This report outlines the use of a relational representation in a Multi-Agent domain to model the behaviour of the whole system. A desired property in this systems is the ability of the team members to work together to achieve a common goal in a cooperative manner. The aim is to define a systematic method to verify the effective collaboration among the members of a team and comparing the different multi-agent behaviours. Using external observations of a Multi-Agent System to analyse, model, recognize agent behaviour could be very useful to direct team actions. In particular, this report focuses on the challenge of autonomous unsupervised sequential learning of the team's behaviour from observations. Our approach allows to learn a symbolic sequence (a relational representation) to translate raw multi-agent, multi-variate observations of a dynamic, complex environment, into a set of sequential behaviours that are characteristic of the team in question, represented by a set of sequences expressed in first-order logic atoms. We propose to use a relational learning algorithm to mine meaningful frequent patterns among the relational sequences to characterise team behaviours. We compared the performance of two teams in the RoboCup four-legged league environment, that have a very different approach to the game. One uses a Case Based Reasoning approach, the other uses a pure reactive behaviour.

Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries, the standard query language in databases, have recently gained significant attention as an expressive formalism for querying Description Logic knowledge bases. Several different techniques for deciding conjunctive query entailment are available for a wide range of DLs. Nevertheless, the combination of nominals, inverse roles, and number restrictions in OWL 1 and OWL 2 DL causes unsolvable problems for the techniques hitherto available. We tackle this problem and present a decidability result for entailment of unions of conjunctive queries in the DL ALCHOIQb that contains all three problematic constructors simultaneously. Provided that queries contain only simple roles, our result also shows decidability of entailment of (unions of) conjunctive queries in the logic that underpins OWL 1 DL and we believe that the presented results will pave the way for further progress towards conjunctive query entailment decision procedures for the Description Logics underlying the OWL standards.

The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible explanations for the data when making predictions. This integration is often performed using Markov chain Monte Carlo (MCMC) sampling. However, with non-Gaussian observations standard hyperparameter sampling approaches require careful tuning and may converge slowly. In this paper we present a slice sampling approach that requires little tuning while mixing well in both strong- and weak-data regimes.

One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to explain a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory describes entangled decision making, non-commutativity of subsequent decisions, and intention interference of composite prospects. We demonstrate how the violation of the Savage's sure-thing principle (disjunction effect) can be explained as a result of the interference of intentions, when making decisions under uncertainty. The conjunction fallacy is also explained by the presence of the interference terms. We demonstrate that all known anomalies and paradoxes, documented in the context of classical decision theory, are reducible to just a few mathematical archetypes, all of which finding straightforward explanations in the frame of the developed quantum approach.

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and scalability. Unfortunately, this 1-norm MKL is rarely observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary norms, like p-norms with p>1. Empirically, we demonstrate that the interleaved optimization strategies are much faster compared to the commonly used wrapper approaches. A theoretical analysis and an experiment on controlled artificial data experiment sheds light on the appropriateness of sparse, non-sparse and $\ell_\infty$-norm MKL in various scenarios. Empirical applications of p-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research into symmetry breaking. This paper is a condensed version of a larger work in progress.

Concept drift refers to a non stationary learning problem over time. The training and the application data often mismatch in real life problems. In this report we present a context of concept drift problem 1. We focus on the issues relevant to adaptive training set formation. We present the framework and terminology, and formulate a global picture of concept drift learners design. We start with formalizing the framework for the concept drifting data in Section 1. In Section 2 we discuss the adaptivity mechanisms of the concept drift learners. In Section 3 we overview the principle mechanisms of concept drift learners. In this chapter we give a general picture of the available algorithms and categorize them based on their properties. Section 5 discusses the related research fields and Section 5 groups and presents major concept drift applications. This report is intended to give a bird's view of concept drift research field, provide a context of the research and position it within broad spectrum of research fields and applications.

For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has measure at most epsilon. Immediate corollaries include the fact that a family with finite VC dimension has finite bracketing numbers, and satisfies uniform laws of large numbers for every ergodic process. From these corollaries, we derive analogous results for VC major and VC graph families of functions.

Motivated by authentication, intrusion and spam detection applications we consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the learner has a sample from a target distribution and the goal is to construct a classifier capable of distinguishing observations from the target distribution from observations emitted from an unknown other distribution. The ideal SCC classifier must guarantee a given tolerance for the false-positive error (false alarm rate) while minimizing the false negative error (intruder pass rate). Viewing SCC as a two-person zero-sum game we identify both deterministic and randomized optimal classification strategies for different game variants. We demonstrate that randomized classification can provide a significant advantage. In the deterministic setting we show how to reduce SCC to two-class classification where in the two-class problem the other class is a synthetically generated distribution. We provide an efficient and practical algorithm for constructing and solving the two class problem. The algorithm distinguishes low density regions of the target distribution and is shown to be consistent.