fixes formula

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: