Application of stochastic processes to real-time auctions and information propagation in social networks.

Summary In this thesis, we study two applications of stochastic processes to Internet marketing. The first chapter focuses on the scoring of Internet users for real-time auctions. This problem consists in finding the probability that a given Internet user performs an action of interest, called conversion, within a few days after the display of an advertising banner. We show that Hawkes processes are a natural model of this phenomenon but that state-of-the-art algorithms are not applicable to the size of data typically used in industrial applications. We therefore develop two new non-parametric inference algorithms that are several orders of magnitude faster than previous methods. We show empirically that the first one performs better than the state-of-the-art competitors, and that the second one can be applied to even larger datasets without paying too high a price in terms of predictive power. The resulting algorithms have been implemented with very good performances for several years at 1000 mercy, the leading marketing agency being the industrial partner of this CIFRE thesis, where they have become an important production asset. The second chapter focuses on diffusive processes on graphs which are an important tool to model the propagation of a viral marketing operation on social networks. We establish the first theoretical bounds on the total number of nodes reached by a contagion under any graph and diffusion dynamics, and show the existence of two distinct regimes: the sub-critical regime where at most $O(sqrt{n})$ nodes will be infected, where $n$ is the size of the network, and the over-critical regime where $O(n)$ nodes can be infected. We also study the behavior with respect to the observation time $T$ and highlight the existence of critical times below which a diffusion, even an over-critical one in the long run, behaves in a sub-critical way. Finally, we extend our work to percolation and epidemiology, where we improve existing results.