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arxiv_topic_modeling

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Automated Word Puzzle Generation via Topic Dictionaries

Balazs Pinter, Gyula Voros, Zoltan Szabo, Andras Lorincz

We propose a general method for automated word puzzle generation. Contrary to previous approaches in this novel field, the presented method does not rely on highly structured datasets obtained with serious human annotation effort: it only needs an unstructured and unannotated corpus (i.e., document collection) as input. The method builds upon two additional pillars: (i) a topic model, which induces a topic dictionary from the input corpus (examples include e.g., latent semantic analysis, group-structured dictionaries or latent Dirichlet allocation), and (ii) a semantic similarity measure of word pairs. Our method can (i) generate automatically a large number of proper word puzzles of different types, including the odd one out, choose the related word and separate the topics puzzle. (ii) It can easily create domain-specific puzzles by replacing the corpus component. (iii) It is also capable of automatically generating puzzles with parameterizable levels of difficulty suitable for, e.g., beginners or intermediate learners.

http://arxiv.org/abs/1206.0377v1

cs.CL, math.CO, 68T50, 15A23, I.2.7; G.2.3; G.1.2

Posterior contraction of the population polytope in finite admixture models

XuanLong Nguyen

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.

http://arxiv.org/abs/1206.0068v3

math.ST, cs.LG, stat.TH

Theory of Dependent Hierarchical Normalized Random Measures

Changyou Chen, Wray Buntine, Nan Ding

This paper presents theory for Normalized Random Measures (NRMs), Normalized Generalized Gammas (NGGs), a particular kind of NRM, and Dependent Hierarchical NRMs which allow networks of dependent NRMs to be analysed. These have been used, for instance, for time-dependent topic modelling. In this paper, we first introduce some mathematical background of completely random measures (CRMs) and their construction from Poisson processes, and then introduce NRMs and NGGs. Slice sampling is also introduced for posterior inference. The dependency operators in Poisson processes and for the corresponding CRMs and NRMs is then introduced and Posterior inference for the NGG presented. Finally, we give dependency and composition results when applying these operators to NRMs so they can be used in a network with hierarchical and dependent relations.

http://arxiv.org/abs/1205.4159v2

cs.LG, math.ST, stat.ML, stat.TH

Multilingual Topic Models for Unaligned Text

Jordan Boyd-Graber, David Blei

We develop the multilingual topic model for unaligned text (MuTo), a probabilistic model of text that is designed to analyze corpora composed of documents in two languages. From these documents, MuTo uses stochastic EM to simultaneously discover both a matching between the languages and multilingual latent topics. We demonstrate that MuTo is able to find shared topics on real-world multilingual corpora, successfully pairing related documents across languages. MuTo provides a new framework for creating multilingual topic models without needing carefully curated parallel corpora and allows applications built using the topic model formalism to be applied to a much wider class of corpora.

http://arxiv.org/abs/1205.2657v1

cs.CL, cs.IR, cs.LG, stat.ML

On Smoothing and Inference for Topic Models

Arthur Asuncion, Max Welling, Padhraic Smyth, Yee Whye Teh

Latent Dirichlet analysis, or topic modeling, is a flexible latent variable framework for modeling high-dimensional sparse count data. Various learning algorithms have been developed in recent years, including collapsed Gibbs sampling, variational inference, and maximum a posteriori estimation, and this variety motivates the need for careful empirical comparisons. In this paper, we highlight the close connections between these approaches. We find that the main differences are attributable to the amount of smoothing applied to the counts. When the hyperparameters are optimized, the differences in performance among the algorithms diminish significantly. The ability of these algorithms to achieve solutions of comparable accuracy gives us the freedom to select computationally efficient approaches. Using the insights gained from this comparative study, we show how accurate topic models can be learned in several seconds on text corpora with thousands of documents.

http://arxiv.org/abs/1205.2662v1

cs.LG, stat.ML

A Spectral Algorithm for Latent Dirichlet Allocation

Animashree Anandkumar, Dean P. Foster, Daniel Hsu, Sham M. Kakade, Yi-Kai Liu

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 $k\times k$ matrices, where $k$ is the number of latent factors (e.g. the number of topics), rather than in the $d$-dimensional observed space (typically $d \gg k$).

