We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model, we maximize the likelihood of observing u_i to find both the model parameters for the 1-D MOG as well as the projection vector w. First, we derive an EM algorithm for estimating the PMOG model. Next, we show how the PMOG model can be applied to the problem of blind source separation (BSS). In contrast to conventional BSS where an objective function based on an approximation to differential entropy is minimized, PMOG based BSS simply minimizes the differential entropy of projected sources by fitting a flexible MOG model in the projected 1-D space while simultaneously optimizing the projection vector w. The advantage of PMOG over conventional BSS algorithms is the more flexible fitting of non-Gaussian source densities without assuming near-Gaussianity (as in conventional BSS) and still retaining computational feasibility.

The problem of mining patterns in graph-structured data has received considerable attention in recent years, as it has many interesting applications in such diverse areas as biology, the life sciences, the World Wide Web, or social sciences. In the present work we introduce a novel class of patterns, called tree queries, and we present algorithms for mining these tree queries and tree-query associations in a large data graph. This article is based on two earlier conference papers [17, 20]. Tree queries are powerful tree-shaped patterns, inspired by conjunctive database queries [18]. In comparison to the kinds of patterns used in most other graph mining approaches, tree queries have some extra features: - Patterns may have"existential" nodes: any occurrence of the pattern must have a copy of such a node, but existential nodes are not counted when determining the number of occurrences.

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.

Previously, it has been proven that for any undirected graph there exists a regular Gaussian distribution that is faithful to it (Lněnička & Matúš, 2007, Corollary 3). A stronger result has been proven for acyclic directed graphs: In certain measure-theoretic sense, almost all the regular Gaussian distributions that factorize with respect to an acyclic directed graph are faithful to it (Spirtes et al., 1993, Theorem 3.2). Therefore, this paper extends the latter result to chain graphs. It is worth mentioning that we have recently proved in (Peña, 2009) a result analogous to the one in this paper but for strictly positive discrete probability distributions with arbitrary prescribed sample space. It is also worth noticing that a result analogous to the one in this paper has been proven in (Levitz et al., 2001, Theorem 6.1) under the

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

In recent years, the significant growth of RDF data used in numerous applications has made its efficient and scalable manipulation an important issue. In this paper, we present RDFViewS, a system capable of choosing the most suitable views to materialize, in order to minimize the query response time for a specific SPARQL query workload, while taking into account the view maintenance cost and storage space constraints. Our system employs practical algorithms and heuristics to navigate through the search space of potential view configurations, and exploits the possibly available semantic information - expressed via an RDF Schema - to ensure the completeness of the query evaluation.

When users rate objects, a sophisticated algorithm that takes into account ability or reputation may produce a fairer or more accurate aggregation of ratings than the straightforward arithmetic average. Recently a number of authors have proposed different co-determination algorithms where estimates of user and object reputation are refined iteratively together, permitting accurate measures of both to be derived directly from the rating data. However, simulations demonstrating these methods' efficacy assumed a continuum of rating values, consistent with typical physical modelling practice, whereas in most actual rating systems only a limited range of discrete values (such as a 5-star system) is employed. We perform a comparative test of several co-determination algorithms with different scales of discrete ratings and show that this seemingly minor modification in fact has a significant impact on algorithms' performance. Paradoxically, where rating resolution is low, increased noise in users' ratings may even improve the overall performance of the system.

This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant individual variability. Our method builds on the framework of latent Diricihlet allocation (LDA) and its extension to hierarchical Dirichlet processes, which allows us to characterize each series as switching between latent ``topics'', where each topic is characterized as a distribution over ``words'' that specify the series dynamics. However, unlike standard applications of LDA, we discover the words as we learn the model. We apply this model to the task of tracking the physiological signals of premature infants; our model obtains clinically significant insights as well as useful features for supervised learning tasks.

The Logic Programming (LP) community, through the Association for Logic Programming (ALP) and its Executive Committee, decided to introduce for 2010 important changes in the way the main yearly results in LP and related areas are published. Whereas such results have appeared to date in standalone volumes of proceedings of the yearly International Conferences on Logic Programming (ICLP), and this method -fully in the tradition of Computer Science (CS)- has served the community well, it was felt that an effort needed to be made to achieve a higher level of compatibility with the publishing mechanisms of other fields outside CS. In order to achieve this goal without giving up the traditional CS conference format a different model has been adopted starting in 2010 in which the yearly ICLP call for submissions takes the form of a joint call for a) full papers to be considered for publication in a special issue of the journal, and b) shorter technical communications to be considered for publication in a separate, standalone volume, with both kinds of papers being presented by their authors at the conference. Together, the journal special issue and the volume of short technical communications constitute the proceedings of ICLP. This 26th International Conference on Logic Programming Special Issue is the first of a series of yearly special issues of Theory and Practice of Logic Programming (TPLP) putting this new model into practice.

A key factor that can dramatically reduce the search space during constraint solving is the criterion under which the variable to be instantiated next is selected. For this purpose numerous heuristics have been proposed. Some of the best of such heuristics exploit information about failures gathered throughout search and recorded in the form of constraint weights, while others measure the importance of variable assignments in reducing the search space. In this work we experimentally evaluate the most recent and powerful variable ordering heuristics, and new variants of them, over a wide range of benchmarks. Results demonstrate that heuristics based on failures are in general more efficient. Based on this, we then derive new revision ordering heuristics that exploit recorded failures to efficiently order the propagation list when arc consistency is maintained during search. Interestingly, in addition to reducing the number of constraint checks and list operations, these heuristics are also able to cut down the size of the explored search tree.