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Thread: Symbolic regression and experimental methodology

  1. #1 Symbolic regression and experimental methodology 
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    Oct 2010
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    I am currently giving the final touch to a paper on application of symbolic regression to petrophysics (a branch of geology applied mainly to oil and gas industry).

    First a quick overview of symbolic regression.
    In ordinary regression, one tries to fit data to a given class of function. This can be a linear function y=ax+b, where a and b are calculated, or quadratic, cubic, exponential or power regression. In all cases, the form of the function is known.
    Symbolic regression is searching both the parameters and the form of the equations simultaneously. The algorithm is using method based on evolutionary computation for searching the space of mathematical expressions while minimizing various error metrics.


    Now, 2 of my reviewers are objecting on the methodology used. They say that one must have first a theory or an idea of the theory before throwing an equation.
    With symbolic regression, you can get equations based on an unknown theory. And for them, this is a flaw in methodology. You could create a whole theory based on an equation which is just not right and applies to a very local set of data (basically create a theory biaised by over-fit / over-learn of the algorithm). Or get the right equation and the wrong theory, thus flawing the works or interpretation for the future.

    To my opinion, this is a false problem. Because symbolic regression algorithm gives you a list of equations with accuracy and complexity. Consequently, it's up to you to chose the one you want. I believe a lot of (if not most) discoveries were based on unknown equations which were explained a-posteriori. The setting up of a theory is where the real creativity of the researcher can be expressed, where intuition and intelligence is really playing its role.

    What is your opinion on this 'automated scientist' ? Do you think this introduces a flaw in our methodology ? Or, to the contrary, it helps to make our work easier ?


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