http://arxiv.org/abs/1204.6703v4

cs.LG, stat.ML

Residual Belief Propagation for Topic Modeling

Jia Zeng, Xiao-Qin Cao, Zhi-Qiang Liu

Fast convergence speed is a desired property for training latent Dirichlet allocation (LDA), especially in online and parallel topic modeling for massive data sets. This paper presents a novel residual belief propagation (RBP) algorithm to accelerate the convergence speed for training LDA. The proposed RBP uses an informed scheduling scheme for asynchronous message passing, which passes fast-convergent messages with a higher priority to influence those slow-convergent messages at each learning iteration. Extensive empirical studies confirm that RBP significantly reduces the training time until convergence while achieves a much lower predictive perplexity than other state-of-the-art training algorithms for LDA, including variational Bayes (VB), collapsed Gibbs sampling (GS), loopy belief propagation (BP), and residual VB (RVB).

http://arxiv.org/abs/1204.6610v1

cs.LG, cs.IR

Concept Modeling with Superwords

Khalid El-Arini, Emily B. Fox, Carlos Guestrin

In information retrieval, a fundamental goal is to transform a document into concepts that are representative of its content. The term "representative" is in itself challenging to define, and various tasks require different granularities of concepts. In this paper, we aim to model concepts that are sparse over the vocabulary, and that flexibly adapt their content based on other relevant semantic information such as textual structure or associated image features. We explore a Bayesian nonparametric model based on nested beta processes that allows for inferring an unknown number of strictly sparse concepts. The resulting model provides an inherently different representation of concepts than a standard LDA (or HDP) based topic model, and allows for direct incorporation of semantic features. We demonstrate the utility of this representation on multilingual blog data and the Congressional Record.

http://arxiv.org/abs/1204.2523v1

stat.ML, cs.CL, cs.IR, cs.LG

Learning Topic Models - Going beyond SVD

Sanjeev Arora, Rong Ge, Ankur Moitra

Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both in machine learning and in theory have suggested a probabilistic model for documents, whereby documents arise as a convex combination of (i.e. distribution on) a small number of topic vectors, each topic vector being a distribution on words (i.e. a vector of word-frequencies). Similar models have since been used in a variety of application areas; the Latent Dirichlet Allocation or LDA model of Blei et al. is especially popular. Theoretical studies of topic modeling focus on learning the model's parameters assuming the data is actually generated from it. Existing approaches for the most part rely on Singular Value Decomposition(SVD), and consequently have one of two limitations: these works need to either assume that each document contains only one topic, or else can only recover the span of the topic vectors instead of the topic vectors themselves. This paper formally justifies Nonnegative Matrix Factorization(NMF) as a main tool in this context, which is an analog of SVD where all vectors are nonnegative. Using this tool we give the first polynomial-time algorithm for learning topic models without the above two limitations. The algorithm uses a fairly mild assumption about the underlying topic matrix called separability, which is usually found to hold in real-life data. A compelling feature of our algorithm is that it generalizes to models that incorporate topic-topic correlations, such as the Correlated Topic Model and the Pachinko Allocation Model. We hope that this paper will motivate further theoretical results that use NMF as a replacement for SVD - just as NMF has come to replace SVD in many applications.

http://arxiv.org/abs/1204.1956v2

cs.LG, cs.DS, cs.IR

A New Approach to Speeding Up Topic Modeling

Jia Zeng, Zhi-Qiang Liu, Xiao-Qin Cao

Latent Dirichlet allocation (LDA) is a widely-used probabilistic topic modeling paradigm, and recently finds many applications in computer vision and computational biology. In this paper, we propose a fast and accurate batch algorithm, active belief propagation (ABP), for training LDA. Usually batch LDA algorithms require repeated scanning of the entire corpus and searching the complete topic space. To process massive corpora having a large number of topics, the training iteration of batch LDA algorithms is often inefficient and time-consuming. To accelerate the training speed, ABP actively scans the subset of corpus and searches the subset of topic space for topic modeling, therefore saves enormous training time in each iteration. To ensure accuracy, ABP selects only those documents and topics that contribute to the largest residuals within the residual belief propagation (RBP) framework. On four real-world corpora, ABP performs around $10$ to $100$ times faster than state-of-the-art batch LDA algorithms with a comparable topic modeling accuracy.

