The proposed submission deals with an interesting and important problem: how to automatically learn the potentially complex temporal influence structures for the multivariate Hawkes process. The proposed neutrally self-modulating multivariate point process model can capture a range of superadditive, subadditive, or even subtractive influence structures from the historical events on the future event, and the model is quite flexible. Also, the model in evaluated on both the synthetic and the real data, and yields a competitive likelihood and prediction accuracy under missing data. Compared with existing work, one potential contribution of this submission is in the increased flexibility of the proposed model. First, in modeling the intensity function, a non-linear transfer function is introduced and is applied to the original defined intensity for multivariate Hawkes processes.

Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal dependencies, MHPs have proven to be notoriously difficult to scale, what has limited their applications to relatively small domains. In this work, we propose a novel model and computational approach to overcome this important limitation. By exploiting a characteristic sparsity pattern in real-world diffusion processes, we show that our approach allows to compute the exact likelihood and gradients of an MHP -- independently of the ambient dimensions of the underlying network. We show on synthetic and real-world datasets that our model does not only achieve state-of-the-art predictive results, but also improves runtime performance by multiple orders of magnitude compared to standard methods on sparse event sequences. In combination with easily interpretable latent variables and influence structures, this allows us to analyze diffusion processes at previously unattainable scale.

The recent widespread of availability of sensors, as part of the IoT, presents the opportunity to learn the properties of compound distributions in practical applications. Understanding temporal distributions by observations collected from the IoT can advance many intelligent applications. In this paper we develop an algorithm to learn influence between stochastic processes using observations obtained from the IoT. The proposed method learns these processes using temporal models independently, and then attempts to recover the underlying distribution of influence between them. Experimental results are provided which demonstrate the effectiveness of our method. This approach is useful in applications that require an understanding of how partially observed high-level processes can influence each other given a set of observations at different times.

Social influence is a fundamental issue in social network analysis and has attracted tremendous attention with the rapid growth of online social networks. However, existing research mainly focuses on studying peer influence. This paper introduces a novel notion of structural influence and studies how to efficiently discover structural influence patterns from social streams. We present three sampling algorithms with theoretical unbiased guarantee to speed up the discovery process. Experiments on a big microblogging dataset show that the proposed sampling algorithms can achieve a 10 times speedup compared to the exact influence pattern mining algorithm, with an average error rate of only 1.0%. The extracted structural influence patterns have many applications. We apply them to predict retweet behavior, with performance being significantly improved.

This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.