We investigate ways in which to improve the interpretability of LDA topic models by better analyzing and visualizing their outputs. We focus on examining what we refer to as topic similarity networks: graphs in which nodes represent latent topics in text collections and links represent similarity among topics. We describe efficient and effective approaches to both building and labeling such networks. Visualizations of topic models based on these networks are shown to be a powerful means of exploring, characterizing, and summarizing large collections of unstructured text documents. They help to "tease out" non-obvious connections among different sets of documents and provide insights into how topics form larger themes. We demonstrate the efficacy and practicality of these approaches through two case studies: 1) NSF grants for basic research spanning a 14 year period and 2) the entire English portion of Wikipedia.
The logistic normal distribution has recently been adapted via the transformation of multivariate Gaus- sian variables to model the topical distribution of documents in the presence of correlations among topics. In this paper, we propose a probit normal alternative approach to modelling correlated topical structures. Our use of the probit model in the context of topic discovery is novel, as many authors have so far con- centrated solely of the logistic model partly due to the formidable inefficiency of the multinomial probit model even in the case of very small topical spaces. We herein circumvent the inefficiency of multinomial probit estimation by using an adaptation of the diagonal orthant multinomial probit in the topic models context, resulting in the ability of our topic modelling scheme to handle corpuses with a large number of latent topics. An additional and very important benefit of our method lies in the fact that unlike with the logistic normal model whose non-conjugacy leads to the need for sophisticated sampling schemes, our ap- proach exploits the natural conjugacy inherent in the auxiliary formulation of the probit model to achieve greater simplicity. The application of our proposed scheme to a well known Associated Press corpus not only helps discover a large number of meaningful topics but also reveals the capturing of compellingly intuitive correlations among certain topics. Besides, our proposed approach lends itself to even further scalability thanks to various existing high performance algorithms and architectures capable of handling millions of documents.
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 $l_1$ 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, 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 $w_0$, 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].
In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with database size (Heaps' law), here we report a new scaling of the fluctuations around this average (fluctuation scaling analysis). We explain both scaling laws by modeling the usage of words by simple stochastic processes in which the overall distribution of word-frequencies is fat tailed (Zipf's law) and the frequency of a single word is subject to fluctuations across documents (as in topic models). In this framework, the mean and the variance of the vocabulary size can be expressed as quenched averages, implying that: i) the inhomogeneous dissemination of words cause a reduction of the average vocabulary size in comparison to the homogeneous case, and ii) correlations in the co-occurrence of words lead to an increase in the variance and the vocabulary size becomes a non-self-averaging quantity. We address the implications of these observations to the measurement of lexical richness. We test our results in three large text databases (Google-ngram, Enlgish Wikipedia, and a collection of scientific articles).
Standard LDA model suffers the problem that the topic assignment of each word is independent and word correlation hence is neglected. To address this problem, in this paper, we propose a model called Word Related Latent Dirichlet Allocation (WR-LDA) by incorporating word correlation into LDA topic models. This leads to new capabilities that standard LDA model does not have such as estimating infrequently occurring words or multi-language topic modeling. Experimental results demonstrate the effectiveness of our model compared with standard LDA.
In real world industrial applications of topic modeling, the ability to capture gigantic conceptual space by learning an ultra-high dimensional topical representation, i.e., the so-called "big model", is becoming the next desideratum after enthusiasms on "big data", especially for fine-grained downstream tasks such as online advertising, where good performances are usually achieved by regression-based predictors built on millions if not billions of input features. The conventional data-parallel approach for training gigantic topic models turns out to be rather inefficient in utilizing the power of parallelism, due to the heavy dependency on a centralized image of "model". Big model size also poses another challenge on the storage, where available model size is bounded by the smallest RAM of nodes. To address these issues, we explore another type of parallelism, namely model-parallelism, which enables training of disjoint blocks of a big topic model in parallel. By integrating data-parallelism with model-parallelism, we show that dependencies between distributed elements can be handled seamlessly, achieving not only faster convergence but also an ability to tackle significantly bigger model size. We describe an architecture for model-parallel inference of LDA, and present a variant of collapsed Gibbs sampling algorithm tailored for it. Experimental results demonstrate the ability of this system to handle topic modeling with unprecedented amount of 200 billion model variables only on a low-end cluster with very limited computational resources and bandwidth.
While most topic modeling algorithms model text corpora with unigrams, human interpretation often relies on inherent grouping of terms into phrases. As such, we consider the problem of discovering topical phrases of mixed lengths. Existing work either performs post processing to the inference results of unigram-based topic models, or utilizes complex n-gram-discovery topic models. These methods generally produce low-quality topical phrases or suffer from poor scalability on even moderately-sized datasets. We propose a different approach that is both computationally efficient and effective. Our solution combines a novel phrase mining framework to segment a document into single and multi-word phrases, and a new topic model that operates on the induced document partition. Our approach discovers high quality topical phrases with negligible extra cost to the bag-of-words topic model in a variety of datasets including research publication titles, abstracts, reviews, and news articles.
