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Quantitative Finance · Glossaire

Qu'est-ce que « Shapley value, SHAP value » ?

Aussi appelé : Shapley value · SHAP value

Definition 6.5 Machine Learning for Markets · Chapitre 6 — Feature Engineering, Selection and Importance

For a game vv on the set PP of players, the Shapley value of player jj is

ϕj=∑S⊆P∖{j}∣S∣! (∣P∣−∣S∣−1)!∣P∣!(v(S∪{j})−v(S)),\phi_j = \sum_{S\subseteq P\setminus\{j\}}\frac{|S|!\,(|P| - |S| - 1)!}{|P|!}\bigl(v(S\cup\{j\}) - v(S)\bigr),

the only allocation that is efficient (∑jϕj=v(P)−v(∅)\sum_j\phi_j = v(P) - v(\emptyset)), symmetric, zero for a player that adds nothing, and additive across games. A SHAP value is the Shapley value of feature jj for one prediction, with v(S)v(S) the model’s expected output when the features in SS are fixed at their values (Lundberg and Lee, 2017); for tree ensembles it is computed exactly and fast (TreeSHAP).

Four importances of the same boosted trees on the planted task, each as a share of its positive total: the four signal features, the copy x_1b, and the largest of the ten noise features. Permutation, drop-column and SHAP are computed on the 20 000 held-out rows, gain on the training rows. Data: ml_importance.importances.
Figure 6.1. Four importances of the same boosted trees on the planted task, each as a share of its positive total: the four signal features, the copy x1bx_{1b}, and the largest of the ten noise features. Permutation, drop-column and SHAP are computed on the 20 000 held-out rows, gain on the training rows. Data: ml_importance.importances.
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