http://arxiv.org/abs/1204.0170v2

cs.LG, cs.IR

Gaussian Process Topic Models

Amrudin Agovic, Arindam Banerjee

We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs work with both a topic covariance matrix and a document kernel matrix, learning GPTMs involves a novel component-solving a suitable Sylvester equation capturing both topic and document dependencies. The efficacy of GPTMs is demonstrated with experiments evaluating the quality of both topic modeling and embedding.

http://arxiv.org/abs/1203.3462v1

cs.LG, stat.ML

Timeline: A Dynamic Hierarchical Dirichlet Process Model for Recovering Birth/Death and Evolution of Topics in Text Stream

Amr Ahmed, Eric P. Xing

Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics' distribution and popularity are time-evolving. Several models exist that model the evolution of some but not all of the above aspects. In this paper we introduce infinite dynamic topic models, iDTM, that can accommodate the evolution of all the aforementioned aspects. Our model assumes that documents are organized into epochs, where the documents within each epoch are exchangeable but the order between the documents is maintained across epochs. iDTM allows for unbounded number of topics: topics can die or be born at any epoch, and the representation of each topic can evolve according to a Markovian dynamics. We use iDTM to analyze the birth and evolution of topics in the NIPS community and evaluated the efficacy of our model on both simulated and real datasets with favorable outcome.

http://arxiv.org/abs/1203.3463v1

cs.IR, cs.LG, stat.ML

Multidimensional counting grids: Inferring word order from disordered bags of words

Nebojsa Jojic, Alessandro Perina

Models of bags of words typically assume topic mixing so that the words in a single bag come from a limited number of topics. We show here that many sets of bag of words exhibit a very different pattern of variation than the patterns that are efficiently captured by topic mixing. In many cases, from one bag of words to the next, the words disappear and new ones appear as if the theme slowly and smoothly shifted across documents (providing that the documents are somehow ordered). Examples of latent structure that describe such ordering are easily imagined. For example, the advancement of the date of the news stories is reflected in a smooth change over the theme of the day as certain evolving news stories fall out of favor and new events create new stories. Overlaps among the stories of consecutive days can be modeled by using windows over linearly arranged tight distributions over words. We show here that such strategy can be extended to multiple dimensions and cases where the ordering of data is not readily obvious. We demonstrate that this way of modeling covariation in word occurrences outperforms standard topic models in classification and prediction tasks in applications in biology, text modeling and computer vision.

http://arxiv.org/abs/1202.3752v1

cs.IR, cs.CL, cs.LG, stat.ML

Sparse Topical Coding

Jun Zhu, Eric P. Xing

We present sparse topical coding (STC), a non-probabilistic formulation of topic models for discovering latent representations of large collections of data. Unlike probabilistic topic models, STC relaxes the normalization constraint of admixture proportions and the constraint of defining a normalized likelihood function. Such relaxations make STC amenable to: 1) directly control the sparsity of inferred representations by using sparsity-inducing regularizers; 2) be seamlessly integrated with a convex error function (e.g., SVM hinge loss) for supervised learning; and 3) be efficiently learned with a simply structured coordinate descent algorithm. Our results demonstrate the advantages of STC and supervised MedSTC on identifying topical meanings of words and improving classification accuracy and time efficiency.

http://arxiv.org/abs/1202.3778v1

cs.LG, stat.ML

A Topic Modeling Toolbox Using Belief Propagation

Jia Zeng

Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This paper introduces a topic modeling toolbox (TMBP) based on the belief propagation (BP) algorithms. TMBP toolbox is implemented by MEX C++/Matlab/Octave for either Windows 7 or Linux. Compared with existing topic modeling packages, the novelty of this toolbox lies in the BP algorithms for learning LDA-based topic models. The current version includes BP algorithms for latent Dirichlet allocation (LDA), author-topic models (ATM), relational topic models (RTM), and labeled LDA (LaLDA). This toolbox is an ongoing project and more BP-based algorithms for various topic models will be added in the near future. Interested users may also extend BP algorithms for learning more complicated topic models. The source codes are freely available under the GNU General Public Licence, Version 1.0 at https://mloss.org/software/view/399/.

