From 9f14879ad52c2bdbbe38e7f2a125a7fa42dea5f0 Mon Sep 17 00:00:00 2001 From: Yuchen Pei Date: Thu, 30 Apr 2020 22:44:30 +0200 Subject: Corrected a typo when deriving (5) from (4) and (1). --- posts/2018-12-02-lime-shapley.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) 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 -- cgit v1.2.3