Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable hierarchies to those with binary branching structure. This limitation, while computationally convenient, is often undesirable. In this paper we explore a Bayesian hierarchical clustering algorithm that can produce trees with arbitrary branching structure at each node, known as rose trees. We interpret these trees as mixtures over partitions of a data set, and use a computationally efficient, greedy agglomerative algorithm to find the rose trees which have high marginal likelihood given the data. Lastly, we perform experiments which demonstrate that rose trees are better models of data than the typical binary trees returned by other hierarchical clustering algorithms.

We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can estimate the partition function like any other parameter in the model. The estimation is done by optimizing an algebraically simple, well defined objective function, which allows for the use of dedicated optimization methods. We establish consistency of the estimator family and give an expression for the asymptotic covariance matrix, which enables us to further analyze the influence of the nonlinearities and the auxiliary density on estimation performance. Some estimators in our family are particularly stable for a wide range of auxiliary densities. Interestingly, a specific choice of the nonlinearity establishes a connection between density estimation and classification by nonlinear logistic regression. Finally, the optimal amount of auxiliary samples relative to the given amount of the data is considered from the perspective of computational efficiency.

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters by taking advantage of approximations to the conditional posteriors. We empirically demonstrate (1) the effectiveness of this approximation for improving convergence, (2) the benefits of the Dirichlet process model over alternative clustering techniques for ranked data, and (3) the applicability of the approach to exploring large realworld ranking datasets.

We introduce a new graphical model for tracking radio-tagged animals and learning their movement patterns. The model provides a principled way to combine radio telemetry data with an arbitrary set of userdefined, spatial features. We describe an efficient stochastic gradient algorithm for fitting model parameters to data and demonstrate its effectiveness via asymptotic analysis and synthetic experiments. We also apply our model to real datasets, and show that it outperforms the most popular radio telemetry software package used in ecology. We conclude that integration of different data sources under a single statistical framework, coupled with appropriate parameter and state estimation procedures, produces both accurate location estimates and an interpretable statistical model of animal movement.

Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter the conditional dependence between the random variables, and potentially produce significant structural changes in the corresponding graphical models. Therefore, it is of great importance to be able to detect such structural changes from data, so as to gain novel insights into where and how the structural changes take place and help the system adapt to the new environment. Here we report an effective learning strategy to extract structural changes in Gaussian graphical model using l1-regularization based convex optimization. We discuss the properties of the problem formulation and introduce an efficient implementation by the block coordinate descent algorithm. We demonstrate the principle of the approach on a numerical simulation experiment, and we then apply the algorithm to the modeling of gene regulatory networks under different conditions and obtain promising yet biologically plausible results.

Learning algorithms normally assume that there is at most one annotation or label per data point. However, in some scenarios, such as medical diagnosis and on-line collaboration,multiple annotations may be available. In either case, obtaining labels for data points can be expensive and time-consuming (in some circumstances ground-truth may not exist). Semi-supervised learning approaches have shown that utilizing the unlabeled data is often beneficial in these cases. This paper presents a probabilistic semi-supervised model and algorithm that allows for learning from both unlabeled and labeled data in the presence of multiple annotators. We assume that it is known what annotator labeled which data points. The proposed approach produces annotator models that allow us to provide (1) estimates of the true label and (2) annotator variable expertise for both labeled and unlabeled data. We provide numerical comparisons under various scenarios and with respect to standard semi-supervised learning. Experiments showed that the presented approach provides clear advantages over multi-annotator methods that do not use the unlabeled data and over methods that do not use multi-labeler information.

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponential family multi-view learning methods of the partial least squares and canonical correlation analysis, based on a unified representation of EPCA as matrix factorization of the natural parameters of exponential family. The models are based on a new family of priors that are generally usable for all such factorizations. We also introduce new inference strategies, and demonstrate how the methods outperform earlier ones when the Gaussianity assumption does not hold.

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a small set of basis points. Among them, two state-of-the-art methods are sparse pseudo-input Gaussian process (SPGP) (Snelson and Ghahramani, 2006) and variablesigma GP (VSGP) Walder et al. (2008), which generalizes SPGP and allows each basis point to have its own length scale. However, VSGP was only derived for regression. In this paper, we propose a new sparse GP framework that uses expectation propagation to directly approximate general GP likelihoods using a sparse and smooth basis. It includes both SPGP and VSGP for regression as special cases. Plus as an EP algorithm, it inherits the ability to process data online. As a particular choice of approximating family, we blur each basis point with a Gaussian distribution that has a full covariance matrix representing the data distribution around that basis point; as a result, we can summarize local data manifold information with a small set of basis points. Our experiments demonstrate that this framework outperforms previous GP classification methods on benchmark datasets in terms of minimizing divergence to the non-sparse GP solution as well as lower misclassification rate.

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performance. We propose a generalization of the singular value decomposition (SVD) and principal components analysis (PCA) that is appropriate for massive data sets with structured variables or known two-way dependencies. By finding the best low rank approximation of the data with respect to a transposable quadratic norm, our decomposition, entitled the Generalized least squares Matrix Decomposition (GMD), directly accounts for structural relationships. As many variables in high-dimensional settings are often irrelevant or noisy, we also regularize our matrix decomposition by adding two-way penalties to encourage sparsity or smoothness. We develop fast computational algorithms using our methods to perform generalized PCA (GPCA), sparse GPCA, and functional GPCA on massive data sets. Through simulations and a whole brain functional MRI example we demonstrate the utility of our methodology for dimension reduction, signal recovery, and feature selection with high-dimensional structured data.

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.