http://arxiv.org/abs/1201.0838v2

cs.LG

TopicViz: Semantic Navigation of Document Collections

Jacob Eisenstein, Duen Horng "Polo" Chau, Aniket Kittur, Eric P. Xing

When people explore and manage information, they think in terms of topics and themes. However, the software that supports information exploration sees text at only the surface level. In this paper we show how topic modeling -- a technique for identifying latent themes across large collections of documents -- can support semantic exploration. We present TopicViz, an interactive environment for information exploration. TopicViz combines traditional search and citation-graph functionality with a range of novel interactive visualizations, centered around a force-directed layout that links documents to the latent themes discovered by the topic model. We describe several use scenarios in which TopicViz supports rapid sensemaking on large document collections.

http://arxiv.org/abs/1110.6200v2

cs.HC, cs.AI, cs.CL

Kernel Topic Models

Philipp Hennig, David Stern, Ralf Herbrich, Thore Graepel

Latent Dirichlet Allocation models discrete data as a mixture of discrete distributions, using Dirichlet beliefs over the mixture weights. We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with elements of a Hilbert space, admitting kernel topic models (KTM), modelling temporal, spatial, hierarchical, social and other structure between documents. The main challenge is efficient approximate inference on the latent Gaussian. We present an approximate algorithm cast around a Laplace approximation in a transformed basis. The KTM can also be interpreted as a type of Gaussian process latent variable model, or as a topic model conditional on document features, uncovering links between earlier work in these areas.

http://arxiv.org/abs/1110.4713v1

cs.LG, stat.ML

Topological Feature Based Classification

Leto Peel

There has been a lot of interest in developing algorithms to extract clusters or communities from networks. This work proposes a method, based on blockmodelling, for leveraging communities and other topological features for use in a predictive classification task. Motivated by the issues faced by the field of community detection and inspired by recent advances in Bayesian topic modelling, the presented model automatically discovers topological features relevant to a given classification task. In this way, rather than attempting to identify some universal best set of clusters for an undefined goal, the aim is to find the best set of clusters for a particular purpose. Using this method, topological features can be validated and assessed within a given context by their predictive performance. The proposed model differs from other relational and semi-supervised learning models as it identifies topological features to explain the classification decision. In a demonstration on a number of real networks the predictive capability of the topological features are shown to rival the performance of content based relational learners. Additionally, the model is shown to outperform graph-based semi-supervised methods on directed and approximately bipartite networks.

http://arxiv.org/abs/1110.4285v1

cs.SI, physics.soc-ph

Higher-Order Markov Tag-Topic Models for Tagged Documents and Images

Jia Zeng, Wei Feng, William K. Cheung, Chun-Hung Li

This paper studies the topic modeling problem of tagged documents and images. Higher-order relations among tagged documents and images are major and ubiquitous characteristics, and play positive roles in extracting reliable and interpretable topics. In this paper, we propose the tag-topic models (TTM) to depict such higher-order topic structural dependencies within the Markov random field (MRF) framework. First, we use the novel factor graph representation of latent Dirichlet allocation (LDA)-based topic models from the MRF perspective, and present an efficient loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Second, we propose the factor hypergraph representation of TTM, and focus on both pairwise and higher-order relation modeling among tagged documents and images. Efficient loopy BP algorithm is developed to learn TTM, which encourages the topic labeling smoothness among tagged documents and images. Extensive experimental results confirm the incorporation of higher-order relations to be effective in enhancing the overall topic modeling performance, when compared with current state-of-the-art topic models, in many text and image mining tasks of broad interests such as word and link prediction, document classification, and tag recommendation.

http://arxiv.org/abs/1109.5370v1

cs.CV, cs.AI, cs.IR, cs.LG

Latent Semantic Learning with Structured Sparse Representation for Human Action Recognition

