Slide 21
Slide 21 text
Theory
𝐬 𝐳 =
𝟏
𝟏 + 𝐞−𝐳
The Number of Classes: K (= 5)
Retina Image Features (Input of CNN): xi
Rank Label: yi
∈ 0, 1, 2, 3, 4
yi
⟹ y
i
(1), … , y
i
k , … , y
i
(K−1)
y
i
(k) ∈ I yi
> rk
e.g. yi
= 2 ⟹ 1, 1, 0, 0 , y
i
(1 or 2) = 1, y
i
(3 or 4) = 0
(K - 1) binary tasks share the same weight parameter
ωj
, but have independent bias units bk
h xi
=
k=1
K−1
fk
(xi
)
fk
xi
= I P y
i
(k) = 1 > 0.5
P y
i
(k) = 1 = s
j
m
ωj
aj
+ bk
= s(g xi
, W + bk
)
Predicted
Rank
Condition.
f1
xi
≥ f2
xi
≥ … ≥ fK−1
xi
Required for the Ordinal Information and Rank-Monotonicity
=> Let's prove in the next slide!
Output function
of CNN
e.g.
𝐏 𝐲
𝟏
𝐤 = 𝟏 , 𝐏 𝐲
𝟐
𝐤 = 𝟏 , 𝐏 𝐲
𝟑
𝐤 = 𝟏 , 𝐏 𝐲
𝟒
𝐤 = 𝟏 = [ 𝟎. 𝟖, 𝟎. 𝟕, 𝟎. 𝟒, 𝟎. 𝟏 ]
𝐡 𝐱𝐢
= 𝟏 + 𝟏 + 𝟎 + 𝟎 = 𝟐