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The assessment of the reliability of systems which learn from data is a key issue to investigate thoroughly before the actual application of information processing techniques to real-world problems. Over the recent years Gaussian processes and Bayesian neural networks have come to the fore and in this thesis their generalisation capabilities are analysed from theoretical and empirical perspectives. Upper and lower bounds on the learning curve of Gaussian processes are investigated in order to estimate the amount of data required to guarantee a certain level of generalisation performance. In this thesis we analyse the effects on the bounds and the learning curve induced by the smoothness of stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the tightness of the bounds are also discussed. The analysis is supported by several numerical simulations. The generalisation error of a Gaussian process is affected by the dimension of the input vector and may be decreased by input-variable reduction techniques. In conventional approaches to Gaussian process regression, the positive definite matrix estimating the distance between input points is often taken diagonal. In this thesis we show that a general distance matrix is able to estimate the effective dimensionality of the regression problem as well as to discover the linear transformation from the manifest variables to the hidden-feature space, with a significant reduction of the input dimension. Numerical simulations confirm the significant superiority of the general distance matrix with respect to the diagonal one. In the thesis we also present an empirical investigation of the generalisation errors of neural networks trained by two Bayesian algorithms, the Markov Chain Monte Carlo method and the evidence framework; the neural networks have been trained on the task of labelling segmented outdoor images.

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Qualitative reasoning has traditionally been applied in the domain of physical systems, where there are well established and understood laws governing the behaviour of each `component' in the system. Such application has shown that it is possible to produce models which can be used for explaining and predicting the behaviour of physical phenomena and also trouble-shooting. The principles underlying the theory ensure that the models are robust and exhibit consistent behaviour under all conditions. This research examines the validity of applying the theory in the financial domain where such laws may not exist or if they do, may not be universally applicable. In particular, it investigates how far these principles and techniques may be applied in the construction of financial analysis models. Because of the inherent differences in the nature of these two domains, it is argued that a different qualitative value system ought to be employed. The dissertation enlarges on the constraints this places on model descriptions and the effect it may have on the power and usefulness of the resulting models. It also describes the implementation of a system that investigates the implications of applying this theory by way of testing it on situations drawn from both text-books and published financial information.

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This thesis offers a methodology to study and design effective communication mechanisms in human activities. The methodology is focused in the management of complexity. It is argued that complexity is not something objective that can be worked out analytically, but something subjective that depends on the viewpoint. Also it is argued that while certain social contexts may inhibit, others may enhance the viewpoint's capabilities to deal with complexity. Certain organisation structures are more likely than others to allow individuals to release their potentials. Thus, the relevance of studying and designing effective organisations. The first part of the thesis offers a `cybernetic methodology' for problem solving in human activities, the second offers a `method' to study and design organisations. The cybernetics methodology discussed in this work is rooted in second order cybernetics, or the cybernetics of the observing systems (Von Foester 1979, Maturana and Varela 1980). Its main tenet is that the known properties of the real world reside in the individual and not in the world itself. This view, which puts emphasis in a, by nature, one sided and unilateral appreciation of reality, triggers the need for dialogue and conversations to construct it. The `method' to study and design organisations, it based on Beer's Viable System Model (Beer 1979, 1981, 1985). This model permits us to assess how successful is an organisation in coping with its environmental complexity, and, moreover, permits us to establish how to make more effective the responses to this complexity. These features of the model are of great significance in a world where complexity is perceived to be growing at an unthinkable pace. But, `seeing' these features of the model assumes an effective appreciation of organisational complexity; hence the need for the methodological discussions offered by the first part of the thesis.

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