Nested Chinese Restaurant Process (nCRP) topic models are powerful nonparametric Bayesian methods to extract a topic hierarchy from a given text corpus, where the hierarchical structure is automatically determined by the data. Hierarchical Latent Dirichlet Allocation (hLDA) is a popular instance of nCRP topic models. However, hLDA has only been evaluated at small scale, because the existing collapsed Gibbs sampling and instantiated weight variational inference algorithms either are not scalable or sacrifice inference quality with mean-field assumptions. Moreover, an efficient distributed implementation of the data structures, such as dynamically growing count matrices and trees, is challenging. In this paper, we propose a novel partially collapsed Gibbs sampling (PCGS) algorithm, which combines the advantages of collapsed and instantiated weight algorithms to achieve good scalability as well as high model quality. An initialization strategy is presented to further improve the model quality. Finally, we propose an efficient distributed implementation of PCGS through vectorization, pre-processing, and a careful design of the concurrent data structures and communication strategy. Empirical studies show that our algorithm is 111 times more efficient than the previous open-source implementation for hLDA, with comparable or even better model quality. Our distributed implementation can extract 1,722 topics from a 131-million-document corpus with 28 billion tokens, which is 4-5 orders of magnitude larger than the previous largest corpus, with 50 machines in 7 hours.
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm penalty term. The problem as formulated is convex but the memory requirements and complexity of existing interior point methods are prohibitive for problems with more than tens of nodes. We present two new algorithms for solving problems with at least a thousand nodes in the Gaussian case. Our first algorithm uses block coordinate descent, and can be interpreted as recursive l_1-norm penalized regression. Our second algorithm, based on Nesterov's first order method, yields a complexity estimate with a better dependence on problem size than existing interior point methods. Using a log determinant relaxation of the log partition function (Wainwright & Jordan (2006)), we show that these same algorithms can be used to solve an approximate sparse maximum likelihood problem for the binary case. We test our algorithms on synthetic data, as well as on gene expression and senate voting records data.
We present a family of expectation-maximization (EM) algorithms for binary and negative-binomial logistic regression, drawing a sharp connection with the variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results allow a version of this variational-Bayes approach to be re-interpreted as a true EM algorithm. We study several interesting features of the algorithm, and of this previously unrecognized connection with variational Bayes. We also generalize the approach to sparsity-promoting priors, and to an online method whose convergence properties are easily established. This latter method compares favorably with stochastic-gradient descent in situations with marked collinearity.
Information Retrieval (IR) is concerned with the identification of documents in a collection that are relevant to a given information need, usually represented as a query containing terms or keywords, which are supposed to be a good description of what the user is looking for. IR systems may improve their effectiveness (i.e., increasing the number of relevant documents retrieved) by using a process of query expansion, which automatically adds new terms to the original query posed by an user. In this paper we develop a method of query expansion based on Bayesian networks. Using a learning algorithm, we construct a Bayesian network that represents some of the relationships among the terms appearing in a given document collection; this network is then used as a thesaurus (specific for that collection). We also report the results obtained by our method on three standard test collections.
Text clustering is a widely used techniques to automatically draw out patterns from a set of documents. This notion can be extended to customer segmentation in the digital marketing field. As one of its main core is to understand what drives visitors to come, leave and behave on site. One simple way to do this is by reviewing words that they used to arrive on site and what words they used ( what things they searched) once they're on your site. Another usage of text clustering is for document organization or indexing (tagging).