**Abstract**
Commenting is a popular facility provided by news sites. Analyzing such user-generated content has recently attracted research interest. However, in multilingual societies such as India, analyzing such user-generated content is hard due to several reasons: (1) There are more than 20 official languages but linguistic resources are available mainly for Hindi. It is observed that people frequently use romanized text as it is easy and quick using an English keyboard, resulting in multi-glyphic comments, where the texts are in the same language but in different scripts. Such romanized texts are almost unexplored in machine learning so far. (2) In many cases, comments are made on a specific part of the article rather than the topic of the entire article. Off-the-shelf methods such as correspondence LDA are insufficient to model such relationships between articles and comments. In this paper, we extend the notion of correspondence to model multi-lingual, multi-script, and inter-lingual topics in a unified probabilistic model called the Multi-glyphic Correspondence Topic Model (MCTM). Using several metrics, we verify our approach and show that it improves over the state-of-the-art.

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**Abstract**
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 such a collection of documents drawn from admixtures, is NP-hard. Making a strong assumption called separability, Arora et. al. (2012) gave the first provable algorithm for inference. For the widely used LDA model, Anandkumar et. al. (2012) gave a provable algorithm using clever tensor-methods. But Arora et. al. (2012) and Anandkumar et. al. (2012) do not learn topic vectors with bounded \(l_1\) 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 \(l_1\) 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, a 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 the others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on \(w_0\), the lowest probability that a topic is dominant, and is better than Arora et. al. (2012). 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 Arora et. al. (2013).

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**Abstract**
Understanding user generated comments in response to news and blog posts is an important area of research. After ignoring irrelevant comments, one finds that a large fraction, approximately 50%, of the comments are very specific and can be further related to certain parts of the article instead of the entire story. For example, in a recent product review of Google Nexus 7 in ArsTechnica (a popular blog), the reviewer talks about the prospect of “Retina equipped iPad mini” in a few sentences. It is interesting that although the article is on Nexus 7, but a significant number of comments are focused on this specific point regarding “iPad ”. We pose the problem of detecting such comments as specific comments location (SCL) problem. SCL is an important open problem with no prior work.
SCL can be posed as a correspondence problem between comments and the parts of the relevant article, and one could potentially use Corr-LDA type models. Unfortunately, such models do not give satisfactory performance as they are restricted to using a single topic vector per article-comments pair. In this paper we propose to go beyond the single topic vector assumption and propose a novel correspondence topic model, namely SCTM, which admits multiple topic vectors (MTV) per article-comments pair. The resulting inference problem is quite complicated because of MTV and has no off-the-shelf solution. One of the major contributions of this paper is to show that using stick-breaking process as a prior over MTV, one can derive a collapsed Gibbs sampling procedure, which empirically works well for SCL.

SCTM is rigorously evaluated on three datasets, crawled from Yahoo! News (138,000 comments) and two blogs, ArsTechnica (AT) Science (90,000 comments) and AT-Gadget (160,000 comments). We observe that SCTM performs better than Corr-LDA, not only in terms of metrics like perplexity and topic coherence but also discovers more unique topics. We see that this immediately leads to an order of magnitude improvement in F1 score over Corr-LDA for SCL.

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