We study the problem of analyzing influence of various factors affecting individual messages posted in social media. The problem is challenging because of various types of influences propagating through the social media network that act simultaneously on any user. Additionally, the topic composition of the influencing factors and the susceptibility of users to these influences evolve over time. This problem has not studied before, and off-the-shelf models are unsuitable for this purpose. To capture the complex interplay of these various factors, we propose a new non-parametric model called the Dynamic Multi-Relational Chinese Restaurant Process. This accounts for the user network for data generation and also allows the parameters to evolve over time. Designing inference algorithms for this model suited for large scale social-media data is another challenge. To this end, we propose a scalable and multi-threaded inference algorithm based on online Gibbs Sampling. Extensive evaluations on large-scale Twitter and Facebook data show that the extracted topics when applied to authorship and commenting prediction outperform state-of-the-art baselines. More importantly, our model produces valuable insights on topic trends and user personality trends, beyond the capability of existing approaches.
Non-parametric models: The Dirichlet Process (DP) @cite_5 is a prior over a countably infinite set of atoms, and is popularly used as a prior for mixture models (DP Mixture Model) in applications, where the number of clusters is difficult to provide as a parameter. The Chinese Restaurant Process @cite_18 provides a generative description for the Dirichlet Process, and is useful for designing sampling algorithms for DP mixture models. The distributions defined by these models are exchangeable, in that different permutations of the data are equally probable.
@cite_5 @cite_18
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process. This paper extends Ferguson's result to cases where the random measure is a mixing distribution for a parameter which determines the distribution from which observations are made. The conditional distribution of the random measure, given the observations, is no longer that of a simple Dirichlet process, but can be described as being a mixture of Dirichlet processes. This paper gives a formal definition for these mixtures and develops several theorems about their properties, the most important of which is a closure property for such mixtures. Formulas for computing the conditional distribution are derived and applications to problems in bio-assay, discrimination, regression, and mixing distributions are given. Preliminaries.- Bell polynomials, composite structures and Gibbs partitions.- Exchangeable random partitions.- Sequential constructions of random partitions.- Poisson constructions of random partitions.- Coagulation and fragmentation processes.- Random walks and random forests.- The Brownian forest.- Brownian local times, branching and Bessel processes.- Brownian bridge asymptotics for random mappings.- Random forests and the additive coalescent.