[title: line-fit] Shapley, Grad, Fourier, and All That

Carlos Scheidegger, UA CS, HDC Lab
Suresh Venkatasubramanian, Sorelle Friedler, Lizzie Kumar
(U. Utah, Haverford College)

What is this talk

Shapley What?

SV: two classic definitions

Shapley Values and ML Explanations

Some examples

  1. $(0, 0, 0, 2)$: “everyone is needed”
  2. $(0, 1, 1, 2)$: “ships passing in the night”
  3. $(0, 10, 10, 2)$: “we’re each great but not good together”

[title: line-fit] (S&T, 2017): Shapley from Gradients

Take the game on a hypercube, and define the gradient $\nabla$. Decompose $\nabla$ in $\nabla_1, \dots, \nabla_d$ such that $\sum_i \nabla_i = \nabla$.

A picture of the gradient decomposition definition of Shapley Values.

Fourier Transforms

Fourier Transforms

Fourier Transforms

Now we analyze $\nabla^\dagger \nabla_i$

Our result: a novel formula for SVs based on FTs

[title: line-fit] Examples, tying back to ML explanations

Thank you!


  1. Problems with Shapley Values… Kumar et al, ICML 2019, arXiv:2002.11097
  2. Hodge decomposition and the Shapley value of a cooperative game. Stern & Tettenhorst, Games & Econ. Behav. arXiv:1709.08318



[title: line-fit] Grad: Shapley Values from Gradients

$\varphi_i(v) = v_i[U] - v_i[\emptyset]$: proof

The Calculation (1/3)

The Calculation (2/3)

The Calculation (3/3)