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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Dirichlet process (DP) mixture models are the cornerstone of non- parametric Bayesian statistics, and the development of Monte-Carlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of non- parametric Bayesian methods to a variety of practical data analysis problems. However, MCMC sampling can be prohibitively slow, and it is important to ex- plore alternatives. One class of alternatives is provided by variational methods, a class of deterministic algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003). Thus far, varia- tional methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; 2003). In this paper, we present a variational inference algorithm for DP mixtures. We present experiments that compare the algorithm to Gibbs sampling algorithms for DP mixtures of Gaussians and present an application to a large-scale image analysis problem. The class of species sampling mixture models is introduced as an exten- sion of semiparametric models based on the Dirichlet process to models based on the general class of species sampling priors, or equivalently the class of all exchangeable urn distributions. Using Fubini calculus in conjunction with Pitman (1995, 1996), we derive characterizations of the posterior distribution in terms of a posterior par- tition distribution that extend the results of Lo (1984) for the Dirichlet process. These results provide a better understanding of models and have both theoretical and practical applications. To facilitate the use of our models we generalize the work in Brunner, Chan, James and Lo (2001) by extending their weighted Chinese restaurant (WCR) Monte Carlo procedure, an i.i.d. sequential importance sampling (SIS) procedure for approximating posterior mean functionals based on the Dirich- let process, to the case of approximation of mean functionals and additionally their posterior laws in species sampling mixture models. We also discuss collapsed Gibbs sampling, Polya urn Gibbs sampling and a Polya urn SIS scheme. Our framework allows for numerous applications, including multiplicative counting process models subject to weighted gamma processes, as well as nonparametric and semiparamet- ric hierarchical models based on the Dirichlet process, its two-parameter extension, the Pitman-Yor process and finite dimensional Dirichlet priors. Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize inference in such models have relied on introducing approximations, which can lead to inaccuracies in the posterior estimate. In this paper, we describe auxiliary variable representations for the Dirichlet process and the hierarchical Dirichlet process that allow us to perform MCMC using the correct equilibrium distribution, in a distributed manner. We show that our approach allows scalable inference without the deterioration in estimate quality that accompanies existing methods. We present a framework for online inference in the presence of a nonexhaustively defined set of classes that incorporates supervised classification with class discovery and modeling. A Dirichlet process prior (DPP) model defined over class distributions ensures that both known and unknown class distributions originate according to a common base distribution. In an attempt to automatically discover potentially interesting class formations, the prior model is coupled with a suitably chosen data model, and sequential Monte Carlo sampling is used to perform online inference. Our research is driven by a biodetection application, where a new class of pathogen may suddenly appear, and the rapid increase in the number of samples originating from this class indicates the onset of an outbreak.