Bayesian Nonparametric Relational Topic Model through Dependent Gamma Processes

© 2016 IEEE. Traditional relational topic models provide a successful way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, and link prediction, could benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known a priori, which is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model using stochastic processes instead of fixed-dimensional probability distributions in this paper. Specifically, each document is assigned a Gamma process, which represents the topic interest of this document. Although this method provides an elegant solution, it brings additional challenges when mathematically modeling the inherent network structure of typical document network, i.e., two spatially closer documents tend to have more similar topics. Furthermore, we require that the topics are shared by all the documents. In order to resolve these challenges, we use a subsampling strategy to assign each document a different Gamma process from the global Gamma process, and the subsampling probabilities of documents are assigned with a Markov Random Field constraint that inherits the document network structure. Through the designed posterior inference algorithm, we can discover the hidden topics and its number simultaneously. Experimental results on both synthetic and real-world network datasets demonstrate the capabilities of learning the hidden topics and, more importantly, the number of topics

A survey on Bayesian nonparametric learning

© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. Bayesian (machine) learning has been playing a significant role in machine learning for a long time due to its particular ability to embrace uncertainty, encode prior knowledge, and endow interpretability. On the back of Bayesian learning's great success, Bayesian nonparametric learning (BNL) has emerged as a force for further advances in this field due to its greater modelling flexibility and representation power. Instead of playing with the fixed-dimensional probabilistic distributions of Bayesian learning, BNL creates a new “game” with infinite-dimensional stochastic processes. BNL has long been recognised as a research subject in statistics, and, to date, several state-of-the-art pilot studies have demonstrated that BNL has a great deal of potential to solve real-world machine-learning tasks. However, despite these promising results, BNL has not created a huge wave in the machine-learning community. Esotericism may account for this. The books and surveys on BNL written by statisticians are overcomplicated and filled with tedious theories and proofs. Each is certainly meaningful but may scare away new researchers, especially those with computer science backgrounds. Hence, the aim of this article is to provide a plain-spoken, yet comprehensive, theoretical survey of BNL in terms that researchers in the machine-learning community can understand. It is hoped this survey will serve as a starting point for understanding and exploiting the benefits of BNL in our current scholarly endeavours. To achieve this goal, we have collated the extant studies in this field and aligned them with the steps of a standard BNL procedure-from selecting the appropriate stochastic processes through manipulation to executing the model inference algorithms. At each step, past efforts have been thoroughly summarised and discussed. In addition, we have reviewed the common methods for implementing BNL in various machine-learning tasks along with its diverse applications in the real world as examples to motivate future studies