Neural network learning:theoretical foundations

This important work describes recent theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Chapters survey research on pattern classification with binary-output networks, including a discussion of the relevance of the Vapnik Chervonenkis dimension, and of estimates of the dimension for several neural network models. In addition, Anthony and Bartlett develop a model of classification by real-output networks, and demonstrate the usefulness of classification with a "large margin." The authors explain the role of scale-sensitive versions of the Vapnik Chervonenkis dimension in large margin classification, and in real prediction. Key chapters also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient, constructive learning algorithms. The book is self-contained and accessible to researchers and graduate students in computer science, engineering, and mathematics

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Why evolutionary realism underpins evolutionary economic analysis and theory

This paper offers a reply to Jochen Runde's critical appraisal of the ontological framework underpinning Dopfer and Potts's (2008) General Theory of Economic Evolution. We argue that Runde's comprehensive critique contains several of what we perceive to be misunderstandings in relation to the key concepts of ‘generic’ and ‘meso’ that we seek here to unpack and redress.

Intolerance of uncertainty and meta-worry : relative importance in discriminating GAD

This study explored whether intolerance of uncertainty and/or meta-worry discriminate between non-clinical individuals and those diagnosed with generalised anxiety disorder (GAD group). The participants were 107 GAD clients and 91 university students. The students were divided into two groups (high and low GAD symptom groups). A multivariate analysis of covariance (MANCOVA) adjusting for age indicated that intolerance of uncertainty distinguished between the low GAD symptom group and the high GAD symptom group, and between the low GAD symptom group and the GAD group. Meta-worry distinguished all three groups. A discriminant function including intolerance of uncertainty and meta-worry classified 94.4% of the GAD group and 97.9% of the low GAD symptom group. Only 6.8% of the high GAD symptom group was classified correctly, 77.3% of the high GAD symptom group was classified as GAD. Findings indicated that intolerance of uncertainty and meta-worry may assist with the diagnosis and treatment of GAD.