Section: New Results

Genetic Programming

Recently, it has been stated that the complexity of a solution is a good indicator of the amount of overfitting it incurs. However, measuring the complexity of a program, in Genetic Programming, is not a trivial task. In [22] , we study the functional complexity and how it relates with overfitting on symbolic regression problems.We consider two measures of complexity, Slope-based Functional Complexity, inspired by the concept of curvature, and Regularity-based Functional Complexity based on the concept of Holderian regularity. In general, both complexity measures appear to be poor indicators of program overfitting. However, results suggest that Regularity-based Functional Complexity could provide a good indication of overfitting in extreme cases.

During the development of applied systems, an important problem that must be addressed is that of choosing the correct tools for a given domain or scenario. This general task has been addressed by the genetic programming (GP) community by attempting to determine the intrinsic difficulty that a problem poses for a GP search. In [21] , we present an approach to predict the performance of GP applied to data classification, one of the most common problems in computer science. The novelty of the proposal is to extract statistical descriptors and complexity descriptors of the problem data, and from these estimate the expected performance of a GP classifier. We derive two types of predictive models: linear regression models and symbolic regression models evolved with GP. The experimental results show that both approaches provide good estimates of classifier performance, using synthetic and real-world problems for validation. In conclusion, this paper shows that it is possible to accurately predict the expected performance of a GP classifier using a set of descriptors that characterize the problem data.

The analysis of image regularity using Holder exponents can be used to characterize singular structures contained within an image, and provide a compact description of local shape and appearance. However, estimating the Holder exponent is not a trivial task and current methods tend to be slow and complex. Therefore, the goal in [35] is to automatically synthesize image operators that can be used to estimate the Holder regularity of an image. We pose this task as an optimization problem and use Genetic Programming (GP) to search for operators that can approximate a traditional estimator, the oscillations method. In our experiments, GP was able to evolve estimators that achieve a low error and a high correlation with the ground truth estimation. Furthermore, most of the GP estimators are faster than the traditional approaches, in some cases their runtime is orders of magnitude smaller. This result allowed us to implement a real-time estimation of the Holder exponent on a live video signal, the first such implementation in current literature. Moreover, the evolved estimators are used to generate local descriptors of salient image regions, a task for which we obtain a stable and robust matching that is comparable with state-of-the-art methods. In conclusion, the evolved estimators produced by GP could help expand the application domain of Holderian regularity within the fields of image analysis and signal processing.