Algorithm 1.

TGT: Calculating GCEs with a Reference Group. Note that, because λ is applied to all of the explanations, we cannot tune it to guarantee that each explanation is exactly k-sparse.

Input: Model: r

Group Means: ${\overline{x}}_i$(feature space) and ${\overline{r}}_i$(representation space) for i = 0, . . . , l − 1

l1 Regularization Weight: λ

Learning Rate: α

Initialize: δ1, . . . , δl−1 to vectors of 0

while not converged do

Sample i ≠ j from {0, . . . , l − 1}

Construct ti→j (δi→j) using Algorithm 2

Calculate objective: υ = loss(δi→j) using Equation 9

Update the components of δi→j using Algorithm 3

end while

Return: δ1, . . . , δl−1