Point process modeling and optimization of social networks
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Online social media such as Facebook and Twitter and communities such as Wikipedia and Stackoverflow turn to become an inseparable part of today's lifestyle. Users usually participate via a variety of ways like sharing text and photos, asking questions, finding friends, and favoring contents. Theses activities produce sequences of events data whose complex temporal dynamics need to be studied and is of many practical, economic, and societal interest. We propose a novel framework based on multivariate temporal point processes that is used for modeling, optimization, and inference of processes taken place over networks. In the modeling part, we propose a temporal point process model for joint dynamics of information propagation and structure evolution in networks. These two highly intertwined stochastic processes have been predominantly studied separately, ignoring their co-evolutionary dynamics. Our model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks. In the optimization part, we establish the fundamentals of intervention and control in networks by combining the rich area of temporal point processes and the well-developed framework of Markov decision processes. We use point processes to capture both endogenous and exogenous events in social networks and formulate the problem as a Markov decision problem. Our methodology helps finding the optimal policy that balances the high present reward and large penalty on low future outcome in the presence of extensive uncertainties. In the inference part, we propose an intensity-free approach for point processes modeling that transforms the nuisance process to the target one. Furthermore, we train our deep neural network model using a likelihood-free approach leveraging Wasserstein distance between point processes.