Using constraint-based local search, we effectively model and efficiently solve the problem of balancing the traffic demands on portions of the European airspace while ensuring that their capacity constraints are satisfied. The traffic demand of a portion of airspace is the hourly number of flights planned to enter it, and its capacity is the upper bound on this number under which air-traffic controllers can work. Currently, the only form of demand-capacity balancing we allow is ground holding, that is the changing of the take-off times of not yet airborne flights. Experiments with projected European flight plans of the year 2030 show that already this first form of demand-capacity balancing is feasible without incurring too much total delay and that it can lead to a significantly better demand-capacity balance.

Constrained Optimum Path (COP) problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In this paper, we introduce a novel local search modeling for solving some COPs by local search. The modeling features the compositionality, modularity, reuse and strengthens the benefits of Constrained-Based Local Search. We also apply the modeling to the edge-disjoint paths problem (EDP). We show that side constraints can easily be added in the model. Computational results show the significance of the approach.

Keywords: machine learning, consensus, meta-learning, bioinformatics, chemoinformatics, brainstorming, neural networks, support vector machines, decision trees, random forest, genetic algorithms, nearest neighbours, trend vectors Abstract: We present here an introduction to Brainstorming approach, that was recently proposed as a consensus meta-learning technique, and used in several practical applications in bioinformatics and chemoinformatics. In the second step all solutions are gathered and the consensus is build between them. Therefore no early solution, given even by a generally low performing algorithm, is not discarder until the late phase of prediction, when the final conclusion is drawn by comparing different machine learning models. This final phase, i.e. consensus learning, is trying to balance the generality of solution and the overall performance of trained model. 1 INTRODUCTION A novel meta-approach emerging in bioinformatics is called consensus learning. Then all solutions are gathered, and the consensus is build between them. Therefore no early solution, given even by a generally low performing algorithm, is not discarder until the late phase of prediction, when the final conclusion is drawn by comparing different machine learning models.

This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about the hypothesis set: it is a vectorial space, it is a set of pointwise defined functions, and the evaluation functional on this set is a continuous mapping. Based on these principles an original theory is developed generalizing the notion of reproduction kernel Hilbert space to non hilbertian sets. Then it is shown that the hypothesis set of any learning machine has to be a generalized reproducing set. Therefore, thanks to a general "representer theorem", the solution of the learning problem is still a linear combination of a kernel. Furthermore, a way to design these kernels is given. To illustrate this framework some examples of such reproducing sets and kernels are given.

In Probabilistic Risk Management, risk is characterized by two quantities: the magnitude (or severity) of the adverse consequences that can potentially result from the given activity or action, and by the likelihood of occurrence of the given adverse consequences. But a risk seldom exists in isolation: chain of consequences must be examined, as the outcome of one risk can increase the likelihood of other risks. Systemic theory must complement classic PRM. Indeed these chains are composed of many different elements, all of which may have a critical importance at many different levels. Furthermore, when urban catastrophes are envisioned, space and time constraints are key determinants of the workings and dynamics of these chains of catastrophes: models must include a correct spatial topology of the studied risk. Finally, literature insists on the importance small events can have on the risk on a greater scale: urban risks management models belong to self-organized criticality theory. We chose multiagent systems to incorporate this property in our model: the behavior of an agent can transform the dynamics of important groups of them.

Mass spectrometry (MS) is an important technique for chemical profiling which calculates for a sample a high dimensional histogram-like spectrum. A crucial step of MS data processing is the peak picking which selects peaks containing information about molecules with high concentrations which are of interest in an MS investigation. We present a new procedure of the peak picking based on a sparse coding algorithm. Given a set of spectra of different classes, i.e. with different positions and heights of the peaks, this procedure can extract peaks by means of unsupervised learning. Instead of an $l_1$-regularization penalty term used in the original sparse coding algorithm we propose using an elastic-net penalty term for better regularization. The evaluation is done by means of simulation. We show that for a large region of parameters the proposed peak picking method based on the sparse coding features outperforms a mean spectrum-based method. Moreover, we demonstrate the procedure applying it to two real-life datasets.

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.

This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices are approximately distributed according to a Poisson distribution, the number of clusters is estimated by thresholding the Prim's trajectory. The corresponding cluster centroids are then computed in order to initialize the generalized Lloyd's algorithm, also known as $K$-means, which allows to circumvent initialization problems. Some results are derived for evaluating the false positive rate of our cluster detection algorithm, with the help of approximations relevant in Euclidean spaces. Metrics used for measuring similarity between multi-dimensional data points are based on symmetrical divergences. The use of these informational divergences together with the proposed method leads to better results, compared to other clustering methods for the problem of astrophysical data processing. Some applications of this method in the multi/hyper-spectral imagery domain to a satellite view of Paris and to an image of the Mars planet are also presented. In order to demonstrate the usefulness of divergences in our problem, the method with informational divergence as similarity measure is compared with the same method using classical metrics. In the astrophysics application, we also compare the method with the spectral clustering algorithms.

We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if both the covariance matrix of the cause and the structure matrix mapping cause to the effect are independently chosen. The method works for both stochastic and deterministic causal relations, provided that the dimensionality is sufficiently high (in some experiments, 5 was enough). It is applicable to Gaussian as well as non-Gaussian data.

The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiability, or other assumption on the model class need to be made. More formally, we show that for any countable class of models, the distributions selected by MDL (or MAP) asymptotically predict (merge with) the true measure in the class in total variation distance. Implications for non-i.i.d. domains like time-series forecasting, discriminative learning, and reinforcement learning are discussed.