  Many risk-sensitive applications require Machine Learning (ML) models to be
interpretable. Attempts to obtain interpretable models typically rely on
tuning, by trial-and-error, hyper-parameters of model complexity that are only
loosely related to interpretability. We show that it is instead possible to
take a meta-learning approach: an ML model of non-trivial Proxies of Human
Interpretability (PHIs) can be learned from human feedback, then this model can
be incorporated within an ML training process to directly optimize for
interpretability. We show this for evolutionary symbolic regression. We first
design and distribute a survey finalized at finding a link between features of
mathematical formulas and two established PHIs, simulatability and
decomposability. Next, we use the resulting dataset to learn an ML model of
interpretability. Lastly, we query this model to estimate the interpretability
of evolving solutions within bi-objective genetic programming. We perform
experiments on five synthetic and eight real-world symbolic regression
problems, comparing to the traditional use of solution size minimization. The
results show that the use of our model leads to formulas that are, for a same
level of accuracy-interpretability trade-off, either significantly more or
equally accurate. Moreover, the formulas are also arguably more interpretable.
Given the very positive results, we believe that our approach represents an
important stepping stone for the design of next-generation interpretable
(evolutionary) ML algorithms.
