Statistical estimates can often be improved by fusion of data from several different sources. One example is so-called ensemble methods which have been successfully applied in areas such as machine learning for classification and clustering. In this paper, we present an ensemble method to improve community detection by aggregating the information found in an ensemble of community structures. This ensemble can found by re-sampling methods, multiple runs of a stochastic community detection method, or by several different community detection algorithms applied to the same network. The proposed method is evaluated using random networks with community structures and compared with two commonly used community detection methods. The proposed method when applied on a stochastic community detection algorithm performs well with low computational complexity, thus offering both a new approach to community detection and an additional community detection method.

The ability to associate images with natural language sentences that describe what is depicted in them is a hallmark of image understanding, and a prerequisite for applications such as sentence-based image search. In analogy to image search, we propose to frame sentence-based image annotation as the task of ranking a given pool of captions. We introduce a new benchmark collection for sentence-based image description and search, consisting of 8,000 images that are each paired with five different captions which provide clear descriptions of the salient entities and events. We introduce a number of systems that perform quite well on this task, even though they are only based on features that can be obtained with minimal supervision. Our results clearly indicate the importance of training on multiple captions per image, and of capturing syntactic (word order-based) and semantic features of these captions. We also perform an in-depth comparison of human and automatic evaluation metrics for this task, and propose strategies for collecting human judgments cheaply and on a very large scale, allowing us to augment our collection with additional relevance judgments of which captions describe which image. Our analysis shows that metrics that consider the ranked list of results for each query image or sentence are significantly more robust than metrics that are based on a single response per query. Moreover, our study suggests that the evaluation of ranking-based image description systems may be fully automated.

In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and the Parallel Coordinate Descent Method (PCDM) of Richt\'arik and Tak\'a\v{c}. We show that the two methods are equivalent for feasibility problems up to the selection of a single step-size parameter. Furthermore, we prove an improved complexity bound for PCDM under strong convexity, and show that this bound is at least $8(L'/\bar{L})(\omega-1)^2$ times better than the best known bound for DQAM, where $\omega$ is the degree of partial separability and $L'$ and $\bar{L}$ are the maximum and average of the block Lipschitz constants of the gradient of the quadratic penalty appearing in the augmented Lagrangian.

We design a decidable extension of the description logic SROIQ underlying the Web Ontology Language OWL 2. The new logic, called SR+OIQ, supports a controlled use of role axioms whose right-hand side may contain role chains or role unions. We give a tableau algorithm for checking concept satisfiability with respect to SR+OIQ ontologies and prove its soundness, completeness and termination.

We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and well-connected subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called "path coding" penalties. Unlike existing regularization functions that model long-range interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs.

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.

Classifiers based on probabilistic graphical models are very effective. In continuous domains, maximum likelihood is usually used to assess the predictions of those classifiers. When data is scarce, this can easily lead to overfitting. In any probabilistic setting, Bayesian averaging (BA) provides theoretically optimal predictions and is known to be robust to overfitting. In this work we introduce Bayesian Conditional Gaussian Network Classifiers, which efficiently perform exact Bayesian averaging over the parameters. We evaluate the proposed classifiers against the maximum likelihood alternatives proposed so far over standard UCI datasets, concluding that performing BA improves the quality of the assessed probabilities (conditional log likelihood) whilst maintaining the error rate. Overfitting is more likely to occur in domains where the number of data items is small and the number of variables is large. These two conditions are met in the realm of bioinformatics, where the early diagnosis of cancer from mass spectra is a relevant task. We provide an application of our classification framework to that problem, comparing it with the standard maximum likelihood alternative, where the improvement of quality in the assessed probabilities is confirmed.

We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structural equation models with linear functions, the graph can be identified from the joint distribution only up to Markov equivalence classes, assuming faithfulness. In this work, we prove full identifiability if all noise variables have the same variances: the directed acyclic graph can be recovered from the joint Gaussian distribution. Our result has direct implications for causal inference: if the data follow a Gaussian structural equation model with equal error variances and assuming that all variables are observed, the causal structure can be inferred from observational data only. We propose a statistical method and an algorithm that exploit our theoretical findings.

A Bayesian factor graph reduced to normal form (Forney, 2001) consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-divergence criterion using KKT conditions. The learning algorithms are compared with two other updating equations based on a Viterbi-like and on a variational approximation respectively. The performance of the various algorithm is verified on synthetic data sets for various architectures. The objective of this paper is to provide the programmer with explicit algorithms for rapid deployment of Bayesian graphs in the applications.

Complex systems are naturally hybrid: their dynamic behavior is both continuous and discrete. For these systems, maintenance and repair are an increasing part of the total cost of final product. Efficient diagnosis and prognosis techniques have to be adopted to detect, isolate and anticipate faults. This paper presents an original integrated theoretical framework for diagnosis and prognosis of hybrid systems. The formalism used for hybrid diagnosis is enriched in order to be able to follow the evolution of an aging law for each fault of the system. The paper presents a methodology for interleaving diagnosis and prognosis in a hybrid framework.