Abstract-- We discuss the role of random basis function approximators in modeling and control. We analyze the published work on random basis function approximators and demonstrate that their favorable error rate of convergence O(1/n) is guaranteed only with very substantial computational resources. We also discuss implications of our analysis for applications of neural networks in modeling and control. I. INTRODUCTION Efficient modeling and control of complex systems in the presence of uncertainties is important for modern engineering. This is especially true in the domain of intelligent systems that are designed to operate in uncertain environments. Physical models of such relations f(·) are not always available, and it is quite common to use mathematical substitutes such as, e.g., superpositions of (basis) functions that are capable of approximating a-priori unknown f(·) with the required precision.

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.

A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions.

The theoretical basis for a candidate variational principle for the information bottleneck (IB) method is formulated within the ambit of the generalized nonadditive statistics of Tsallis. Given a nonadditivity parameter $ q $, the role of the \textit{additive duality} of nonadditive statistics ($ q^*=2-q $) in relating Tsallis entropies for ranges of the nonadditivity parameter $ q < 1 $ and $ q > 1 $ is described. Defining $ X $, $ \tilde X $, and $ Y $ to be the source alphabet, the compressed reproduction alphabet, and, the \textit{relevance variable} respectively, it is demonstrated that minimization of a generalized IB (gIB) Lagrangian defined in terms of the nonadditivity parameter $ q^* $ self-consistently yields the \textit{nonadditive effective distortion measure} to be the \textit{$ q $-deformed} generalized Kullback-Leibler divergence: $ D_{K-L}^{q}[p(Y|X)||p(Y|\tilde X)] $. This result is achieved without enforcing any \textit{a-priori} assumptions. Next, it is proven that the $q^*-deformed $ nonadditive free energy of the system is non-negative and convex. Finally, the update equations for the gIB method are derived. These results generalize critical features of the IB method to the case of Tsallis statistics.

The main problem addressed by this project is that of the creation of sustainable and meaningful long-term human robot relationships. This is a most important problem towards our ultimate goal of human-robot symbiosis, i.e. harmonious and mutually beneficial living together of the two species. In the shorter term, this is an important problem towards the successful application of robots to numerous areas: disabled and elderly assistance / companionship, supporting education, and more. So far, empirical investigations have shown that we have not advanced significantly yet towards its solution: Although existing robotic systems are interesting to interact with in the short term, it has been shown that after some weeks of quasi-regular encounters, humans gradually lose their interest, and meaningful longer-term human-robot relationships are not established. For example, in the case of Robovie [1], there was a steady and significant decrease in the total time of interaction of the robot with humans over six months - interest had worn off.

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process' behaviour to be partly unknown. Then we use Walley's theory of coherent lower previsions, a generalisation of the Bayesian theory to imprecision, to derive the rule to update beliefs under incompleteness that logically follows from our assumptions, and that we call conservative inference rule. This rule has some remarkable properties: it is an abstract rule to update beliefs that can be applied in any situation or domain; it gives us the opportunity to be neither too optimistic nor too pessimistic about the incompleteness process, which is a necessary condition to draw reliable while strong enough conclusions; and it is a coherent rule, in the sense that it cannot lead to inconsistencies. We give examples to show how the new rule can be applied in expert systems, in parametric statistical inference, and in pattern classification, and discuss more generally the view of incompleteness processes defended here as well as some of its consequences.

Initial open source software (OSS) projects rely on large repositories for hosting and distribution until they become independent. A huge amount of project metadata is collected and maintained in such software repositories providing useful information about projects and their success. In this paper we propose a data mining approach that processes the metadata contained in such OSS repositories. The proposed approach aims at the construction of a classifier that is trained on the metadata of existing projects and predicts the successful continuation of any given OSS. The successfulness of a project is defined with regard to the confidence level of the classifier which predicts that this project will be ported in widely used OSS projects (e.g.

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond-Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al., which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

Lab oratoire TIMC-IMA G (UMR CNRS-UJF 5525) Domaine de La Mer i - Bât. Jean Roget 38706 La T ron he, F ran e F ebruary 19, 2018 Abstra t A e ien t in remen tal learning algorithm for lassi ation tasks, alled NetLines, w ell adapted for b oth binary and real-v alued input patterns is presen ted. It generates small ompa t feedforw ard neural net w orks with one hidden la y er of binary units and binary output units. A on v ergen e theorem ensures that solutions with a nite n um b er of hidden units exist for b oth binary and real-v alued input patterns. An implemen tation for problems with more than t w o lasses, v alid for an y binary lassi er, is prop osed. The generalization error and the size of the resulting net w orks are ompared to the b est published results on w ell-kno wn lassi ation b en hmarks. The relationship b et w een n um b er of w eigh ts, learning apa it y and net w ork's generalization abilit y is w ell understo o d only for the simple p er eptron, a single binary unit whose output is a sigmoidal fun tion of the w eigh ted sum of its inputs. In this 1 ase, e ien t learning algorithms based on theoreti al results allo w the determination of the optimal w eigh ts. Ho w ev er, simple p er eptrons an only generalize those (v ery few) problems in whi h the input patterns are line arly sep ar able (LS).

The need for efficient monitoring of spatio-temporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, these robots have bounded resources, such as limited battery or limited amounts of time to obtain measurements. Thus, careful coordination of their paths is required in order to maximize the amount of information collected, while respecting the resource constraints. In this paper, we present an efficient approach for near-optimally solving the NP-hard optimization problem of planning such informative paths. In particular, we first develop eSIP (efficient Single-robot Informative Path planning), an approximation algorithm for optimizing the path of a single robot. Hereby, we use a Gaussian Process to model the underlying phenomenon, and use the mutual information between the visited locations and remainder of the space to quantify the amount of information collected. We prove that the mutual information collected using paths obtained by using eSIP is close to the information obtained by an optimal solution. We then provide a general technique, sequential allocation, which can be used to extend any single robot planning algorithm, such as eSIP, for the multi-robot problem. This procedure approximately generalizes any guarantees for the single-robot problem to the multi-robot case. We extensively evaluate the effectiveness of our approach on several experiments performed in-field for two important environmental sensing applications, lake and river monitoring, and simulation experiments performed using several real world sensor network data sets.