Rules complement and extend ontologies on the Semantic Web. We refer to these rules as onto-relational since they combine DL-based ontology languages and Knowledge Representation formalisms supporting the relational data model within the tradition of Logic Programming and Deductive Databases. Rule authoring is a very demanding Knowledge Engineering task which can be automated though partially by applying Machine Learning algorithms. In this chapter we show how Inductive Logic Programming (ILP), born at the intersection of Machine Learning and Logic Programming and considered as a major approach to Relational Learning, can be adapted to Onto-Relational Learning. For the sake of illustration, we provide details of a specific Onto-Relational Learning solution to the problem of learning rule-based definitions of DL concepts and roles with ILP.

In this paper, we explore and detail our experiments in a high-dimensionality, multi-class image classification problem often found in the automatic recognition of Sign Languages. Here, our efforts are directed towards comparing the characteristics, advantages and drawbacks of creating and training Support Vector Machines disposed in a Directed Acyclic Graph and Artificial Neural Networks to classify signs from the Brazilian Sign Language (LIBRAS). We explore how the different heuristics, hyperparameters and multi-class decision schemes affect the performance, efficiency and ease of use for each classifier. We provide hyperparameter surface maps capturing accuracy and efficiency, comparisons between DDAGs and 1-vs-1 SVMs, and effects of heuristics when training ANNs with Resilient Backpropagation. We report statistically significant results using Cohen's Kappa statistic for contingency tables.

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, without additional minimum separation assumptions needed by previous computationally efficient estimation procedures. Thus computational and information-theoretic barriers to efficient estimation in mixture models are precluded when the mixture components have means in general position and spherical covariances. Some connections are made to estimation problems related to independent component analysis.

We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random variable; and (2) a mixture of Bartlett--Fejer kernels (or triangle densities) with respect to a two-component mixture of gamma random variables. Both lead to MCMC methods for posterior simulation, and these methods turn out to have complementary domains of maximum efficiency. The first representation is a well known result due to West (1987), and is the better choice for collinear design matrices. The second representation is new, and is more efficient for orthogonal problems, largely because it avoids the need to deal with exponentially tilted stable random variables. It also provides insight into the multimodality of the joint posterior distribution, a feature of the bridge model that is notably absent under ridge or lasso-type priors. We prove a theorem that extends this representation to a wider class of densities representable as scale mixtures of betas, and provide an explicit inversion formula for the mixing distribution. The connections with slice sampling and scale mixtures of normals are explored. On the practical side, we find that the Bayesian bridge model outperforms its classical cousin in estimation and prediction across a variety of data sets, both simulated and real. We also show that the MCMC for fitting the bridge model exhibits excellent mixing properties, particularly for the global scale parameter. This makes for a favorable contrast with analogous MCMC algorithms for other sparse Bayesian models. All methods described in this paper are implemented in the R package BayesBridge. An extensive set of simulation results are provided in two supplemental files.

This note considers how to modify BnB-ADOPT, a well-known algorithm for optimally solving distributed constraint optimization problems, with a double aim: (i) to avoid sending most of the redundant messages and (ii) to handle cost functions of any arity. Some of the messages exchanged by BnB-ADOPT turned out to be redundant. Removing most of the redundant messages increases substantially communication efficiency: the number of exchanged messages is - in most cases - at least three times fewer (keeping the other measures almost unchanged), and termination and optimality are maintained. On the other hand, handling n-ary cost functions was addressed in the original work, but the presence of thresholds makes their practical usage more complex. Both issues - removing most of the redundant messages and efficiently handling n-ary cost functions - can be combined, producing the new version BnB-ADOPT+. Experimentally, we show the benefits of this version over the original one.

Collaborative filtering (CF) aims to predict users' ratings on items according to historical user-item preference data. In many real-world applications, preference data are usually sparse, which would make models overfit and fail to give accurate predictions. Recently, several research works show that by transferring knowledge from some manually selected source domains, the data sparseness problem could be mitigated. However for most cases, parts of source domain data are not consistent with the observations in the target domain, which may misguide the target domain model building. In this paper, we propose a novel criterion based on empirical prediction error and its variance to better capture the consistency across domains in CF settings. Consequently, we embed this criterion into a boosting framework to perform selective knowledge transfer. Comparing to several state-of-the-art methods, we show that our proposed selective transfer learning framework can significantly improve the accuracy of rating prediction tasks on several real-world recommendation tasks.

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the surprising fact that sparse PCA can be easier than PCA in practice, and that it can be reliably applied to very large data sets. This comes from a rigorous feature elimination pre-processing result, coupled with the favorable fact that features in real-life data typically have exponentially decreasing variances, which allows for many features to be eliminated. We introduce a fast block coordinate ascent algorithm with much better computational complexity than the existing first-order ones. We provide experimental results obtained on text corpora involving millions of documents and hundreds of thousands of features. These results illustrate how Sparse PCA can help organize a large corpus of text data in a user-interpretable way, providing an attractive alternative approach to topic models.

With the increased use of ontologies in semantically-enabled applications, the issue of debugging defects in ontologies has become increasingly important. These defects can lead to wrong or incomplete results for the applications. Debugging consists of the phases of detection and repairing. In this paper we focus on the repairing phase of a particular kind of defects, i.e. the missing relations in the is-a hierarchy. Previous work has dealt with the case of taxonomies. In this work we extend the scope to deal with ALC ontologies that can be represented using acyclic terminologies. We present algorithms and discuss a system. This is an extended version of [18].

Protein interaction networks are a promising type of data for studying complex biological systems. However, despite the rich information embedded in these networks, they face important data quality challenges of noise and incompleteness that adversely affect the results obtained from their analysis. Here, we explore the use of the concept of common neighborhood similarity (CNS), which is a form of local structure in networks, to address these issues. Although several CNS measures have been proposed in the literature, an understanding of their relative efficacies for the analysis of interaction networks has been lacking. We follow the framework of graph transformation to convert the given interaction network into a transformed network corresponding to a variety of CNS measures evaluated. The effectiveness of each measure is then estimated by comparing the quality of protein function predictions obtained from its corresponding transformed network with those from the original network. Using a large set of S. cerevisiae interactions, and a set of 136 GO terms, we find that several of the transformed networks produce more accurate predictions than those obtained from the original network. In particular, the $HC.cont$ measure proposed here performs particularly well for this task. Further investigation reveals that the two major factors contributing to this improvement are the abilities of CNS measures, especially $HC.cont$, to prune out noisy edges and introduce new links between functionally related proteins.

For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadratic programs that are parameterized by a single parameter, as for example the Support Vector Machine (SVM). Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. It has been assumed that these piecewise linear solution paths have only linear complexity, i.e. linearly many bends. We prove that for the support vector machine this complexity can be exponential in the number of training points in the worst case. More strongly, we construct a single instance of n input points in d dimensions for an SVM such that at least \Theta(2^{n/2}) = \Theta(2^d) many distinct subsets of support vectors occur as the regularization parameter changes.