Binned chi^2 definition

[alexpearce]

I saw your presentation on “Reweighting distributions with gradient boosting” and it looked great, so gave it go. But now I want to explain it to others, so have to actually understand how it works 😄

One thing I'm not certain on is how the node splitting is determined, i.e. how the value of the split of the training data along a feature axis at a node is determined. You say this is the “symmetrized binned chi^2”, and I'd like to check that my understanding of what that is is correct. I have a notebook to try reproduce your plot. It looks similar, but I might have done something wrong nevertheless. Does it look sensible?

I tried to find where this computation is done in the code, but I couldn't find it. I'm not at all familiar with the general scikit-learn code architecture, so it's just that I have trouble following the flow of all the Xs and ys. Could you point me to where the chi^2 computation is done?

(And, of course, thanks for the excellent package! 🍻)

[arogozhnikov]

Hey, Alex.

I looked through your notebook, and everything is correct there.

I tried to find where this computation is done in the code, but I couldn't find it.

It's a bit tricky, there is a way to substitute optimizing chi^2 with minimizing MSE (and found splits will be identical).

Given that a) most packages are able to optimize MSE out-of-the-box b) I don't want to write one more tree, hep_ml makes use of this trick. In particual, ReweightLossFunction is constructing appropriate X, y parameters for tree to minimize MSE.

(And, of course, thanks for the excellent package! 🍻)

Thanks, you're welcome :)

[alexpearce]

Ah neat, that makes sense. That's for the explanation!