Probabilistic topic modeling is a popular and powerful family of tools for uncovering thematic structure in large sets of unstructured text documents. While much attention has been directed towards the modeling algorithms and their various extensions, comparatively few studies have concerned how to present or visualize topic models in meaningful ways. In this paper, we present a novel design that uses graphs to visually communicate topic structure and meaning. By connecting topic nodes via descriptive keyterms, the graph representation reveals topic similarities, topic meaning and shared, ambiguous keyterms. At the same time, the graph can be used for information retrieval purposes, to find documents by topic or topic subsets. To exemplify the utility of the design, we illustrate its use for organizing and exploring corpora of financial patents.
When building large-scale machine learning (ML) programs, such as big topic models or deep neural nets, one usually assumes such tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners or academic researchers. We consider this challenge in the context of topic modeling on web-scale corpora, and show that with a modest cluster of as few as 8 machines, we can train a topic model with 1 million topics and a 1-million-word vocabulary (for a total of 1 trillion parameters), on a document collection with 200 billion tokens -- a scale not yet reported even with thousands of machines. Our major contributions include: 1) a new, highly efficient O(1) Metropolis-Hastings sampling algorithm, whose running cost is (surprisingly) agnostic of model size, and empirically converges nearly an order of magnitude faster than current state-of-the-art Gibbs samplers; 2) a structure-aware model-parallel scheme, which leverages dependencies within the topic model, yielding a sampling strategy that is frugal on machine memory and network communication; 3) a differential data-structure for model storage, which uses separate data structures for high- and low-frequency words to allow extremely large models to fit in memory, while maintaining high inference speed; and 4) a bounded asynchronous data-parallel scheme, which allows efficient distributed processing of massive data via a parameter server. Our distribution strategy is an instance of the model-and-data-parallel programming model underlying the Petuum framework for general distributed ML, and was implemented on top of the Petuum open-source system. We provide experimental evidence showing how this development puts massive models within reach on a small cluster while still enjoying proportional time cost reductions with increasing cluster size, in comparison with alternative options.
We present a method for coarse-grained cross-lingual alignment of comparable texts: segments consisting of contiguous paragraphs that discuss the same theme (e.g. history, economy) are aligned based on induced multilingual topics. The method combines three ideas: a two-level LDA model that filters out words that do not convey themes, an HMM that models the ordering of themes in the collection of documents, and language-independent concept annotations to serve as a cross-language bridge and to strengthen the connection between paragraphs in the same segment through concept relations. The method is evaluated on English and French data previously used for monolingual alignment. The results show state-of-the-art performance in both monolingual and cross-lingual settings.
The short text has been the prevalent format for information of Internet in recent decades, especially with the development of online social media, whose millions of users generate a vast number of short messages everyday. Although sophisticated signals delivered by the short text make it a promising source for topic modeling, its extreme sparsity and imbalance brings unprecedented challenges to conventional topic models like LDA and its variants. Aiming at presenting a simple but general solution for topic modeling in short texts, we present a word co-occurrence network based model named WNTM to tackle the sparsity and imbalance simultaneously. Different from previous approaches, WNTM models the distribution over topics for each word instead of learning topics for each document, which successfully enhance the semantic density of data space without importing too much time or space complexity. Meanwhile, the rich contextual information preserved in the word-word space also guarantees its sensitivity in identifying rare topics with convincing quality. Furthermore, employing the same Gibbs sampling with LDA makes WNTM easily to be extended to various application scenarios. Extensive validations on both short and normal texts testify the outperformance of WNTM as compared to baseline methods. And finally we also demonstrate its potential in precisely discovering newly emerging topics or unexpected events in Weibo at pretty early stages.
In this work, automatic analysis of themes contained in a large corpora of judgments from public procurement domain is performed. The employed technique is unsupervised latent Dirichlet allocation (LDA). In addition, it is proposed, to use LDA in conjunction with recently developed method of unsupervised keyword extraction. Such an approach improves the interpretability of the automatically obtained topics and allows for better computational performance. The described analysis illustrates a potential of the method in detecting recurring themes and discovering temporal trends in lodged contract appeals. These results may be in future applied to improve information retrieval from repositories of legal texts or as auxiliary material for legal analyses carried out by human experts.