Zhiwu Lu, Yuxin Peng

This paper proposes a novel latent semantic learning method for extracting high-level features (i.e. latent semantics) from a large vocabulary of abundant mid-level features (i.e. visual keywords) with structured sparse representation, which can help to bridge the semantic gap in the challenging task of human action recognition. To discover the manifold structure of midlevel features, we develop a spectral embedding approach to latent semantic learning based on L1-graph, without the need to tune any parameter for graph construction as a key step of manifold learning. More importantly, we construct the L1-graph with structured sparse representation, which can be obtained by structured sparse coding with its structured sparsity ensured by novel L1-norm hypergraph regularization over mid-level features. In the new embedding space, we learn latent semantics automatically from abundant mid-level features through spectral clustering. The learnt latent semantics can be readily used for human action recognition with SVM by defining a histogram intersection kernel. Different from the traditional latent semantic analysis based on topic models, our latent semantic learning method can explore the manifold structure of mid-level features in both L1-graph construction and spectral embedding, which results in compact but discriminative high-level features. The experimental results on the commonly used KTH action dataset and unconstrained YouTube action dataset show the superior performance of our method.

http://arxiv.org/abs/1109.4979v1

cs.MM, cs.AI, cs.LG

On Estimation and Selection for Topic Models

Matthew A. Taddy

This article describes posterior maximization for topic models, identifying computational and conceptual gains from inference under a non-standard parametrization. We then show that fitted parameters can be used as the basis for a novel approach to marginal likelihood estimation, via block-diagonal approximation to the information matrix,that facilitates choosing the number of latent topics. This likelihood-based model selection is complemented with a goodness-of-fit analysis built around estimated residual dispersion. Examples are provided to illustrate model selection as well as to compare our estimation against standard alternative techniques.

http://arxiv.org/abs/1109.4518v3

stat.AP

Learning Topic Models by Belief Propagation

Jia Zeng, William K. Cheung, Jiming Liu

Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This paper represents LDA as a factor graph within the Markov random field (MRF) framework, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly-used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great successes in learning LDA, the proposed BP is competitive in both speed and accuracy as validated by encouraging experimental results on four large-scale document data sets. Furthermore, the BP algorithm has the potential to become a generic learning scheme for variants of LDA-based topic models. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representation.

http://arxiv.org/abs/1109.3437v4

cs.LG

Using Variational Inference and MapReduce to Scale Topic Modeling

Ke Zhai, Jordan Boyd-Graber, Nima Asadi

Latent Dirichlet Allocation (LDA) is a popular topic modeling technique for exploring document collections. Because of the increasing prevalence of large datasets, there is a need to improve the scalability of inference of LDA. In this paper, we propose a technique called ~\emph{MapReduce LDA} (Mr. LDA) to accommodate very large corpus collections in the MapReduce framework. In contrast to other techniques to scale inference for LDA, which use Gibbs sampling, we use variational inference. Our solution efficiently distributes computation and is relatively simple to implement. More importantly, this variational implementation, unlike highly tuned and specialized implementations, is easily extensible. We demonstrate two extensions of the model possible with this scalable framework: informed priors to guide topic discovery and modeling topics from a multilingual corpus.

http://arxiv.org/abs/1107.3765v1

cs.AI, cs.DC

Statistical Topic Models for Multi-Label Document Classification

Timothy N. Rubin, America Chambers, Padhraic Smyth, Mark Steyvers

Machine learning approaches to multi-label document classification have to date largely relied on discriminative modeling techniques such as support vector machines. A drawback of these approaches is that performance rapidly drops off as the total number of labels and the number of labels per document increase. This problem is amplified when the label frequencies exhibit the type of highly skewed distributions that are often observed in real-world datasets. In this paper we investigate a class of generative statistical topic models for multi-label documents that associate individual word tokens with different labels. We investigate the advantages of this approach relative to discriminative models, particularly with respect to classification problems involving large numbers of relatively rare labels. We compare the performance of generative and discriminative approaches on document labeling tasks ranging from datasets with several thousand labels to datasets with tens of labels. The experimental results indicate that probabilistic generative models can achieve competitive multi-label classification performance compared to discriminative methods, and have advantages for datasets with many labels and skewed label frequencies.

