Graphical modelling has a long history in statistics as a tool for the analysis of multivariate data, starting from Wright's path analysis and Gibbs' applications to statistical physics at the beginning of the last century. In its modern form, it was pioneered by Lauritzen and Wermuth and Pearl in the 1980s, and has since found applications in fields as diverse as bioinformatics, customer satisfaction surveys and weather forecasts. Genetics and systems biology are unique among these fields in the dimension of the data sets they study, which often contain several hundreds of variables and only a few tens or hundreds of observations. This raises problems in both computational complexity and the statistical significance of the resulting networks, collectively known as the "curse of dimensionality". Furthermore, the data themselves are difficult to model correctly due to the limited understanding of the underlying mechanisms. In the following, we will illustrate how such challenges affect practical graphical modelling and some possible solutions.

Intelligent game-based learning environments integrate commercial game technologies with AI methods from intelligent tutoring systems and intelligent narrative technologies. This article introduces the CRYSTAL ISLAND intelligent game-based learning environment, which has been under development in the authors’ laboratory for the past seven years. After presenting CRYSTAL ISLAND, the principal technical problems of intelligent game-based learning environments are discussed: narrative-centered tutorial planning, student affect recognition, student knowledge modeling, and student goal recognition. Solutions to these problems are illustrated with research conducted with the CRYSTAL ISLAND learning environment.

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the L\'{e}vy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.

During the last two decades there has been a growing interest in Particle Filtering (PF). However, PF suffers from two long-standing problems that are referred to as sample degeneracy and impoverishment. We are investigating methods that are particularly efficient at Particle Distribution Optimization (PDO) to fight sample degeneracy and impoverishment, with an emphasis on intelligence choices. These methods benefit from such methods as Markov Chain Monte Carlo methods, Mean-shift algorithms, artificial intelligence algorithms (e.g., Particle Swarm Optimization, Genetic Algorithm and Ant Colony Optimization), machine learning approaches (e.g., clustering, splitting and merging) and their hybrids, forming a coherent standpoint to enhance the particle filter. The working mechanism, interrelationship, pros and cons of these approaches are provided. In addition, Approaches that are effective for dealing with high-dimensionality are reviewed. While improving the filter performance in terms of accuracy, robustness and convergence, it is noted that advanced techniques employed in PF often causes additional computational requirement that will in turn sacrifice improvement obtained in real life filtering. This fact, hidden in pure simulations, deserves the attention of the users and designers of new filters.

We pursue an early stopping technique that helps Gaussian Restricted Boltzmann Machines (GRBMs) to gain good natural image representations in terms of overcompleteness and data fitting. GRBMs are widely considered as an unsuitable model for natural images because they gain non-overcomplete representations which include uniform filters that do not represent useful image features. We have recently found that GRBMs once gain and subsequently lose useful filters during their training, contrary to this common perspective. We attribute this phenomenon to a tradeoff between overcompleteness of GRBM representations and data fitting. To gain GRBM representations that are overcomplete and fit data well, we propose a measure for GRBM representation quality, approximated mutual information, and an early stopping technique based on this measure. The proposed method boosts performance of classifiers trained on GRBM representations.

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.

Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models.

How humans achieve long-term goals in an uncertain environment, via repeated trials and noisy observations, is an important problem in cognitive science. We investigate this behavior in the context of a multi-armed bandit task. We compare human behavior to a variety of models that vary in their representational and computational complexity. Our result shows that subjects' choices, on a trial-to- trial basis, are best captured by a "forgetful" Bayesian iterative learning model [21] in combination with a partially myopic decision policy known as Knowledge Gradient [7]. This model accounts for subjects' trial-by-trial choice better than a number of other previously proposed models, including optimal Bayesian learning and risk minimization, ε-greedy and win-stay-lose-shift. It has the added benefit of being closest in performance to the optimal Bayesian model than all the other heuristic models that have the same computational complexity (all are significantly less complex than the optimal model). These results constitute an advancement in the theoretical understanding of how humans negotiate the tension between exploration and exploitation in a noisy, imperfectly known environment.

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for matrix reconstruction. We have also successfully applied the proposed algorithm to a clustering problem, by formulating the problem of clustering as a low-rank matrix reconstruction problem with an additional structural property. Numerical experiments show that the proposed algorithm outperforms Lloyd's K-means algorithm.

This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a hard clustering with convergence guarantees similar to those of the k-means algorithm. Empirical results from a synthetic test with moving Gaussian clusters and a test with real ADS-B aircraft trajectory data demonstrate that the algorithm requires orders of magnitude less computational time than contemporary probabilistic and hard clustering algorithms, while providing higher accuracy on the examined datasets.