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I would like to use Permutation Feature Importance (PFI) with a set of different models coming from a bootstrap procedure.

I was looking at the algorithm here and was wondering how it can be used when the model is not just one.

$Algorithm$

  • Compute the reference score $s$ of the model $m$ on data $D$ (for instance the accuracy for a classifier or the $R^2$ for a regressor).

  • For each feature $j$ (column of $D$):

    • For each repetition $k$ in $1,...,K$:

      • Randomly shuffle column $j$ of dataset $D$ to generate a corrupted version of the data named $\tilde{D}_{k,j}$.

      • Compute the score $s_{k,j}$ of model $m$ on corrupted data $\tilde{D}_{k,j}$.

    • Compute importance $i_j$ for feature $f_j$ defined as $i_j = s-\frac{1}{K}\sum{_{k=1}^{K}s_{k,j}}$

I can think of a simple way which is taking the mean score per feature from every model but I am not sure if this can be done or if there are other ways to do that.

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    $\begingroup$ Taking the mean PFI of all the models is probably the easiest option. $\endgroup$ Commented Sep 26, 2023 at 8:33
  • $\begingroup$ Thanks! I was wondering if there was any paper or book where they did this before, but it makes sense. $\endgroup$
    – umbe1987
    Commented Sep 26, 2023 at 9:59
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    $\begingroup$ As shown at stats.stackexchange.com/questions/626376 this permutation measure does not perform correctly when there is strong multicollinearity. $\endgroup$ Commented Sep 26, 2023 at 10:37
  • $\begingroup$ Thanks, I am aware of this and I am performing variable selection and avoid multicollinearity before this step. $\endgroup$
    – umbe1987
    Commented Sep 26, 2023 at 11:14

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