second algorithm, which we call the Ratio with Tours (RT)-estimator, is a modified form of respondent-driven sampling (RDS) that accommodates the idea of regeneration. Results: We study the methods via simulations on real networks. We observe that the trajectories of RL-estimator are much more stable than those of standard random walk based estimation procedures, and its error performance is comparable to that of respondent-driven sampling (RDS) which has a smaller asymptotic variance than many other estimators. Simulation studies also show that the mean squared error of RT-esti-mator decays much faster than that of RDS with time. Conclusion: The newly developed RW based estimators (RL-and RT-estimators) allow to avoid burn-in period, provide better control of stability along the sample path, and overall reduce the estimation time. Our estimators can be applied in social and complex networks.

International audience; Function estimation on Online Social Networks (OSN) is an important field of study in complex network analysis. An efficient way to do function estimation on large networks is to use random walks. We can then defer to the extensive theory of Markov chains to do error analysis of these estimators. In this work we compare two existing techniques, Metropolis-Hastings MCMC and Respondent-Driven Sampling, that use random walks to do function estimation and compare them with a new reinforcement learning based technique. We provide both theoretical and empirical analyses for the estimators we consider.

International audience; Are Online Social Network (OSN) A users more likely to form friendships with those with similar attributes? Do users at an OSN B score content more favorably than OSN C users? Such questions frequently arise in the context of Social Network Analysis (SNA) but often crawling an OSN network via its Application Programming Interface (API) is the only way to gather data from a third party. To date, these partial API crawls are the majority of public datasets and the synonym of lack of statistical guarantees in incomplete-data comparisons, severely limiting SNA research progress. Using regenerative properties of the random walks, we propose estimation techniques based on short crawls that have proven statistical guarantees. Moreover, our short crawls can be implemented in massively distributed algorithms. We also provide an adaptive crawler that makes our method parameter-free, significantly improving our statistical guarantees. We then derive the Bayesian approximation of the posterior of the estimates, and in addition, obtain an estima-tor for the expected value of node and edge statistics in an equivalent configuration model or Chung-Lu random graph model of the given network (where nodes are connected randomly) and use it as a basis for testing null hypotheses. The theoretical results are supported with simulations on a variety of real-world networks.

International audience; In this paper we address the problem of finding top k eigenvalues and corresponding eigenvectors of symmetric graph matrices in networks in a distributed way. We propose a novel idea called complex power iterations in order to decompose the eigenvalues and eigenvectors at node level, analogous to time-frequency analysis in signal processing. At each node, eigenvalues correspond to the frequencies of spectral peaks and respective eigenvector components are the amplitudes at those points. Based on complex power iterations and motivated from fluid diffusion processes in networks, we devise distributed algorithms with different orders of approximation. We also introduce a Monte Carlo technique with gossiping which substantially reduces the computational overhead. An equivalent parallel random walk algorithm is also presented. We validate the algorithms with simulations on real-world networks. Our formulation of the spectral decomposition can be easily adapted to a simple algorithm based on quantum random walks. With the advent of quantum computing, the proposed quantum algorithm will be extremely useful.

This paper considers cooperative spectrum sensing algorithms for Cognitive Radios which focus on reducing the number of samples to make a reliable detection. We develop an energy efficient detector with low detection delay using decentralized sequential hypothesis testing. Our algorithm at the Cognitive Radios employs an asynchronous transmission scheme which takes into account the noise at the fusion center. We start with a distributed algorithm, DualSPRT, in which Cognitive Radios sequentially collect the observations, make local decisions using SPRT (Sequential Probability Ratio Test) and send them to the fusion center. The fusion center sequentially processes these received local decisions corrupted by noise, using an SPRT-like procedure to arrive at a final decision. We theoretically analyse its probability of error and average detection delay. We also asymptotically study its performance. Even though DualSPRT performs asymptotically well, a modification at the fusion node provides more control over the design of the algorithm parameters which then performs better at the usual operating probabilities of error in Cognitive Radio systems. We also analyse the modified algorithm theoretically. Later we modify these algorithms to handle uncertainties in SNR and fading., Comment: 13 pages. 12 figures, submitted to journal