Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks.

We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data.

This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs, that does not require that the vertices in each DAG share a common ordering. Furthermore, we allow also for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.

One of the goals of any scientific study is to identify regularities in obs ervations and classify them into possibly separate and simpler structures or c ategories. These categories can in turn be used to make inferences on the obj ects of interest. The major advantage of this approach is that one breaks down a co mplicated reality into a collection of simpler structures. In a similar way, in patte rn recognition one is concern with discovery of regularities in data but t hrough use of computer algorithms which can be used to classify the data int o different categories [Bis06]. Independent of ones point of view, any such ana lysis must start with definition of the categories. If one has sufficient informa tion about the categories and their members, it is an easy task to establish a precis e definition. However, for most real life situations this is not the case and the no tion of category cannot be precisely defined. Under such conditions a fru itful approach is to consider a category as collection of objects which are likely to sh are the same properties.

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univariate Gibbs sampling on Markov Random Fields (MRFs) will be fast mixing, in a precise sense. Further, an algorithm is given to project onto this set of fast-mixing parameters in the Euclidean norm. Following recent work, we give an example use of this to project in various divergence measures, comparing univariate marginals obtained by sampling after projection to common variational methods and Gibbs sampling on the original parameters.

Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the assumption of chordality which ensures that efficient scoring methods can be used. In general, non-chordal graphs have intractable normalizing constants which renders the calculation of Bayesian and other scores difficult beyond very small-scale systems. Recently, there has been a surge of interest towards the use of regularized pseudo-likelihood methods for structural learning of large-scale Markov network models, as such an approach avoids the assumption of chordality. The currently available methods typically necessitate the use of a tuning parameter to adapt the level of regularization for a particular dataset, which can be optimized for example by cross-validation. Here we introduce a Bayesian version of pseudo-likelihood scoring of Markov networks, which enables an automatic regularization through marginalization over the nuisance parameters in the model. We prove consistency of the resulting MPL estimator for the network structure via comparison with the pseudo information criterion. Identification of the MPL-optimal network on a prescanned graph space is considered with both greedy hill climbing and exact pseudo-Boolean optimization algorithms. We find that for reasonable sample sizes the hill climbing approach most often identifies networks that are at a negligible distance from the restricted global optimum. Using synthetic and existing benchmark networks, the marginal pseudo-likelihood method is shown to generally perform favorably against recent popular inference methods for Markov networks.

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We present an explicit, algebraic EM-update rule for the models, yielding two fast and experimentally validated algorithms for signal recovery. Experimental results show that our algorithms outperform state-of-the-art methods on a wide range of sparsity levels and amplitudes in terms of reconstruction accuracy, convergence rate and sparsity. The largest improvement can be observed for sparse signals with high amplitudes.

In real world industrial applications of topic modeling, the ability to capture gigantic conceptual space by learning an ultra-high dimensional topical representation, i.e., the so-called "big model", is becoming the next desideratum after enthusiasms on "big data", especially for fine-grained downstream tasks such as online advertising, where good performances are usually achieved by regression-based predictors built on millions if not billions of input features. The conventional data-parallel approach for training gigantic topic models turns out to be rather inefficient in utilizing the power of parallelism, due to the heavy dependency on a centralized image of "model". Big model size also poses another challenge on the storage, where available model size is bounded by the smallest RAM of nodes. To address these issues, we explore another type of parallelism, namely model-parallelism, which enables training of disjoint blocks of a big topic model in parallel. By integrating data-parallelism with model-parallelism, we show that dependencies between distributed elements can be handled seamlessly, achieving not only faster convergence but also an ability to tackle significantly bigger model size. We describe an architecture for model-parallel inference of LDA, and present a variant of collapsed Gibbs sampling algorithm tailored for it. Experimental results demonstrate the ability of this system to handle topic modeling with unprecedented amount of 200 billion model variables only on a low-end cluster with very limited computational resources and bandwidth.

Identifying latent structure in large data matrices is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are locally co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for biclustering to infer subsets of co-regulated genes whose covariation may be observed in only a subset of the samples. Our biclustering method, BicMix, has desirable properties, including allowing overcomplete representations of the data, computational tractability, and jointly modeling unknown confounders and biological signals. Compared with related biclustering methods, BicMix recovers latent structure with higher precision across diverse simulation scenarios. Further, we develop a method to recover gene co-expression networks from the estimated sparse biclustering matrices. We apply BicMix to breast cancer gene expression data and recover a gene co-expression network that is differential across ER+ and ER- samples.

Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from labeled training data. We make two contributions. First, we show how to reparameterize a DPP's kernel matrix with multiple kernel functions, thus enhancing modeling flexibility. Second, we propose a novel parameter estimation technique based on the principle of large margin separation. In contrast to the state-of-the-art method of maximum likelihood estimation, our large-margin loss function explicitly models errors in selecting the target subsets, and it can be customized to trade off different types of errors (precision vs. recall). Extensive empirical studies validate our contributions, including applications on challenging document and video summarization, where flexibility in modeling the kernel matrix and balancing different errors is indispensable.