Pareto front

[ianhbell]

Has there been any thought given to pareto front optimization? There's always a tradeoff between tree size and model fidelity, which I gather you handle with parsimony. But the other alternative is to keep any model that is non-dominated by the pareto front. I couldn't see any clear way of hacking that into gplearn.

[trevorstephens]

Sounds interesting @ianhbell ... Got a citation in mind?

[Ohjeah]

This should be a good point to start reading: https://www.iitk.ac.in/kangal/Deb_NSGA-II.pdf

[remiadon]

Hi, @ianhbell

Just for ciriosity, if I define a complexity measure (yielding the number of nodes in the tree representation of an expression), and use this complexity measure inside my custom fitness, a bit like so

from sklearn.metrics import r2_score
def my_custom_fitness(expr, X, y_true):
    y_pred = make_prediction(expr, X)
    return r2_score(y_pred, y_true) - (complexity(expr) / 1000)

Therefore:

• for two expressions yielding the same r2_score, my_custom_fitness would favour the simplest one
• for two expressions having the same complexity (i.e the first one is as simple as the second one), my_custom_fitness would the one that yields the best r2_score

Given these properties, the expression found at the end of fit would be on the pareto front (at least the one drawn considering all evaluated expressions)

Am I missing something ?

[remiadon]

Answering to myself with a reference

PARETO-FRONT EXPLOITATION IN SYMBOLIC REGRESSION

Written at page 294 :

There is, however, a significant difference between using a Pareto front as a post-run analysis tool vs. actively optimizing the Pareto front during a GP-run. In the latter case the Pareto front becomes the objective that is being optimized instead of the fitness (accuracy) of the “best” mode

So yes, I was missing something big