Latent dirichlet allocation

doi:10.5555/944919.944937

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Latent dirichlet allocation

Journal Article•DOI•

Latent dirichlet allocation

David M. Blei¹, Andrew Y. Ng², Michael I. Jordan¹•Institutions (2)

University of California, Berkeley¹, Stanford University²

01 Mar 2003-Journal of Machine Learning Research (JMLR.org)-Vol. 3, pp 993-1022

TL;DR: This work proposes a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams, and Hofmann's aspect model.

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Abstract: We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

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Proceedings Article•DOI•

Topic Modeling of Short Texts: A Pseudo-Document View

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Yuan Zuo¹, Junjie Wu¹, Hui Zhang¹, Hao Lin¹, Fei Wang¹, Ke Xu¹, Hui Xiong² - Show less +3 more•Institutions (2)

Beihang University¹, Rutgers University²

13 Aug 2016

TL;DR: An in-depth semantic analysis is taken to unveil directly the fabulous function of pseudo documents in finding cross-text word co-occurrences for topic modeling.

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Abstract: Recent years have witnessed the unprecedented growth of online social media, which empower short texts as the prevalent format for information of Internet. Given the nature of sparsity, however, short text topic modeling remains a critical yet much-watched challenge in both academy and industry. Rich research efforts have been put on building different types of probabilistic topic models for short texts, among which the self aggregation methods without using auxiliary information become an emerging solution for providing informative cross-text word co-occurrences. However, models along this line are still rarely seen, and the representative one Self-Aggregation Topic Model (SATM) is prone to overfitting and computationally expensive. In light of this, in this paper, we propose a novel probabilistic model called Pseudo-document-based Topic Model (PTM) for short text topic modeling. PTM introduces the concept of pseudo document to implicitly aggregate short texts against data sparsity. By modeling the topic distributions of latent pseudo documents rather than short texts, PTM is expected to gain excellent performance in both accuracy and efficiency. A Sparsity-enhanced PTM (SPTM for short) is also proposed by applying Spike and Slab prior, with the purpose of eliminating undesired correlations between pseudo documents and latent topics. Extensive experiments on various real-world data sets with state-of-the-art baselines demonstrate the high quality of topics learned by PTM and its robustness with reduced training samples. It is also interesting to show that i) SPTM gains a clear edge over PTM when the number of pseudo documents is relatively small, and ii) the constraint that a short text belongs to only one pseudo document is critically important for the success of PTM. We finally take an in-depth semantic analysis to unveil directly the fabulous function of pseudo documents in finding cross-text word co-occurrences for topic modeling.

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176 citations

Cites background from "Latent dirichlet allocation"

...Standard topic models [2, 4] assume a document is generated from a mixture of topics, where a topic is a probabilistic distribution of words....
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...As one of the most typical probabilistic topic model, LDA [2] has achieved great success in modeling text collections like news articles, research papers and blogs....
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...Being one of the most classical topic models, LDA [2] can induce sparsity as its Dirichlet prior approaches zero....
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Proceedings Article•DOI•

Bayesian Co-clustering

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Hanhuai Shan¹, Arindam Banerjee¹•Institutions (1)

University of Minnesota¹

15 Dec 2008

TL;DR: This paper presents Bayesian co-clustering models, that allow a mixed membership in row and column clusters, and proposes a fast variational algorithm for inference and parameter estimation.

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Abstract: In recent years, co-clustering has emerged as a powerful data mining tool that can analyze dyadic data connecting two entities. However, almost all existing co-clustering techniques are partitional, and allow individual rows and columns of a data matrix to belong to only one cluster. Several current applications, such as recommendation systems and market basket analysis, can substantially benefit from a mixed membership of rows and columns. In this paper, we present Bayesian co-clustering (BCC) models, that allow a mixed membership in row and column clusters. BCC maintains separate Dirichlet priors for rows and columns over the mixed membership and assumes each observation to be generated by an exponential family distribution corresponding to its row and column clusters. We propose a fast variational algorithm for inference and parameter estimation. The model is designed to naturally handle sparse matrices as the inference is done only based on the non-missing entries. In addition to finding a co-cluster structure in observations, the model outputs a low dimensional co-embedding, and accurately predicts missing values in the original matrix. We demonstrate the efficacy of the model through experiments on both simulated and real data.

