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Proximal Gradient Methods
Proximal Gradient Methods
3 selected
Difficulty 5-7
3 unseen
View topic
Intermediate
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0 answered
2 intermediate
1 advanced
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Question 1 of 3
120s
intermediate (5/10)
compute
The proximal operator of a convex function
g
is
prox
η
g
(
v
)
=
ar
g
min
x
{
g
(
x
)
+
2
η
1
∥
x
−
v
∥
2
}
. For
g
(
x
)
=
λ
∥
x
∥
1
, what does the proximal operator compute?
Hide and think first
A.
Coordinate-wise scaling by
1/
(
1
+
η
λ
)
, similar to ridge regression shrinkage but without sparsity
B.
Soft thresholding
sign
(
v
i
)
⋅
max
(
∣
v
i
∣
−
η
λ
,
0
)
applied coordinate-wise across every index
C.
Hard thresholding, where each coordinate is set to zero if
∣
v
i
∣
<
η
λ
and otherwise kept unchanged
D.
Orthogonal projection onto the
ℓ
1
ball of radius
λ
, which is a constrained projection problem
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