Shike Mei and Jun Zhu and Jerry Zhu
Much research in Bayesian modeling has been done to elicit a prior distribution that incorporates domain knowledge. We present a novel and more direct approach by imposing First-Order Logic (FOL) rules on the posterior distribution. Our approach unifies FOL and Bayesian modeling under the regularized Bayesian framework. In addition, our approach automatically estimates the uncertainty of FOL rules when they are produced by humans, so that reliable rules are incorporated while unreliable ones are ignored. We apply our approach to latent topic modeling tasks and demonstrate that by combining FOL knowledge and Bayesian modeling, we both improve the task performance and discover more structured latent representations in unsupervised and supervised learning.
Tianlin Shi and Jun Zhu
Online Passive-Aggressive (PA) learning is an effective framework for performing max-margin online learning. But the deterministic formulation and estimated single large-margin model could limit its capability in discovering descriptive structures underlying complex data. This paper presents online Bayesian Passive-Aggressive (BayesPA) learning, which subsumes the online PA and extends naturally to incorporate latent variables and perform nonparametric Bayesian inference, thus providing great flexibility for explorative analysis. We apply BayesPA to topic modeling and derive efficient online learning algorithms for max-margin topic models. We further develop nonparametric methods to resolve the number of topics. Experimental results on real datasets show that our approaches significantly improve time efficiency while maintaining comparable results with the batch counterparts.
Jian Tang and Zhaoshi Meng and Xuanlong Nguyen and Qiaozhu Mei and Ming Zhang
Topic models such as the latent Dirichlet allocation (LDA) have become a standard staple in the modeling toolbox of machine learning. They have been applied to a vast variety of data sets, contexts, and tasks to varying degrees of success. However, to date there is almost no formal theory explicating the LDA's behavior, and despite its familiarity there is very little systematic analysis of and guidance on the properties of the data that affect the inferential performance of the model. This paper seeks to address this gap, by providing a systematic analysis of factors which characterize the LDA's performance. We present theorems elucidating the posterior contraction rates of the topics as the amount of data increases, and a thorough supporting empirical study using synthetic and real data sets, including news and web-based articles and tweet messages. Based on these results we provide practical guidance on how to identify suitable data sets for topic models, and how to specify particular model parameters.
Zhiyuan Chen and Bing Liu
Topic modeling has been commonly used to discover topics from document collections. However, unsupervised models can generate many incoherent topics. To address this problem, several knowledge-based topic models have been proposed to incorporate prior domain knowledge from the user. This work advances this research much further and shows that without any user input, we can mine the prior knowledge automatically and dynamically from topics already found from a large number of domains. This paper first proposes a novel method to mine such prior knowledge dynamically in the modeling process, and then a new topic model to use the knowledge to guide the model inference. What is also interesting is that this approach offers a novel lifelong learning algorithm for topic discovery, which exploits the big (past) data and knowledge gained from such data for subsequent modeling. Our experimental results using product reviews from 50 domains demonstrate the effectiveness of the proposed approach.