http://arxiv.org/abs/1107.2462v2

stat.ML, cs.LG

The Discrete Infinite Logistic Normal Distribution

John Paisley, Chong Wang, David Blei

We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection of gamma-distributed random variables, and study its statistical properties. We consider applications to topic modeling and derive a variational inference algorithm for approximate posterior inference. We study the empirical performance of the DILN topic model on four corpora, comparing performance with the HDP and the correlated topic model (CTM). To deal with large-scale data sets, we also develop an online inference algorithm for DILN and compare with online HDP and online LDA on the Nature magazine, which contains approximately 350,000 articles.

http://arxiv.org/abs/1103.4789v3

stat.ML

A test of time-dependent theories of stellar convection

T. Gastine, B. Dintrans

Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf's formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes.

http://arxiv.org/abs/1103.3164v1

astro-ph.SR

Proximal Methods for Hierarchical Sparse Coding

Rodolphe Jenatton, Julien Mairal, Guillaume Obozinski, Francis Bach

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and we propose in this paper efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the L1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally organize in a prespecified arborescent structure, leading to a better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models.

http://arxiv.org/abs/1009.2139v4

stat.ML

Tree-Structured Stick Breaking Processes for Hierarchical Data

Ryan Prescott Adams, Zoubin Ghahramani, Michael I. Jordan

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

http://arxiv.org/abs/1006.1062v1

stat.ME, stat.ML

Agents, Bookmarks and Clicks: A topical model of Web traffic

Mark Meiss, Bruno Gonçalves, José J. Ramasco, Alessandro Flammini, Filippo Menczer

Analysis of aggregate and individual Web traffic has shown that PageRank is a poor model of how people navigate the Web. Using the empirical traffic patterns generated by a thousand users, we characterize several properties of Web traffic that cannot be reproduced by Markovian models. We examine both aggregate statistics capturing collective behavior, such as page and link traffic, and individual statistics, such as entropy and session size. No model currently explains all of these empirical observations simultaneously. We show that all of these traffic patterns can be explained by an agent-based model that takes into account several realistic browsing behaviors. First, agents maintain individual lists of bookmarks (a non-Markovian memory mechanism) that are used as teleportation targets. Second, agents can retreat along visited links, a branching mechanism that also allows us to reproduce behaviors such as the use of a back button and tabbed browsing. Finally, agents are sustained by visiting novel pages of topical interest, with adjacent pages being more topically related to each other than distant ones. This modulates the probability that an agent continues to browse or starts a new session, allowing us to recreate heterogeneous session lengths. The resulting model is capable of reproducing the collective and individual behaviors we observe in the empirical data, reconciling the narrowly focused browsing patterns of individual users with the extreme heterogeneity of aggregate traffic measurements. This result allows us to identify a few salient features that are necessary and sufficient to interpret the browsing patterns observed in our data. In addition to the descriptive and explanatory power of such a model, our results may lead the way to more sophisticated, realistic, and effective ranking and crawling algorithms.

http://arxiv.org/abs/1003.5327v1

cs.NI, cs.IR, cs.MA, physics.soc-ph

Hierarchical Web Page Classification Based on a Topic Model and Neighboring Pages Integration

Wongkot Sriurai, Phayung Meesad, Choochart Haruechaiyasak

Most Web page classification models typically apply the bag of words (BOW) model to represent the feature space. The original BOW representation, however, is unable to recognize semantic relationships between terms. One possible solution is to apply the topic model approach based on the Latent Dirichlet Allocation algorithm to cluster the term features into a set of latent topics. Terms assigned into the same topic are semantically related. In this paper, we propose a novel hierarchical classification method based on a topic model and by integrating additional term features from neighboring pages. Our hierarchical classification method consists of two phases: (1) feature representation by using a topic model and integrating neighboring pages, and (2) hierarchical Support Vector Machines (SVM) classification model constructed from a confusion matrix. From the experimental results, the approach of using the proposed hierarchical SVM model by integrating current page with neighboring pages via the topic model yielded the best performance with the accuracy equal to 90.33% and the F1 measure of 90.14%; an improvement of 5.12% and 5.13% over the original SVM model, respectively.

