diff options
| -rw-r--r-- | microposts/gavin-belson.md | 7 | ||||
| -rw-r--r-- | posts/2018-12-02-lime-shapley.md | 7 |
2 files changed, 12 insertions, 2 deletions
diff --git a/microposts/gavin-belson.md b/microposts/gavin-belson.md new file mode 100644 index 0000000..d41674c --- /dev/null +++ b/microposts/gavin-belson.md @@ -0,0 +1,7 @@ +--- +date: 2018-12-11 +--- + +> I don’t know about you people, but I don’t want to live in a world where someone else makes the world a better place better than we do. + +Gavin Belson, Silicon Valley S2E1. diff --git a/posts/2018-12-02-lime-shapley.md b/posts/2018-12-02-lime-shapley.md index 152036b..394f6fb 100644 --- a/posts/2018-12-02-lime-shapley.md +++ b/posts/2018-12-02-lime-shapley.md @@ -13,7 +13,8 @@ and SHAP papers to my attention. The research was done while working at KTH mathematics department. _If you are reading on a mobile device, you may need to "request desktop site" -for equations to be properly displayed. This post is licensed under CC BY-SA._ +for the equations to be properly displayed. This post is licensed under CC BY-SA +and GNU FDL._ Shapley values -------------- @@ -32,7 +33,7 @@ $S - i := S \setminus \{i\}$ and $S + i := S \cup \{i\}$) $$\phi_i(v) = \sum_{S: i \in S} {(n - s)! (s - 1)! \over n!} (v(S) - v(S - i)).$$ -$\phi_i(v)$ is an expectation: +It is not hard to see that $\phi_i(v)$ can be viewed as an expectation: $$\phi_i(v) = \mathbb E_{S \sim \nu_i} (v(S) - v(S - i))$$ @@ -188,6 +189,8 @@ $q(0) = q(n) = \infty$. In Lundberg-Lee (2017), $c$ is chosen to be $1 / n$, see Theorem 2 there. +In Charnes et. al. 1988, the $w_i$s are called the generalised Shapley values. + **Proof**. The Lagrangian is $$L(w, \lambda) = \sum_{S \subset N} (v(S) - w(S))^2 q(s) - \lambda(w(N) - v(N) + v(\emptyset)).$$ |