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diff --git a/posts/2018-12-02-lime-shapley.md b/posts/2018-12-02-lime-shapley.md index d21f594..a73d32e 100644 --- a/posts/2018-12-02-lime-shapley.md +++ b/posts/2018-12-02-lime-shapley.md @@ -265,6 +265,8 @@ value $\phi_i(v)$, where $$v(S) = \mathbb E_{z \sim \mu} (f(z) | z_S = x_S). \qquad (7)$$ So it is a conditional expectation where $z_i$ is clamped for $i \in S$. +In fact, the definition of feature contributions in this form predates +Lundberg-Lee 2017. For example, it can be found in Strumbelj-Kononenko 2014. One simplification is to assume the $n$ features are independent, thus $\mu = \mu_1 \times \mu_2 \times ... \times \mu_n$. In this case, (7) @@ -346,6 +348,7 @@ References - Strumbelj, Erik, and Igor Kononenko. "An Efficient Explanation of Individual Classifications Using Game Theory." J. Mach. Learn. Res. 11 (March 2010): 1--18. +- Strumbelj, Erik, and Igor Kononenko. “Explaining Prediction Models and Individual Predictions with Feature Contributions.” Knowledge and Information Systems 41, no. 3 (December 2014): 647–65. <https://doi.org/10.1007/s10115-013-0679-x>. - Young, H. P. “Monotonic Solutions of Cooperative Games.” International Journal of Game Theory 14, no. 2 (June 1, 1985): 65–72. <https://doi.org/10.1007/BF01769885>. |