Slide 51
Slide 51 text
Hardt's Method
50
[Hardt+ 16]
Given unfair predicted class, , and a sensitive feature, , a fair class, ,
is predicted maximizing accuracy under an equalized odds condition
✽ True class, , cannot be used by this predictor
̂
Y S Y∘
Y
true positive ratio (TPR) Pr[Y∘
=1 ∣ S=s, Y=1]
false positive ratio (FPR) Pr[Y∘
=1 ∣ S=s, Y=0]
perfectly accurate point
FPR & PPR
can be matched
satisfying
equalized odds
the most
accurate
point satisfying
an equalized
odds condition
feasible region
for S=0
feasible region
for S=1
{
Pr[Y∘=1 ∣ ̂
Y=1,S=1] = 1.0
Pr[Y∘=1 ∣ ̂
Y=0,S=1] = 0.0 {
Pr[Y∘=1 ∣ ̂
Y=1,S=1] = 1.0
Pr[Y∘=1 ∣ ̂
Y=0,S=1] = 1.0
{
Pr[Y∘=1 ∣ ̂
Y=1,S=1] = 0.0
Pr[Y∘=1 ∣ ̂
Y=0,S=1] = 1.0
{
Pr[Y∘=1 ∣ ̂
Y=1,S=1] = 0.0
Pr[Y∘=1 ∣ ̂
Y=0,S=1] = 0.0