marginal contrib

1 files changed, 2 insertions, 2 deletions

diff --git a/main.tex b/main.tex
index d14e668..b4c1861 100644
--- a/main.tex
+++ b/main.tex
@@ -498,9 +498,9 @@ For all $\lambda\in[0,1]^{n},$
         - \sum_{\substack{S\subseteq\mathcal{N}\\ i\in \mathcal{N}\setminus S}}
         P_{\mathcal{N}\setminus\{i\}}^\lambda(S)V(S)
     \end{multline*}
-    Finally, the marginal contribution of $i$ to
+    By the Sherman-Morisson formula, the marginal contribution of $i$ to
     $S$ is
-  $      \Delta_i V(S)\defeq V(S\cup\{i\}) - V(S) = \frac{1}{2}\log\left(1 + \mu \T{x_i} A(S)^{-1}x_i\right)$.
+  $  V(S\cup\{i\}) - V(S) = \frac{1}{2}\log\left(1 +  \T{x_i} A(S)^{-1}x_i\right)$.
 Using this,
     \begin{displaymath}
         \partial_i F_\mathcal{N}(\lambda) =