Analysing Symbolic Regression Benchmarks under a Meta-Learning Approach

Luiz Otavio Vilas Boas Oliveira; Joao Francisco Barreto da Silva Martins; Luis Fernando Miranda; Gisele Lobo Pappa

doi:10.1145/3205651.3208293

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arXiv · 1805.10365

Analysing Symbolic Regression Benchmarks under a Meta-Learning Approach

Luiz Otavio Vilas Boas Oliveira·Joao Francisco Barreto da Silva Martins·Luis Fernando Miranda·Gisele Lobo Pappa

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Abstract

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.

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Luiz Otavio Vilas Boas Oliveira, Joao Francisco Barreto da Silva Martins, Luis Fernando Miranda, Gisele Lobo Pappa. 2018-05-25. Analysing Symbolic Regression Benchmarks under a Meta-Learning Approach. https://doi.org/10.1145/3205651.3208293

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