How Noisy Data Affects Geometric Semantic Genetic Programming

Noise is a consequence of acquiring and pre-processing data from the environment, and shows fluctuations from different sources---e.g., from sensors, signal processing technology or even human error. As a machine learning technique, Genetic Programming (GP) is not immune to this problem, which the field has frequently addressed. Recently, Geometric Semantic Genetic Programming (GSGP), a semantic-aware branch of GP, has shown robustness and high generalization capability. Researchers believe these characteristics may be associated with a lower sensibility to noisy data. However, there is no systematic study on this matter. This paper performs a deep analysis of the GSGP performance over the presence of noise. Using 15 synthetic datasets where noise can be controlled, we added different ratios of noise to the data and compared the results obtained with those of a canonical GP. The results show that, as we increase the percentage of noisy instances, the generalization performance degradation is more pronounced in GSGP than GP. However, in general, GSGP is more robust to noise than GP in the presence of up to 10% of noise, and presents no statistical difference for values higher than that in the test bed.Comment: 8 pages, In proceedings of Genetic and Evolutionary Computation Conference (GECCO 2017), Berlin, German

Sequential Symbolic Regression with Genetic Programming

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transformation is performed according to the semantic distances between the desired and obtained outputs and a geometric semantic operator. The rationale behind SSR is that, after generating a suboptimal function f via symbolic regression, the output errors can be approximated by another function in a subsequent iteration. The method was tested in eight polynomial functions, and compared with canonical genetic programming (GP) and geometric semantic genetic programming (SGP). Results showed that SSR significantly outperforms SGP and presents no statistical difference to GP. More importantly, they show the potential of the proposed strategy: an effective way of applying geometric semantic operators to combine different (partial) solutions, avoiding the exponential growth problem arising from the use of these operators

Analysing Symbolic Regression Benchmarks under a Meta-Learning Approach

The definition of a concise and effective testbed for Genetic Programming (GP) is a recurrent matter in the research community. This paper takes a new step in this direction, proposing a different approach to measure the quality of the symbolic regression benchmarks quantitatively. The proposed approach is based on meta-learning and uses a set of dataset meta-features---such as the number of examples or output skewness---to describe the datasets. Our idea is to correlate these meta-features with the errors obtained by a GP method. These meta-features define a space of benchmarks that should, ideally, have datasets (points) covering different regions of the space. An initial analysis of 63 datasets showed that current benchmarks are concentrated in a small region of this benchmark space. We also found out that number of instances and output skewness are the most relevant meta-features to GP output error. Both conclusions can help define which datasets should compose an effective testbed for symbolic regression methods.Comment: 8 pages, 3 Figures, Proceedings of Genetic and Evolutionary Computation Conference Companion, Kyoto, Japa

Semantic variation operators for multidimensional genetic programming

Multidimensional genetic programming represents candidate solutions as sets of programs, and thereby provides an interesting framework for exploiting building block identification. Towards this goal, we investigate the use of machine learning as a way to bias which components of programs are promoted, and propose two semantic operators to choose where useful building blocks are placed during crossover. A forward stagewise crossover operator we propose leads to significant improvements on a set of regression problems, and produces state-of-the-art results in a large benchmark study. We discuss this architecture and others in terms of their propensity for allowing heuristic search to utilize information during the evolutionary process. Finally, we look at the collinearity and complexity of the data representations that result from these architectures, with a view towards disentangling factors of variation in application.Comment: 9 pages, 8 figures, GECCO 201