http://arxiv.org/abs/1003.1510v1

cs.LG

Supervised Topic Models

David M. Blei, Jon D. McAuliffe

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive an approximate maximum-likelihood procedure for parameter estimation, which relies on variational methods to handle intractable posterior expectations. Prediction problems motivate this research: we use the fitted model to predict response values for new documents. We test sLDA on two real-world problems: movie ratings predicted from reviews, and the political tone of amendments in the U.S. Senate based on the amendment text. We illustrate the benefits of sLDA versus modern regularized regression, as well as versus an unsupervised LDA analysis followed by a separate regression.

http://arxiv.org/abs/1003.0783v1

stat.ML

Syntactic Topic Models

Jordan Boyd-Graber, David M. Blei

The syntactic topic model (STM) is a Bayesian nonparametric model of language that discovers latent distributions of words (topics) that are both semantically and syntactically coherent. The STM models dependency parsed corpora where sentences are grouped into documents. It assumes that each word is drawn from a latent topic chosen by combining document-level features and the local syntactic context. Each document has a distribution over latent topics, as in topic models, which provides the semantic consistency. Each element in the dependency parse tree also has a distribution over the topics of its children, as in latent-state syntax models, which provides the syntactic consistency. These distributions are convolved so that the topic of each word is likely under both its document and syntactic context. We derive a fast posterior inference algorithm based on variational methods. We report qualitative and quantitative studies on both synthetic data and hand-parsed documents. We show that the STM is a more predictive model of language than current models based only on syntax or only on topics.

http://arxiv.org/abs/1002.4665v1

cs.CL, cs.AI, math.ST, stat.TH

MedLDA: A General Framework of Maximum Margin Supervised Topic Models

Jun Zhu, Amr Ahmed, Eric P. Xing

Supervised topic models utilize document's side information for discovering predictive low dimensional representations of documents. Existing models apply the likelihood-based estimation. In this paper, we present a general framework of max-margin supervised topic models for both continuous and categorical response variables. Our approach, the maximum entropy discrimination latent Dirichlet allocation (MedLDA), utilizes the max-margin principle to train supervised topic models and estimate predictive topic representations that are arguably more suitable for prediction tasks. The general principle of MedLDA can be applied to perform joint max-margin learning and maximum likelihood estimation for arbitrary topic models, directed or undirected, and supervised or unsupervised, when the supervised side information is available. We develop efficient variational methods for posterior inference and parameter estimation, and demonstrate qualitatively and quantitatively the advantages of MedLDA over likelihood-based topic models on movie review and 20 Newsgroups data sets.

http://arxiv.org/abs/0912.5507v1

stat.ML, stat.ME

Scalable Inference for Latent Dirichlet Allocation

James Petterson, Tiberio Caetano

We investigate the problem of learning a topic model - the well-known Latent Dirichlet Allocation - in a distributed manner, using a cluster of C processors and dividing the corpus to be learned equally among them. We propose a simple approximated method that can be tuned, trading speed for accuracy according to the task at hand. Our approach is asynchronous, and therefore suitable for clusters of heterogenous machines.

http://arxiv.org/abs/0909.4603v1

cs.LG

Hierarchical relational models for document networks

Jonathan Chang, David M. Blei

We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a fixed vocabulary. For each pair of documents, the RTM models their link as a binary random variable that is conditioned on their contents. The model can be used to summarize a network of documents, predict links between them, and predict words within them. We derive efficient inference and estimation algorithms based on variational methods that take advantage of sparsity and scale with the number of links. We evaluate the predictive performance of the RTM for large networks of scientific abstracts, web documents, and geographically tagged news.