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176 citations

Cites background or methods or result from "Latent dirichlet allocation"

...where [i]1 1 , [j] k2 1 , [u] n1 1 , [v] n2 1 , φ1ui is the i th component of φ1 for row u, φ2vj is the j th component of φ2 for column v, and similarly for γ1ui and γ2vj , and Ψ(·) is the digamma function [7]....
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...As compared to the variational approximation used in BNB [5] and LDA [7], where the cluster assignment z for every single feature has a variational discrete distribution, in our approximation there is only one variational discrete distribution for an entire row/column....
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...To estimate the Dirichlet parameters (α1, α2), one can use an efficient Newton update as shown in [7, 5] for LDA and BNB....
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...Variational inference [7] and Gibbs sampling [11] are two most popular approaches proposed to address the problem....
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...Recall that the perplexity [7] of a dataset X is defined as: perp(X) = exp(− log p(X)/N), where N is the number of non-missing entries....
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Posted Content•

Syntactic Topic Models

[...]

Jordan Boyd-Graber¹, David M. Blei¹•Institutions (1)

Princeton University¹

25 Feb 2010-arXiv: Computation and Language

TL;DR: The syntactic topic model (STM) is developed, a nonparametric Bayesian model of parsed documents that generates words that are both thematically and syntactically constrained, which combines the semantic insights of topic models with the syntactic information available from parse trees.

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Abstract: 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.

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176 citations

Cites background from "Latent dirichlet allocation"

...It can be thought of as the “infinite” topic version of latent Dirichlet allocation (LDA) [13]....
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Proceedings Article•

Predicting Legislative Roll Calls from Text

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Sean Gerrish¹, David M. Blei¹•Institutions (1)

Princeton University¹

28 Jun 2011

TL;DR: This work develops several predictive models linking legislative sentiment to legislative text and derives approximate posterior inference algorithms based on variational methods that predict specific voting patterns with high accuracy across 12 years of legislative data.

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Abstract: We develop several predictive models linking legislative sentiment to legislative text. Our models, which draw on ideas from ideal point estimation and topic models, predict voting patterns based on the contents of bills and infer the political leanings of legislators. With supervised topics, we provide an exploratory window into how the language of the law is correlated with political support. We also derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we predict specific voting patterns with high accuracy.

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176 citations

Proceedings Article•DOI•

Probabilistic dyadic data analysis with local and global consistency

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Deng Cai¹, Xuanhui Wang², Xiaofei He¹•Institutions (2)

Zhejiang University¹, University of Illinois at Urbana–Champaign²

14 Jun 2009

TL;DR: This work introduces a probabilistic framework for modeling both the topical and geometrical structure of the dyadic data that explicitly takes into account the local manifold structure.

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Abstract: Dyadic data arises in many real world applications such as social network analysis and information retrieval. In order to discover the underlying or hidden structure in the dyadic data, many topic modeling techniques were proposed. The typical algorithms include Probabilistic Latent Semantic Analysis (PLSA) and Latent Dirichlet Allocation (LDA). The probability density functions obtained by both of these two algorithms are supported on the Euclidean space. However, many previous studies have shown naturally occurring data may reside on or close to an underlying submanifold. We introduce a probabilistic framework for modeling both the topical and geometrical structure of the dyadic data that explicitly takes into account the local manifold structure. Specifically, the local manifold structure is modeled by a graph. The graph Laplacian, analogous to the Laplace-Beltrami operator on manifolds, is applied to smooth the probability density functions. As a result, the obtained probabilistic distributions are concentrated around the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach.

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176 citations

Cites background or methods from "Latent dirichlet allocation"

...To address this issue, Latent Dirichlet Allocation (LDA) (Blei et al., 2003) is then proposed....
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...DATA AND EXPERIMENTAL SETTINGS The experimental settings in this work are basically the same as those in (Blei et al., 2003)....
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...However, the number of parameters of PLSA grows linearly with the number of documents, which suggests that PLSA is prone to over.tting (Blei et al., 2003)....
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...Two of the most well known topic modeling algorithms include Probabilistic Latent Semantic Analysis (PLSA) (Hofmann, 2001) and Latent Dirichlet Allocation (LDA) (Blei et al., 2003)....
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...The linear growth in parameters suggests that the model is prone to over.tting (Blei et al., 2003)....
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References

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Book•

Handbook of mathematical functions : with formulas, graphs, and mathematical tables

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Milton Abramowitz, Irene A. Stegun

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17,608 citations

Book•

Bayesian Data Analysis

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Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin¹ - Show less +2 more•Institutions (1)

University of California, Irvine¹

01 Jan 1995

TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.

