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authorYuchen Pei <me@ypei.me>2020-04-30 22:44:30 +0200
committerYuchen Pei <me@ypei.me>2020-04-30 22:44:30 +0200
commit9f14879ad52c2bdbbe38e7f2a125a7fa42dea5f0 (patch)
treef0a50b17d108093a6dfd910cc5c4a8c45aa8a92b
parent1f308d0425752168611ded7af72d1f953abdf843 (diff)
Corrected a typo when deriving (5) from (4) and (1).
-rw-r--r--posts/2018-12-02-lime-shapley.md2
1 files changed, 1 insertions, 1 deletions
diff --git a/posts/2018-12-02-lime-shapley.md b/posts/2018-12-02-lime-shapley.md
index c78a1e3..ef9d938 100644
--- a/posts/2018-12-02-lime-shapley.md
+++ b/posts/2018-12-02-lime-shapley.md
@@ -231,7 +231,7 @@ $$\sum_i \sum_{S: i \in S} v(S) q(s) = \sum_{S \subset N} s v(S) q(s). \qquad (4
Plugging (3)(4) in (1), we have
-$${1 \over 2} \lambda = {1 \over n} \left(\sum_{S \subset N} s q(s) v(S) - \sum_{s = 1}^n s {n - 1 \choose s - 1} q(s) (v(N) - v(\emptyset))\right). \qquad (5)$$
+$${1 \over 2} \lambda = {1 \over n} \left(\sum_{s = 1}^n s {n - 1 \choose s - 1} q(s) (v(N) - v(\emptyset)) - \sum_{S \subset N} s q(s) v(S) \right). \qquad (5)$$
Plugging (5)(2) in (0) and solve for $w_i$, we have