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Traditional Relational Topic Models provide a way to discover the hiddentopics from a document network. Many theoretical and practical tasks, such asdimensional reduction, document clustering, link prediction, benefit from thisrevealed knowledge. However, existing relational topic models are based on anassumption that the number of hidden topics is known in advance, and this isimpractical in many real-world applications. Therefore, in order to relax thisassumption, we propose a nonparametric relational topic model in this paper.Instead of using fixed-dimensional probability distributions in its generativemodel, we use stochastic processes. Specifically, a gamma process is assignedto each document, which represents the topic interest of this document.Although this method provides an elegant solution, it brings additionalchallenges when mathematically modeling the inherent network structure oftypical document network, i.e., two spatially closer documents tend to havemore similar topics. Furthermore, we require that the topics are shared by allthe documents. In order to resolve these challenges, we use a subsamplingstrategy to assign each document a different gamma process from the globalgamma process, and the subsampling probabilities of documents are assigned witha Markov Random Field constraint that inherits the document network structure.Through the designed posterior inference algorithm, we can discover the hiddentopics and its number simultaneously. Experimental results on both syntheticand real-world network datasets demonstrate the capabilities of learning thehidden topics and, more importantly, the number of topics.

Nonparametric Relational Topic Models through Dependent Gamma Processes