From ac2c2db4e977d01daa01a879e4d6ac42616dee76 Mon Sep 17 00:00:00 2001 From: Christoph Molnar Date: Thu, 21 Feb 2019 15:18:50 +0100 Subject: [PATCH] fixes formula --- manuscript/05.9-agnostic-shapley.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/manuscript/05.9-agnostic-shapley.Rmd b/manuscript/05.9-agnostic-shapley.Rmd index 4c16df69a..ce63193f0 100644 --- a/manuscript/05.9-agnostic-shapley.Rmd +++ b/manuscript/05.9-agnostic-shapley.Rmd @@ -221,7 +221,7 @@ The Shapley value is defined via a value function val of players in S. The Shapley value of a feature value is its contribution to the payout, weighted and summed over all possible feature value combinations: -$$\phi_j(val)=\sum_{S\subseteq\{x_{1},\ldots,x_{p}\}\setminus\{x_j\}}\frac{|S|!\left(p-|S|-1\right)!}{p!}\left(val\left(S\cup\{x_j}\right)-val(S)\right)$$ +$$\phi_j(val)=\sum_{S\subseteq\{x_{1},\ldots,x_{p}\}\setminus\{x_j\}}\frac{|S|!\left(p-|S|-1\right)!}{p!}\left(val\left(S\cup\{x_j\}\right)-val(S)\right)$$ where S is a subset of the features used in the model, x is the vector of feature values of the instance to be explained and p the number of features. $val_x(S)$ is the prediction for feature values in set S that are marginalized over features that are not included in set S: