A small lending model scores each applicant from two inputs,
- x1: annual income, in thousands
- x2: years in their current job
using
s=0.1x1+5max(0, x2−2)−8
and approves the application only if s>0.
One applicant has an income of 40 thousand and has been in their job for 1 year. They are refused.
The bank's tooling produces two explanations for the refusal:
- A saliency reading: for each input, the partial derivative of s with respect to that input, evaluated at this applicant. It shows which inputs, if changed slightly, would move the score most.
- A what-would-change-it explanation: for each input on its own, how different it would have had to be for the application to be approved, with the other input left as it is.
Which statement about these two explanations is correct?