www-ai.cs.tu-dortmund.de/de/LEHRE/SEMINARE/SS21/TrustworthyAIMachineLearning/joachims2017a.pdf
′) = 1|no-swap) = pk · P (ci(y
′) = 1| ei(y′) = 1)
P (ci(y ′) = 1|swap-k-and-r) = pr · P (ci(y
′) = 1| ei(y′) = 1)
where
P (ci(y ′) = 1| ei(y′) = 1)
= ∑
v∈{0,1}
P (ci(y ′)=1| ri(y′)=v, ei(y
′)=1) · P (ri(y [...] following objective,
ŵ = argminw,ξ 1
2 w · w +
C
n
n∑ j=1
1
qj
∑ y∈Yj
ξjy
s.t. ∀y ∈ Y1\{y1} : w · [φ(x1, y1)− φ(x1, y)] ≥ 1−ξ1y ...
∀y ∈ Yn\{yn} : w · [φ(xn, yn)− φ(xn, y)] ≥ 1−ξny ∀j∀y : ξjy ≥ 0.
C is a re [...] with probabil- ity 1 and an irrelevant result is clicked with probability 0, but instead, for 1 ≥ ε+ > ε− ≥ 0,
P (ci(y) = 1| ri(y) = 1, oi(y) = 1) = ε+,
P (ci(y) = 1| ri(y) = 0, oi(y) = 1) = ε−.
The first …