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. Author manuscript; available in PMC: 2013 Jan 20.
Published in final edited form as: IEEE Trans Biomed Eng. 2012 Mar 5;59(6):1572–1582. doi: 10.1109/TBME.2012.2189771

Fig. 4.

Fig. 4

Effect of increasing the range of extrapolation: Comparison of RMS errors of symbolic and polynomial regressions across increasing ranges of extrapolation, expressed as a percentage by volume of the region in θ – θ – θ space enclosed by the training dataset. The plots show mean and standard errors calculated across five runs for each regression type and training dataset size for the three tendons of the experimental robotic finger. While cubic and quartic regressions have lower RMS errors for data points within the range of training (0% extrapolation), symbolic regression outperforms polynomial regressions for all ranges of extrapolation. The stem plots show the percentage of extrapolation achievable with each regression type to maintain the RMS error below 5%. Symbolic regression can extrapolate to much larger ranges of data compared to the different polynomial regressions for the same RMS prediction error.