Counterfactual Explanation

Definition

$x^{\prime }$ close to $x$ (in some distance) with $f(x^{\prime })\ne f(x)$: “If your income were 500 Euro higher, you would get the credit” (Wachter, Mittelstadt, Russell 2017).

Formula

Linear score $s(x)=w^{\top }x+b$, single feature $j$: change $x_j$ by $-s(x)/w_j$. Example $s=0.5\text{income}-2\text{debts}+0.1\text{age}-20=-3$: income $+6$, debts $-1.5$ or age $+30$.

Which counterfactual is “smallest” depends on the distance and scaling. As recourse it can be non-actionable (age), invalidated by simultaneous changes or retraining, and for complex models (random forests) not stable or monotone around the counterfactual. Counterfactual fairness in Lecture 9.1 uses the same idea with a causal model.

Appears in

• Lecture 9.2, counterfactual explanations and recourse
• Lecture 9.2, exam-style task
• Lecture 9.1, counterfactual fairness

Related concepts

• Feature Attribution
• Fairness Criteria