A family of probabilistic time series models is developed to analyze the time evolution of topics in large document collections. The approach is to use state space models on the natural parameters of the multinomial distributions that represent the topics. Variational approximations based on Kalman filters and nonparametric wavelet regression are developed to carry out approximate posterior inference over the latent topics. In addition to giving quantitative, predictive models of a sequential corpus, dynamic topic models provide a qualitative window into the contents of a large document collection. The models are demonstrated by analyzing the OCR'ed archives of the journal Science from 1880 through 2000.

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on ℓ1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results provide sufficient conditions on the triple (n, p, d) and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes n = Ω(d 3 log p) with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of n = Ω(d 2 log p) suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.

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.Comment: Published at http://dx.doi.org/10.1214/07-AOAS114 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Language modeling approaches to information retrieval are attractive and promising because they connect the problem of retrieval with that of language model estimation, which has been studied extensively in other application areas such as speech recognition. The basic idea of these approaches is to estimate a language model for each document, and to then rank documents by the likelihood of the query according to the estimated language model. A central issue in language model estimation is smoothing, the problem of adjusting the maximum likelihood estimator to compensate for data sparseness. In this article, we study the problem of language model smoothing and its influence on retrieval performance. We examine the sensitivity of retrieval performance to the smoothing parameters and compare several popular smoothing methods on different test collections. Experimental results show that not only is the retrieval performance generally sensitive to the smoothing parameters, but also the sensitivity pattern is affected by the query type, with performance being more sensitive to smoothing for verbose queries than for keyword queries. Verbose queries also generally require more aggressive smoothing to achieve optimal performance. This suggests that smoothing plays two different role-to make the estimated document language model more accurate and to "explain" the noninformative words in the query. In order to decouple these two distinct roles of smoothing, we propose a two-stage smoothing strategy, which yields better sensitivity patterns and facilitates the setting of smoothing parameters automatically. We further propose methods for estimating the smoothing parameters automatically. Evaluation on five different databases and four types of queries indicates that the two-stage smoothing method with the proposed parameter estimation methods consistently gives retrieval performance that is close to-or better than-the best results achieved using a single smoothing method and exhaustive parameter search on the test data.

We present a new class of methods for high dimensional non-parametric regression and classification called sparse additive models. Our methods combine ideas from sparse linear modelling and additive non-parametric regression. We derive an algorithm for fitting the models that is practical and effective even when the number of covariates is larger than the sample size. Sparse additive models are essentially a functional version of the grouped lasso of Yuan and Lin. They are also closely related to the COSSO model of Lin and Zhang but decouple smoothing and sparsity, enabling the use of arbitrary non-parametric smoothers. We give an analysis of the theoretical properties of sparse additive models and present empirical results on synthetic and real data, showing that they can be effective in fitting sparse non-parametric models in high dimensional data. Copyright (c) 2009 Royal Statistical Society.