http://arxiv.org/abs/0909.4331v3

stat.AP

Text Modeling using Unsupervised Topic Models and Concept Hierarchies

Chaitanya Chemudugunta, Padhraic Smyth, Mark Steyvers

Statistical topic models provide a general data-driven framework for automated discovery of high-level knowledge from large collections of text documents. While topic models can potentially discover a broad range of themes in a data set, the interpretability of the learned topics is not always ideal. Human-defined concepts, on the other hand, tend to be semantically richer due to careful selection of words to define concepts but they tend not to cover the themes in a data set exhaustively. In this paper, we propose a probabilistic framework to combine a hierarchy of human-defined semantic concepts with statistical topic models to seek the best of both worlds. Experimental results using two different sources of concept hierarchies and two collections of text documents indicate that this combination leads to systematic improvements in the quality of the associated language models as well as enabling new techniques for inferring and visualizing the semantics of a document.

http://arxiv.org/abs/0808.0973v1

cs.AI, cs.IR

Modeling Loosely Annotated Images with Imagined Annotations

Hong Tang, Nozha Boujemma, Yunhao Chen

In this paper, we present an approach to learning latent semantic analysis models from loosely annotated images for automatic image annotation and indexing. The given annotation in training images is loose due to: (1) ambiguous correspondences between visual features and annotated keywords; (2) incomplete lists of annotated keywords. The second reason motivates us to enrich the incomplete annotation in a simple way before learning topic models. In particular, some imagined keywords are poured into the incomplete annotation through measuring similarity between keywords. Then, both given and imagined annotations are used to learning probabilistic topic models for automatically annotating new images. We conduct experiments on a typical Corel dataset of images and loose annotations, and compare the proposed method with state-of-the-art discrete annotation methods (using a set of discrete blobs to represent an image). The proposed method improves word-driven probability Latent Semantic Analysis (PLSA-words) up to a comparable performance with the best discrete annotation method, while a merit of PLSA-words is still kept, i.e., a wider semantic range.

http://arxiv.org/abs/0805.4508v1

cs.IR, cs.AI, H.3.3

Modeling Online Reviews with Multi-grain Topic Models

Ivan Titov, Ryan McDonald

In this paper we present a novel framework for extracting the ratable aspects of objects from online user reviews. Extracting such aspects is an important challenge in automatically mining product opinions from the web and in generating opinion-based summaries of user reviews. Our models are based on extensions to standard topic modeling methods such as LDA and PLSA to induce multi-grain topics. We argue that multi-grain models are more appropriate for our task since standard models tend to produce topics that correspond to global properties of objects (e.g., the brand of a product type) rather than the aspects of an object that tend to be rated by a user. The models we present not only extract ratable aspects, but also cluster them into coherent topics, e.g., `waitress' and `bartender' are part of the same topic `staff' for restaurants. This differentiates it from much of the previous work which extracts aspects through term frequency analysis with minimal clustering. We evaluate the multi-grain models both qualitatively and quantitatively to show that they improve significantly upon standard topic models.

http://arxiv.org/abs/0801.1063v1

cs.IR, cs.DB, H.2.8; H.3.1; H.4

Correction: A correlated topic model of Science

David M. Blei, John D. Lafferty

Correction to Annals of Applied Statistics 1 (2007) 17--35 [doi:10.1214/07-AOAS114]

http://arxiv.org/abs/0712.1486v1

stat.AP

A correlated topic model of Science

David M. Blei, John D. Lafferty

Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics, each of which is a distribution over the vocabulary. A limitation of LDA is the inability to model topic correlation even though, for example, a document about genetics is more likely to also be about disease than X-ray astronomy. This limitation stems from the use of the Dirichlet distribution to model the variability among the topic proportions. In this paper we develop the correlated topic model (CTM), where the topic proportions exhibit correlation via the logistic normal distribution [J. Roy. Statist. Soc. Ser. B 44 (1982) 139--177]. We derive a fast variational inference algorithm for approximate posterior inference in this model, which is complicated by the fact that the logistic normal is not conjugate to the multinomial. We apply the CTM to the articles from Science published from 1990--1999, a data set that comprises 57M words. The CTM gives a better fit of the data than LDA, and we demonstrate its use as an exploratory tool of large document collections.

http://arxiv.org/abs/0708.3601v2

stat.AP