Noisy fitness evaluation in genetic algorithms and the dynamics of learning

A theoretical model is presented which describes selection in a genetic algorithm (GA) under a stochastic fitness measure and correctly accounts for finite population effects. Although this model describes a number of selection schemes, we only consider Boltzmann selection in detail here as results for this form of selection are particularly transparent when fitness is corrupted by additive Gaussian noise. Finite population effects are shown to be of fundamental importance in this case, as the noise has no effect in the infinite population limit. In the limit of weak selection we show how the effects of any Gaussian noise can be removed by increasing the population size appropriately. The theory is tested on two closely related problems: the one-max problem corrupted by Gaussian noise and generalization in a perceptron with binary weights. The averaged dynamics can be accurately modelled for both problems using a formalism which describes the dynamics of the GA using methods from statistical mechanics. The second problem is a simple example of a learning problem and by considering this problem we show how the accurate characterization of noise in the fitness evaluation may be relevant in machine learning. The training error (negative fitness) is the number of misclassified training examples in a batch and can be considered as a noisy version of the generalization error if an independent batch is used for each evaluation. The noise is due to the finite batch size and in the limit of large problem size and weak selection we show how the effect of this noise can be removed by increasing the population size. This allows the optimal batch size to be determined, which minimizes computation time as well as the total number of training examples required.

Type 2 diabetes and dog walking:patients' longitudinal perspectives about implementing and sustaining physical activity

Background - Physical activity is particularly important for people with type 2 diabetes, as evidence suggests that any reduction in sedentary time is good for metabolic health. Aim - To explore type 2 diabetes patients' talk about implementing and sustaining physical activity. Design of study - Longitudinal, qualitative study using repeat in-depth interviews with 20 patients over 4 years following clinical diagnosis. Setting - Patients were recruited from 16 general practices and three hospitals across Lothian, Scotland. Results - Discussion, and salience, of physical activity was marginal in patient accounts of their diabetes management. Patients claimed to have only received vague and non-specific guidance about physical activity from health professionals, and emphasised a perceived lack of interest and encouragement. Aside from walking, physical activities which were adopted tended to attenuate over time. Patients' accounts revealed how walking a dog assisted this kind of activity maintenance over time. Three main themes are highlighted in the analysis: 1) incidental walking; 2) incremental physical activity gains; and 3) augmenting physical activity maintenance. The problems arising from walking without a dog (for example, lack of motivation) are also examined. Conclusion - Asking patients about pet preferences might seem tangential to medical interactions. However, encouraging dog walking or identifying another interest that promotes a regular commitment to undertake physical activity may yield long-term health benefits.