Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also inefficient for large count values and requires averaging over many samples to reduce variance. On the other hand, variational Bayesian inference is efficient and accurate for large count values but suffers from bias for small counts. We propose a hybrid algorithm that combines the best of both worlds: it samples very small counts and applies variational updates to large counts. This hybridization is shown to significantly improve testset perplexity relative to variational inference at no computational cost.

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inference. The latent likelihood of the data and its gradients are computable in closed form via Tutte's directed matrix tree theorem using determinants and inverses of the out-Laplacian. This novel likelihood subsumes iid likelihood, is exchangeable and yields efficient unsupervised and semi-supervised learning algorithms. In addition to handling taxonomy and phylogenetic datasets the out-tree assumption performs surprisingly well as a semi-parametric density estimator on standard iid datasets. Experiments with unsupervised and semisupervised learning are shown on various UCI and taxonomy datasets.

Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference process is first defined to be the minimization of a convex function, inspired by free energy approximations. Learning is then done directly in terms of the performance of the inference process at univariate marginal prediction. The main novelty is that this is a direct minimization of emperical risk, where the risk measures the accuracy of predicted marginals.

We present an algorithm that identifies the reasoning patterns of agents in a game, by iteratively examining the graph structure of its Multi-Agent Influence Diagram (MAID) representation. If the decision of an agent participates in no reasoning patterns, then we can effectively ignore that decision for the purpose of calculating a Nash equilibrium for the game. In some cases, this can lead to exponential time savings in the process of equilibrium calculation. Moreover, our algorithm can be used to enumerate the reasoning patterns in a game, which can be useful for constructing more effective computerized agents interacting with humans.

The paper introduces AND/OR importance sampling for probabilistic graphical models. In contrast to importance sampling, AND/OR importance sampling caches samples in the AND/OR space and then extracts a new sample mean from the stored samples. We prove that AND/OR importance sampling may have lower variance than importance sampling; thereby providing a theoretical justification for preferring it over importance sampling. Our empirical evaluation demonstrates that AND/OR importance sampling is far more accurate than importance sampling in many cases.

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the marginal likelihood and contains many regularised risk approaches as special cases. Furthermore, we derive an efficient and provably convergent optimisation algorithm.

The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree distribution. The degree-corrected block model can accommodate arbitrary degree distributions within communities. But since it takes the vertex degrees as parameters rather than generating them, it cannot use them to help it classify the vertices, and its natural generalization to directed graphs cannot even use the orientations of the edges. In this paper, we present variants of the block model with the best of both worlds: they can use vertex degrees and edge orientations in the classification process, while tolerating heavy-tailed degree distributions within communities. We show that for some networks, including synthetic networks and networks of word adjacencies in English text, these new block models achieve a higher accuracy than either standard or degree-corrected block models.

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 10^64 solutions. We show that these problems are NP-hard even if the underlying graph structure of the problem has low treewidth and the variables take on a bounded number of states, and that they admit no provably good approximation if variables can take on an arbitrary number of states.

The current paradigm in student modeling has continued to show the power of its simplifying assumption of knowledge as a binary and monotonically increasing construct, the value of which directly causes the outcome of student answers to questions. Recent efforts have focused on optimizing the prediction accuracy of responses to questions using student models. Incorporating individual student parameter interactions has been an interpretable and principled approach which has improved the performance of this task, as demonstrated by its application in the 2010 KDD Cup challenge on Educational Data. Performance prediction, however, can have limited practical utility. The greatest utility of such student models can be their ability to model the tutor and the attributes of the tutor which are causing learning. Harnessing the same simplifying assumption of learning used in student modeling, we can turn this model on its head to effectively tease out the tutor attributes causing learning and begin to optimize the tutor model to benefit the student model.

This work discusses the problem of sparse signal recovery when there is correlation among the values of non-zero entries. We examine intra-vector correlation in the context of the block sparse model and inter-vector correlation in the context of the multiple measurement vector model, as well as their combination. Algorithms based on the sparse Bayesian learning are presented and the benefits of incorporating correlation at the algorithm level are discussed. The impact of correlation on the limits of support recovery is also discussed highlighting the different impact intra-vector and inter-vector correlations have on such limits.