Analytic Continued Fractions for Regression: Results on 352 datasets from the physical sciences

Abstract

We report on the results of a new memetic algorithm that employs analytic continued fractions as the basic representation of mathematical functions used for regression problems. We study the performance of our method in comparison with other ten machine learning approaches provided by the scikit-learn software collection. We used 352 datasets collected by Schaffer, which originated from real experiments in the physical sciences at the turn of the 20 th century for which measurements were tabulated, and a governing functional relationship was postulated. Using leave-one-out cross-validation, in training our method ranks first in 350 out of the 352 datasets. Only six machine learning algorithms ranked first in at least one of the 352 datasets on testing; our approach ranked first 192 times, i.e. more all of the other algorithms combined. The results favourably speak about the robustness of our methodology. We conclude that the use of analytic continued fractions in regression deserves further study and we also advocate that Schaffer's data collection should also be included in the repertoire of datasets to test the performance of machine learning and regression algorithms.

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