Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel used within the model, efficient algorithms to train SVMs have been devised under the name of Core Vector Machines (CVMs). This framework exploits the equivalence of the resulting learning problem with the task of building a Minimal Enclosing Ball (MEB) problem in a feature space, where data is implicitly embedded by a kernel function. In this paper, we improve on the CVM approach by proposing two novel methods to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast method to approximate the solution of a MEB problem. In contrast to CVMs, our algorithms do not require to compute the solutions of a sequence of increasingly complex QPs and are defined by using only analytic optimization steps. Experiments on a large collection of datasets show that our methods scale better than CVMs in most cases, sometimes at the price of a slightly lower accuracy. As CVMs, the proposed methods can be easily extended to machine learning problems other than binary classification. However, effective classifiers are also obtained using kernels which do not satisfy the condition required by CVMs and can thus be used for a wider set of problems.

Traffic regulation must be respected by all vehicles, either human- or computer- driven. However, extreme traffic situations might exhibit practical cases in which a vehicle should safely and reasonably relax traffic regulation, e.g., in order not to be indefinitely blocked and to keep circulating. In this paper, we propose a high-level representation of an automated vehicle, other vehicles and their environment, which can assist drivers in taking such "illegal" but practical relaxation decisions. This high-level representation (an ontology) includes topological knowledge and inference rules, in order to compute the next high-level motion an automated vehicle should take, as assistance to a driver. Results on practical cases are presented.

The standard training method of Conditional Random Fields (CRFs) is very slow for large-scale applications. As an alternative, piecewise training divides the full graph into pieces, trains them independently, and combines the learned weights at test time. In this paper, we present \emph{separate} training for undirected models based on the novel Co-occurrence Rate Factorization (CR-F). Separate training is a local training method. In contrast to MEMMs, separate training is unaffected by the label bias problem. Experiments show that separate training (i) is unaffected by the label bias problem; (ii) reduces the training time from weeks to seconds; and (iii) obtains competitive results to the standard and piecewise training on linear-chain CRFs.

Most network-based protein (or gene) function prediction methods are based on the assumption that the labels of two adjacent proteins in the network are likely to be the same. However, assuming the pairwise relationship between proteins or genes is not complete, the information a group of genes that show very similar patterns of expression and tend to have similar functions (i.e. the functional modules) is missed. The natural way overcoming the information loss of the above assumption is to represent the gene expression data as the hypergraph. Thus, in this paper, the three un-normalized, random walk, and symmetric normalized hypergraph Laplacian based semi-supervised learning methods applied to hypergraph constructed from the gene expression data in order to predict the functions of yeast proteins are introduced. Experiment results show that the average accuracy performance measures of these three hypergraph Laplacian based semi-supervised learning methods are the same. However, their average accuracy performance measures of these three methods are much greater than the average accuracy performance measures of un-normalized graph Laplacian based semi-supervised learning method (i.e. the baseline method of this paper) applied to gene co-expression network created from the gene expression data.

Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in parallel (and possibly interacting) have summed time-evolution operators. From this foundation, algorithms for simulation, inference and model reduction may be systematically derived. The useful consequences are potentially far-reaching in computational science, machine learning and beyond. Hybrid compositional stochastic modeling/probabilistic programming approaches may also be possible.

Computational thinking is a new problem solving method named for its extensive use of computer science techniques. It synthesizes critical thinking and existing knowledge and applies them to solve complex technological problems. The term was coined by J. Wing [1], but the relationship between computational and critical thinking, the two modes of thinking in solving problems, has not been yet clearly established. This paper aims in shedding some light into this relationship. We also present two classroom experiments performed recently at the Graduate Technological Educational Institute (TEI) of Patras, Greece. The result of these experiment give a strong indication that the use of computers as a tool for problem solving enhances the students‟ abilities in solving real world problems involving mathematical modelling. This is crossed by earlier findings of other researchers for the problem solving process in general (not only for mathematical problems).

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies the CSA-ES on composites of strictly increasing functions with affine linear functions through the investigation of its underlying Markov chains. Rigorous results on the change and the variation of the step size are derived with and without cumulation. The step-size diverges geometrically fast in most cases. Furthermore, the influence of the cumulation parameter is studied.

Gaussian belief propagation (GaBP) is an iterative algorithm for computing the mean of a multivariate Gaussian distribution, or equivalently, the minimum of a multivariate positive definite quadratic function. Sufficient conditions, such as walk-summability, that guarantee the convergence and correctness of GaBP are known, but GaBP may fail to converge to the correct solution given an arbitrary positive definite quadratic function. As was observed in previous work, the GaBP algorithm fails to converge if the computation trees produced by the algorithm are not positive definite. In this work, we will show that the failure modes of the GaBP algorithm can be understood via graph covers, and we prove that a parameterized generalization of the min-sum algorithm can be used to ensure that the computation trees remain positive definite whenever the input matrix is positive definite. We demonstrate that the resulting algorithm is closely related to other iterative schemes for quadratic minimization such as the Gauss-Seidel and Jacobi algorithms. Finally, we observe, empirically, that there always exists a choice of parameters such that the above generalization of the GaBP algorithm converges.

In this paper we propose an extension of Defeasible Logic to represent and compute three concepts of defeasible permission. In particular, we discuss different types of explicit permissive norms that work as exceptions to opposite obligations. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a new operator representing ordered sequences of strong permissions which derogate from prohibitions. The logical system is studied from a computational standpoint and is shown to have liner computational complexity. The concept of permission plays an important role in many normative domains in that it may be crucial in characterising notions such as those of authorisation and derogation [11,30,33]. For example, sometimes it may happen that we mistakenly drive to a building site, or a roadwork restricted area, with signs out saying "No admittance.

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter estimation problems arising in detailed combustion kinetics.