The accuracy of machine learning systems is a widely studied research topic. Established techniques such as cross-validation predict the accuracy on unseen data of the classifier produced by applying a given learning method to a given training data set. However, they do not predict whether incurring the cost of obtaining more data and undergoing further training will lead to higher accuracy. In this paper we investigate techniques for making such early predictions. We note that when a machine learning algorithm is presented with a training set the classifier produced, and hence its error, will depend on the characteristics of the algorithm, on training set's size, and also on its specific composition. In particular we hypothesise that if a number of classifiers are produced, and their observed error is decomposed into bias and variance terms, then although these components may behave differently, their behaviour may be predictable. We test our hypothesis by building models that, given a measurement taken from the classifier created from a limited number of samples, predict the values that would be measured from the classifier produced when the full data set is presented. We create separate models for bias, variance and total error. Our models are built from the results of applying ten different machine learning algorithms to a range of data sets, and tested with "unseen" algorithms and datasets. We analyse the results for various numbers of initial training samples, and total dataset sizes. Results show that our predictions are very highly correlated with the values observed after undertaking the extra training. Finally we consider the more complex case where an ensemble of heterogeneous classifiers is trained, and show how we can accurately estimate an upper bound on the accuracy achievable after further training.

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.

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.

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premise-based procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms.

Communication networks have evolved from specialized, research and tactical transmission systems to large-scale and highly complex interconnections of intelligent devices, increasingly becoming more commercial, consumer-oriented, and heterogeneous. Propelled by emergent social networking services and high-definition streaming platforms, network traffic has grown explosively thanks to the advances in processing speed and storage capacity of state-of-the-art communication technologies. As "netizens" demand a seamless networking experience that entails not only higher speeds, but also resilience and robustness to failures and malicious cyber-attacks, ample opportunities for signal processing (SP) research arise. The vision is for ubiquitous smart network devices to enable data-driven statistical learning algorithms for distributed, robust, and online network operation and management, adaptable to the dynamically-evolving network landscape with minimal need for human intervention. The present paper aims at delineating the analytical background and the relevance of SP tools to dynamic network monitoring, introducing the SP readership to the concept of dynamic network cartography -- a framework to construct maps of the dynamic network state in an efficient and scalable manner tailored to large-scale heterogeneous networks.