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Abstract: FUNDAMENTALS OF BAYESIAN INFERENCE Probability and Inference Single-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian Approaches Hierarchical Models FUNDAMENTALS OF BAYESIAN DATA ANALYSIS Model Checking Evaluating, Comparing, and Expanding Models Modeling Accounting for Data Collection Decision Analysis ADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional Approximations REGRESSION MODELS Introduction to Regression Models Hierarchical Linear Models Generalized Linear Models Models for Robust Inference Models for Missing Data NONLINEAR AND NONPARAMETRIC MODELS Parametric Nonlinear Models Basic Function Models Gaussian Process Models Finite Mixture Models Dirichlet Process Models APPENDICES A: Standard Probability Distributions B: Outline of Proofs of Asymptotic Theorems C: Computation in R and Stan Bibliographic Notes and Exercises appear at the end of each chapter.

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16,079 citations

"Latent dirichlet allocation" refers background in this paper

...Finally, Griffiths and Steyvers (2002) have presented a Markov chain Monte Carlo algorithm for LDA....
[...]
...Structures similar to that shown in Figure 1 are often studied in Bayesian statistical modeling, where they are referred to ashierarchical models(Gelman et al., 1995), or more precisely asconditionally independent hierarchical models(Kass and Steffey, 1989)....
[...]
...Structures similar to that shown in Figure 1 are often studied in Bayesian statistical modeling, where they are referred to as hierarchical models (Gelman et al., 1995), or more precisely as conditionally independent hierarchical models (Kass and Steffey, 1989)....
[...]

Journal Article•DOI•

Indexing by Latent Semantic Analysis

[...]

Scott Deerwester¹, Susan T. Dumais², George W. Furnas², Thomas K. Landauer², Richard A. Harshman³ - Show less +1 more•Institutions (3)

University of Chicago¹, Telcordia Technologies², University of Western Ontario³

01 Sep 1990-Journal of the Association for Information Science and Technology

TL;DR: A new method for automatic indexing and retrieval to take advantage of implicit higher-order structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries.

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Abstract: A new method for automatic indexing and retrieval is described. The approach is to take advantage of implicit higher-order structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries. The particular technique used is singular-value decomposition, in which a large term by document matrix is decomposed into a set of ca. 100 orthogonal factors from which the original matrix can be approximated by linear combination. Documents are represented by ca. 100 item vectors of factor weights. Queries are represented as pseudo-document vectors formed from weighted combinations of terms, and documents with supra-threshold cosine values are returned. initial tests find this completely automatic method for retrieval to be promising.

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12,443 citations

"Latent dirichlet allocation" refers methods in this paper

...To address these shortcomings, IR researchers have proposed several other dimensionality reduction techniques, most notably latent semantic indexing (LSI) (Deerwester et al., 1990)....
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...To address these shortcomings, IR researchers have proposed several other dimensionality reduction techniques, most notablylatent semantic indexing (LSI)(Deerwester et al., 1990)....
[...]

Book•

Introduction to Modern Information Retrieval

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Gerard Salton, Michael J. McGill

01 Jan 1983

TL;DR: Reading is a need and a hobby at once and this condition is the on that will make you feel that you must read.

...read moreread less

Abstract: Some people may be laughing when looking at you reading in your spare time. Some may be admired of you. And some may want be like you who have reading hobby. What about your own feel? Have you felt right? Reading is a need and a hobby at once. This condition is the on that will make you feel that you must read. If you know are looking for the book enPDFd introduction to modern information retrieval as the choice of reading, you can find here.

...read moreread less

12,059 citations

"Latent dirichlet allocation" refers background or methods in this paper

...In the populartf-idf scheme (Salton and McGill, 1983), a basic vocabulary of “words” or “terms” is chosen, and, for each document in the corpus, a count is formed of the number of occurrences of each word....
[...]
...We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model....
[...]

Book•

Theory of probability

[...]

Harold Jeffreys, R. Bruce Lindsay

01 Jan 1939

TL;DR: In this paper, the authors introduce the concept of direct probabilities, approximate methods and simplifications, and significant importance tests for various complications, including one new parameter, and various complications for frequency definitions and direct methods.

...read moreread less

Abstract: 1. Fundamental notions 2. Direct probabilities 3. Estimation problems 4. Approximate methods and simplifications 5. Significance tests: one new parameter 6. Significance tests: various complications 7. Frequency definitions and direct methods 8. General questions

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7,086 citations