A model-agnostic variable importance method can be used with arbitrary
prediction functions. Here we present some model-free methods that do not
require access to the prediction function. This is useful when that function is
proprietary and not available, or just extremely expensive. It is also useful
when studying residuals from a model. The cohort Shapley (CS) method is
model-free but has exponential cost in the dimension of the input space. A
supervised on-manifold Shapley method from Frye et al. (2020) is also model
free but requires as input a second black box model that has to be trained for
the Shapley value problem. We introduce an integrated gradient version of
cohort Shapley, called IGCS, with cost $\mathcal{O}(nd)$. We show that over the
vast majority of the relevant unit cube that the IGCS value function is close
to a multilinear function for which IGCS matches CS. We use some area under the
curve (AUC) measures to quantify the performance of IGCS. On a problem from
high energy physics we verify that IGCS has nearly the same AUCs as CS. We also
use it on a problem from computational chemistry in 1024 variables. We see
there that IGCS attains much higher AUCs than we get from Monte Carlo sampling.
The code is publicly available at
this https URL.

本文提出了一个称为集体 Shapley（CS）方法，具有指数成本，以及需要第二个黑匣子模型作为输入的受监督的流形 Shapley 方法。并且引入了一种名为 IGCS 的集成梯度版本的 cohort Shapley，通过某些曲线下面积度量证明其性能与 CS 几乎相同。