Learning meaningful topic models with massive document collections which contain millions of documents and billions of tokens is challenging because of two reasons: First, one needs to deal with a large number of topics (typically in the order of thousands). Second, one needs a scalable and efficient way of distributing the computation across multiple machines. In this paper we present a novel algorithm F+Nomad LDA which simultaneously tackles both these problems. In order to handle large number of topics we use an appropriately modified Fenwick tree. This data structure allows us to sample from a multinomial distribution over $T$ items in $O(\log T)$ time. Moreover, when topic counts change the data structure can be updated in $O(\log T)$ time. In order to distribute the computation across multiple processor we present a novel asynchronous framework inspired by the Nomad algorithm of \cite{YunYuHsietal13}. We show that F+Nomad LDA significantly outperform state-of-the-art on massive problems which involve millions of documents, billions of words, and thousands of topics.
Topic models are a way to discover underlying themes in an otherwise unstructured collection of documents. In this study, we specifically used the Latent Dirichlet Allocation (LDA) topic model on a dataset of Yelp reviews to classify restaurants based off of their reviews. Furthermore, we hypothesize that within a city, restaurants can be grouped into similar "clusters" based on both location and similarity. We used several different clustering methods, including K-means Clustering and a Probabilistic Mixture Model, in order to uncover and classify districts, both well-known and hidden (i.e. cultural areas like Chinatown or hearsay like "the best street for Italian restaurants") within a city. We use these models to display and label different clusters on a map. We also introduce a topic similarity heatmap that displays the similarity distribution in a city to a new restaurant.
Topic models have achieved significant successes in analyzing large-scale text corpus. In practical applications, we are always confronted with the challenge of model selection, i.e., how to appropriately set the number of topics. Following recent advances in topic model inference via tensor decomposition, we make a first attempt to provide theoretical analysis on model selection in latent Dirichlet allocation. Under mild conditions, we derive the upper bound and lower bound on the number of topics given a text collection of finite size. Experimental results demonstrate that our bounds are accurate and tight. Furthermore, using Gaussian mixture model as an example, we show that our methodology can be easily generalized to model selection analysis for other latent models.
In the domain of online advertising, our aim is to serve the best ad to a user who visits a certain webpage, to maximize the chance of a desired action to be performed by this user after seeing the ad. While it is possible to generate a different prediction model for each user to tell if he/she will act on a given ad, the prediction result typically will be quite unreliable with huge variance, since the desired actions are extremely sparse, and the set of users is huge (hundreds of millions) and extremely volatile, i.e., a lot of new users are introduced everyday, or are no longer valid. In this paper we aim to improve the accuracy in finding users who will perform the desired action, by assigning each user to a cluster, where the number of clusters is much smaller than the number of users (in the order of hundreds). Each user will fall into the same cluster with another user if their event history are similar. For this purpose, we modify the probabilistic latent semantic analysis (pLSA) model by assuming the independence of the user and the cluster id, given the history of events. This assumption helps us to identify a cluster of a new user without re-clustering all the users. We present the details of the algorithm we employed as well as the distributed implementation on Hadoop, and some initial results on the clusters that were generated by the algorithm.
We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our key algorithmic insight for estimation is to establish a statistical connection between M4 and topic models by viewing pairwise comparisons as words, and users as documents. This key insight leads us to explore Mallows components with a separable structure and leverage recent advances in separable topic discovery. While separability appears to be overly restrictive, we nevertheless show that it is an inevitable outcome of a relatively small number of latent Mallows components in a world of large number of items. We then develop an algorithm based on robust extreme-point identification of convex polygons to learn the reference rankings, and is provably consistent with polynomial sample complexity guarantees. We demonstrate that our new model is empirically competitive with the current state-of-the-art approaches in predicting real-world preferences.
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.
We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, $\vartheta$, is a probability distribution over probability distributions $p$, where each such $p$ is a probability distribution over $[n] = \{1,2,\dots,n\}$. When we sample from $\vartheta$, we do not observe $p$ directly, but only indirectly and in very noisy fashion, by sampling from $[n]$ repeatedly, independently $K$ times from the distribution $p$. The problem is to infer $\vartheta$ to high accuracy in transportation (earthmover) distance. We give the first efficient algorithms for learning this mixture model without making any restricting assumptions on the structure of the distribution $\vartheta$. We bound the quality of the solution as a function of the size of the samples $K$ and the number of samples used. Our model and results have applications to a variety of unsupervised learning scenarios, including learning topic models and collaborative filtering.
We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. We adopt the geometric view of admixture models - alternatively known as topic models - as a data generating mechanism for points randomly sampled from the interior of a (convex) population polytope, whose extreme points correspond to the population structure variables of interest. Rates of posterior contraction are established with respect to Hausdorff metric and a minimum matching Euclidean metric defined on polytopes. Tools developed include posterior asymptotics of hierarchical models and arguments from convex geometry.