This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The setting is one where we only have samples from certain observed variables in the tree, and our goal is to estimate the tree structure (i.e., the graph of how the underlying hidden variables are connected to each other and to the observed variables). We propose the Spectral Recursive Grouping algorithm, an efficient and simple bottom-up procedure for recovering the tree structure from independent samples of the observed variables. Our finite sample size bounds for exact recovery of the tree structure reveal certain natural dependencies on underlying statistical and structural properties of the underlying joint distribution. Furthermore, our sample complexity guarantees have no explicit dependence on the dimensionality of the observed variables, making the algorithm applicable to many high-dimensional settings.

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, an Indian Buffet-like generative process for network growth, and a simple and efficient Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

Factored Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) form a powerful framework for multiagent planning under uncertainty, but optimal solutions require a rigid history-based policy representation. In this paper we allow inter-agent communication which turns the problem in a centralized Multiagent POMDP (MPOMDP). We map belief distributions over state factors to an agent's local actions by exploiting structure in the joint MPOMDP policy. The key point is that when sparse dependencies between the agents' decisions exist, often the belief over its local state factors is sufficient for an agent to unequivocally identify the optimal action, and communication can be avoided. We formalize these notions by casting the problem into convex optimization form, and present experimental results illustrating the savings in communication that we can obtain.

We consider the problem of estimating Shannon's entropy H in the under-sampled regime, where the number of possible symbols may be unknown or countably infinite. Pitman-Yor processes (a generalization of Dirichlet processes) provide tractable prior distributions over the space of countably infinite discrete distributions, and have found major applications in Bayesian non-parametric statistics and machine learning. Here we show that they also provide natural priors for Bayesian entropy estimation, due to the remarkable fact that the moments of the induced posterior distribution over H can be computed analytically. We derive formulas for the posterior mean (Bayes' least squares estimate) and variance under such priors. Moreover, we show that a fixed Dirichlet or Pitman-Yor process prior implies a narrow prior on H, meaning the prior strongly determines the entropy estimate in the under-sampled regime.

Markov logic is a widely used tool in statistical relational learning, which uses a weighted first-order logic knowledge base to specify a Markov random field (MRF) or a conditional random field (CRF). In many applications, a Markov logic network (MLN) is trained in one domain, but used in a different one. This paper focuses on dynamic Markov logic networks, where the domain of time points typically varies between training and testing. It has been previously pointed out that the marginal probabilities of truth assignments to ground atoms can change if one extends or reduces the domains of predicates in an MLN. We show that in addition to this problem, the standard way of unrolling a Markov logic theory into a MRF may result in time-inhomogeneity of the underlying Markov chain. Furthermore, even if these representational problems are not significant for a given domain, we show that the more practical problem of generating samples in a sequential conditional random field for the next slice relying on the samples from the previous slice has high computational cost in the general case, due to the need to estimate a normalization factor for each sample.

Biased labelers are a systemic problem in crowdsourcing, and a comprehensive toolbox for handling their responses is still being developed. A typical crowdsourcing application can be divided into three steps: data collection, data curation, and learning. At present these steps are often treated separately. We present Bayesian Bias Mitigation for Crowdsourcing (BBMC), a Bayesian model to unify all three. Most data curation methods account for the {\it effects} of labeler bias by modeling all labels as coming from a single latent truth.

Discrete mixtures are used routinely in broad sweeping applications ranging from unsupervised settings to fully supervised multi-task learning. Indeed, finite mixtures and infinite mixtures, relying on Dirichlet processes and modifications, have become a standard tool. One important issue that arises in using discrete mixtures is low separation in the components; in particular, different components can be introduced that are very similar and hence redundant. Such redundancy leads to too many clusters that are too similar, degrading performance in unsupervised learning and leading to computational problems and an unnecessarily complex model in supervised settings. Redundancy can arise in the absence of a penalty on components placed close together even when a Bayesian approach is used to learn the number of components.

We consider infinite-horizon stationary $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. Using Value and Policy Iteration with some error $\epsilon$ at each iteration, it is well-known that one can compute stationary policies that are $\frac{2\gamma{(1-\gamma) 2}\epsilon$-optimal. After arguing that this guarantee is tight, we develop variations of Value and Policy Iteration for computing non-stationary policies that can be up to $\frac{2\gamma}{1-\gamma}\epsilon$-optimal, which constitutes a significant improvement in the usual situation when $\gamma$ is close to $1$. Surprisingly, this shows that the problem of computing near-optimal non-stationary policies'' is much simpler than that of computing near-optimal stationary policies''. Papers published at the Neural Information Processing Systems Conference.

We propose a new sparse Bayesian model for multi-task regression and classification. The model is able to capture correlations between tasks, or more specifically a low-rank approximation of the covariance matrix, while being sparse in the features. We introduce a general family of group sparsity inducing priors based on matrix-variate Gaussian scale mixtures. We show the amount of sparsity can be learnt from the data by combining an approximate inference approach with type II maximum likelihood estimation of the hyperparameters. Empirical evaluations on data sets from biology and vision demonstrate the applicability of the model, where on both regression and classification tasks it achieves competitive predictive performance compared to previously proposed methods.

Conditional Markov Chains (also known as Linear-Chain Conditional Random Fields in the literature) are a versatile class of discriminative models for the distribution of a sequence of hidden states conditional on a sequence of observable variables. Large-sample properties of Conditional Markov Chains have been first studied by Sinn and Poupart [1]. The paper extends this work in two directions: first, mixing properties of models with unbounded feature functions are being established; second, necessary conditions for model identifiability and the uniqueness of maximum likelihood estimates are being given. Papers published at the Neural Information Processing Systems Conference.