Probabilistic topic models are a suite of algorithms whose aim is to discover the

Statistical topic models provide a general data-driven framework for automated discovery of highlevel 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. 1.

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.

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. 1

As the rapid development of all kinds of online databases, huge heterogeneous information networks thus derived are ubiquitous. Detecting evolutionary communities in these networks can help people better understand the structural evolution of the networks. However, most of the current community evolution analysis is based on the homogeneous networks, while a real community usually involves different types of objects in a heterogeneous network. For example, when referring to a research community, it contains a set of authors, a set of conferences or journals and a set of terms. In this paper, we study the problem of detecting evolutionary multi-typed communities defined as net-clusters in dynamic heterogeneous networks. A Dirichlet Process Mixture Model-based generative model is proposed to model the community generations. At each time stamp, a clustering of communities with the best cluster number that can best explain the current and historical networks are automatically detected. A Gibbs sampling-based inference algorithm is provided to inference the model. Also, the evolution structure can be read from the model, which can help users better understand the birth, split and death of communities. Experiments on two real datasets, namely DBLP and Delicious.com, have shown the effectiveness of the algorithm.

Statistics has both optimistic and pessimistic faces, with the Bayesian perspective often associated with the former and the frequentist perspective with the latter, but with foundational thinkers such as Jim Berger reminding us that statistics is fundamentally a Janus-like creature with two faces. In creating one field out of two perspectives, one of the unifying

Real world networks exhibit a complex set of phenomena such as underlying hierarchical organization, multiscale interaction, and varying topologies of communities. Most existing methods do not adequately capture the intrinsic interplay among such phenomena. We propose a nonparametric Multiscale Community Blockmodel (MSCB) to model the generation of hierarchies in social communities, selective membership of actors to subsets of these communities, and the resultant networks due to within- and cross- community interactions. By using the nested Chinese Restaurant Process, our model automatically infers the hierarchy structure from the data. We develop a collapsed Gibbs sampling algorithm for posterior inference, conduct extensive validation using synthetic networks, and demonstrate the utility of our model in real-world datasets such as predator-prey networks and citation networks. 1

Categories are often organized into hierarchical taxonomies, that is, tree structures where each node represents a labeled category, and a node’s parent and children are, respectively, the category’s supertype and subtypes. A natural question is whether it is possible to reconstruct category taxonomies in cases where we are not given explicit information about how categories are related to each other, but only a sample of observations of the members of each category. In this paper, we introduce a nonparametric Bayesian model of multi-level category learning, an extension of the hierarchical Dirichlet process (HDP) that we call the tree-HDP. We demonstrate the ability of the tree-HDP to reconstruct simulated datasets of artificial taxonomies, and show that it produces similar performance to human learners on a taxonomy inference task.

We introduce HD (or “Hierarchical-Deep”) models, a new compositional learning architecture that integrates deep learning models with structured hierarchical Bayesian models. Specifically we show how we can learn a hierarchical Dirichlet process (HDP) prior over the activities of the top-level features in a Deep Boltzmann Machine (DBM). This compound HDP-DBM model learns to learn novel concepts from very few training examples, by learning low-level generic features, high-level features that capture correlations among low-level features, and a category hierarchy for sharing priors over the high-level features that are typical of different kinds of concepts. We present efficient learning and inference algorithms for the HDP-DBM model and show that it is able to learn new concepts from very few examples on CIFAR-100 object recognition, handwritten character recognition, and human motion capture datasets. 1

It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in one-byone at a distinguished source vertex, successive particles proceed along directed edges according to an appropriate stochastic mechanism, and each particle comes to rest once it encounters an unoccupied vertex. Examples include the binary and digital search tree processes, the random recursive tree process and generalizations of it arising from nested instances of Pitman’s two-parameter Chinese restaurant process, tree-growth models associated with Mallows ’ φ model of random permutations and with Schützenberger’s non-commutative q-binomial theorem, and a construction due to Luczak and Winkler that grows uniform random binary trees in a Markovian manner. We introduce a framework that encompasses such Markov chains, and we characterize their asymptotic behavior by analyzing in detail their Doob-Martin compactifications, Poisson boundaries and tail σ-fields.