Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known in advance, and this is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model in this paper. Instead of using fixed-dimensional probability distributions in its generative model, we use stochastic processes. Specifically, a gamma process is assigned to each document, 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.
Since the finite relational topic models are our comparative model, we introduce a relational topic model @cite_20 here in detail. The corresponding graphical representation is shown in Fig. , and the generative process is as follows, where @math is the topic distribution of a document, @math is the word distribution of topic @math , @math is the topic index of word @math in document @math , @math is observed word @math in document @math . All these variables are same with the original LDA @cite_11 . The different and significant part is the variable @math , which denotes the observed document link. This model uses a Generalized Linear Model @cite_19 to model the generation of the document links. One problem with this model is that the number of topics needs to be pre-defined and for some real-world applications, this is not trivial.
@cite_19 @cite_20 @cite_11
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Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. For LDA model, [6] gave a provable algorithm using tensor-methods. But [4,6] do not learn topic vectors with bounded @math error (a natural measure for probability vectors). Our aim is to develop a model which makes intuitive and empirically supported assumptions and to design an algorithm with natural, simple components such as SVD, which provably solves the inference problem for the model with bounded @math error. A topic in LDA and other models is essentially characterized by a group of co-occurring words. Motivated by this, we introduce topic specific Catchwords, group of words which occur with strictly greater frequency in a topic than any other topic individually and are required to have high frequency together rather than individually. A major contribution of the paper is to show that under this more realistic assumption, which is empirically verified on real corpora, a singular value decomposition (SVD) based algorithm with a crucial pre-processing step of thresholding, can provably recover the topics from a collection of documents drawn from Dominant admixtures. Dominant admixtures are convex combination of distributions in which one distribution has a significantly higher contribution than others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on @math , the lowest probability that a topic is dominant, and is better than [4]. Empirical evidence shows that on several real world corpora, both Catchwords and Dominant admixture assumptions hold and the proposed algorithm substantially outperforms the state of the art [5]. The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on @math matrices, where @math is the number of latent factors (e.g. the number of topics), rather than in the @math -dimensional observed space (typically @math ). Algorithms such as Latent Dirichlet Allocation (LDA) have achieved significant progress in modeling word document relationships. These algorithms assume each word in the document was generated by a hidden topic and explicitly model the word distribution of each topic as well as the prior distribution over topics in the document. Given these parameters, the topics of all words in the same document are assumed to be independent. In this paper, we propose modeling the topics of words in the document as a Markov chain. Specifically, we assume that all words in the same sentence have the same topic, and successive sentences are more likely to have the same topics. Since the topics are hidden, this leads to using the well-known tools of Hidden Markov Models for learning and inference. We show that incorporating this dependency allows us to learn better topics and to disambiguate words that can belong to different topics. Quantitatively, we show that we obtain better perplexity in modeling documents with only a modest increase in learning and inference complexity. We introduce the author-topic model, a generative model for documents that extends Latent Dirichlet Allocation (LDA; Blei, Ng, & Jordan, 2003) to include authorship information. Each author is associated with a multinomial distribution over topics and each topic is associated with a multinomial distribution over words. A document with multiple authors is modeled as a distribution over topics that is a mixture of the distributions associated with the authors. We apply the model to a collection of 1,700 NIPS conference papers and 160,000 CiteSeer abstracts. Exact inference is intractable for these datasets and we use Gibbs sampling to estimate the topic and author distributions. We compare the performance with two other generative models for documents, which are special cases of the author-topic model: LDA (a topic model) and a simple author model in which each author is associated with a distribution over words rather than a distribution over topics. We show topics recovered by the author-topic model, and demonstrate applications to computing similarity between authors and entropy of author output.