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Automated discovery of test statistics using genetic programming

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Abstract

The process of developing new test statistics is laborious, requiring the manual development and evaluation of mathematical functions that satisfy several theoretical properties. Automating this process, hitherto not done, would greatly accelerate the discovery of much-needed, new test statistics. This automation is a challenging problem because it requires the discovery method to know something about the desirable properties of a good test statistic in addition to having an engine that can develop and explore candidate mathematical solutions with an intuitive representation. In this paper we describe a genetic programming-based system for the automated discovery of new test statistics. Specifically, our system was able to discover test statistics as powerful as the t test for comparing sample means from two distributions with equal variances.

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Acknowledgements

This work was supported by National Institutes of Health (USA) Grants LM012601, AI116794, and DK112217. We would like to thank the reviewers for the thoughtful suggestions.

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Author notes

  1. Jason H. Moore and Randal S. Olson contributed equally to this paper.

Authors and Affiliations

  1. Institute for Biomedical Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Jason H. Moore, Randal S. Olson, Yong Chen & Moshe Sipper

  2. Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel

    Moshe Sipper

Authors
  1. Jason H. Moore
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  2. Randal S. Olson
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  3. Yong Chen
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  4. Moshe Sipper
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Correspondence to Moshe Sipper.

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Moore, J.H., Olson, R.S., Chen, Y. et al. Automated discovery of test statistics using genetic programming. Genet Program Evolvable Mach 20, 127–137 (2019). https://doi.org/10.1007/s10710-018-9338-z

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  • DOI: https://doi.org/10.1007/s10710-018-9338-z

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