We define a probability distribution over equivalence classes of binary matrices with a finite number of rows and an unbounded number of columns. This distribution

Previous work in social network analysis (SNA) has modeled the existence of links from one entity to another, but not the language content or topics on those links. We present the Author-Recipient-Topic (ART) model for social network analysis, which learns topic distributions based on the direction-sensitive messages sent between entities. The model builds on Latent Dirichlet Allocation (LDA) and the Author-Topic (AT) model, adding the key attribute that distribution over topics is conditioned distinctly on both the sender and recipient—steering the discovery of topics according to the relationships between people. We give results on both the Enron email corpus and a researcher’s email archive, providing evidence not only that clearly relevant topics are discovered, but that the ART model better predicts people’s roles. 1 Introduction and Related Work Social network analysis (SNA) is the study of mathematical models for interactions among people, organizations and groups. With the recent availability of large datasets of human

Given a set of images containing multiple object categories, we seek to discover those categories and their image locations without supervision. We achieve this using generative models from the statistical text literature: probabilistic Latent Semantic Analysis (pLSA), and Latent Dirichlet Allocation (LDA). In text analysis these are used to discover topics in a corpus using the bag-of-words document representation. Here we discover topics as object categories, so that an image containing instances of several categories is modelled as a mixture of topics. The models are applied to images by using a visual analogue of a word, formed by vector quantizing SIFT like region descriptors. We investigate a set of increasingly demanding scenarios, starting with image sets containing only two object categories through to sets containing multiple categories (including airplanes, cars, faces, motorbikes, spotted cats) and background clutter. The object categories sample both intra-class and scale variation, and both the categories and their approximate spatial layout are found without supervision. We also demonstrate classification of unseen images and images containing multiple objects. Performance of the proposed unsupervised method is compared to the semi-supervised approach of [7].

Processing language requires the retrieval of concepts from memory in response to an ongoing stream of information. This retrieval is facilitated if one can infer the gist of a sentence, conversation, or document computational problem underlying the extraction and use of gist, formulating this problem as a rational statistical inference. This leads to a novel approach to semantic representation in which word meanings are represented in terms of a set of probabilistic topics. The topic model performs well in predicting word association and the effects of semantic association and ambiguity on a variety of language-processing and memory tasks. It also provides a foundation for developing more richly structured statistical models of language, as the generative process assumed in the topic model can easily be extended to incorporate other kinds of semantic and syntactic structure.

We propose a new hierarchical Bayesian n-gram model of natural languages. Our model makes use of a generalization of the commonly used Dirichlet distributions called Pitman-Yor processes which produce power-law distributions more closely resembling those in natural languages. We show that an approximation to the hierarchical Pitman-Yor language model recovers the exact formulation of interpolated Kneser-Ney, one of the best smoothing methods for n-gram language models. Experiments verify that our model gives cross entropy results superior to interpolated Kneser-Ney and comparable to modified Kneser-Ney. 1

Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. In contrast with most existing models, our approach captures the intrinsic uncertainty in the number and identity of objects depicted in a given image. Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DP in which a set of stochastically transformed mixture components are shared between multiple groups of data. For visual scenes, mixture components describe the spatial structure of visual features in an object–centered coordinate frame, while transformations model the object positions in a particular image. Learning and inference in the TDP, which has many potential applications beyond computer vision, is based on an empirically effective Gibbs sampler. Applied to a dataset of partially labeled street scenes, we show that the TDP’s inclusion of spatial structure improves detection performance, and allows unsupervised discovery of object categories. 1

Developing better methods for segmenting continuous text into words is important for improving the processing of Asian languages, and may shed light on how humans learn to segment speech. We propose two new Bayesian word segmentation methods that assume unigram and bigram models of word dependencies respectively. The bigram model greatly outperforms the unigram model (and previous probabilistic models), demonstrating the importance of such dependencies for word segmentation. We also show that previous probabilistic models rely crucially on suboptimal search procedures. 1

We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models. 1 1

Variational inference methods, including mean field methods and loopy belief propagation, have been widely used for approximate probabilistic inference in graphical models. While often less accurate than MCMC, variational methods provide a fast deterministic approximation to marginal and conditional probabilities. Such approximations can be particularly useful in high dimensional problems where sampling methods are too slow to be effective. A limitation of current methods, however, is that they are restricted to parametric probabilistic models. MCMC does not have such a limitation; indeed, MCMC samplers have been developed for the Dirichlet process (DP), a nonparametric distribution on distributions (Ferguson, 1973) that is the cornerstone of Bayesian nonparametric statistics (Escobar & West, 1995; Neal, 2000). In this paper, we develop a meanfield variational approach to approximate inference for the Dirichlet process, where the approximate posterior is based on the truncated stick-breaking construction (Ishwaran & James, 2001). We compare our approach to DP samplers for Gaussian DP mixture models. 1.

“Bag of words ” models have enjoyed much attention and achieved good performances in recent studies of object categorization. In most of these works, local patches are modeled as basic building blocks of an image, analogous to words in text documents. In most previous works using the “bag of words ” models (e.g. [4, 20, 7]), the local patches are assumed to be independent with each other. In this paper, we relax the independence assumption and model explicitly the inter-dependency of the local regions. Similarly to previous work, we represent images as a collection of patches, each of which belongs to a latent “theme ” that is shared across images as well as categories. We learn the theme distributions and patch distributions over the themes in a hierarchical structure [22]. In particular, we introduce a linkage structure over the latent themes to encode the dependencies of the patches. This structure enforces the semantic connections among the patches by facilitating better clustering of the themes. As a result, our models for object categories tend to be more discriminative than the ones obtained under the independent patch assumption. We show highly competitive categorization results on both the Caltech 4 and Caltech 101 object category datasets. By examining the distributions of the latent themes for each object category, we construct an object taxonomy using the 101 object classes from the Caltech 101 datasets. 1.