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.

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.

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.

Our project aims at supporting the creation of sustainable and meaningful longer-term human-robot relationships through the creation of embodied robots with face recognition and natural language dialogue capabilities, which exploit and publish social information available on the web (Facebook). Our main underlying experimental hypothesis is that such relationships can be significantly enhanced if the human and the robot are gradually creating a pool of shared episodic memories that they can co-refer to (shared memories), and if they are both embedded in a social web of other humans and robots they both know and encounter (shared friends). In this paper, we are presenting such a robot, which as we will see achieves two significant novelties.

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.

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.

A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of binary units and binary output units. A convergence theorem ensures that solutions with a finite number of hidden units exist for both binary and real-valued input patterns. An implementation for problems with more than two classes, valid for any binary classifier, is proposed. The generalization error and the size of the resulting networks are compared to the best published results on well-known classification benchmarks. Early stopping is shown to decrease overfitting, without improving the generalization performance.

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.

Recently, considerable focus has been given to the problem of determining the boundary between tractable and intractable planning problems. In this paper, we study the complexity of planning in the class C_n of planning problems, characterized by unary operators and directed path causal graphs. Although this is one of the simplest forms of causal graphs a planning problem can have, we show that planning is intractable for C_n (unless P = NP), even if the domains of state variables have bounded size. In particular, we show that plan existence for C_n^k is NP-hard for k>=5 by reduction from CNFSAT. Here, k denotes the upper bound on the size of the state variable domains. Our result reduces the complexity gap for the class C_n^k to cases k=3 and k=4 only, since C_n^2 is known to be tractable.

This paper presents a tree-to-tree transduction method for sentence compression. Our model is based on synchronous tree substitution grammar, a formalism that allows local distortion of the tree topology and can thus naturally capture structural mismatches. We describe an algorithm for decoding in this framework and show how the model can be trained discriminatively within a large margin framework. Experimental results on sentence compression bring significant improvements over a state-of-the-art model.