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McDiarmid's Inequality
McDiarmid's Inequality
3 questions
Difficulty 5-5
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Intermediate
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spot the error
McDiarmid's inequality requires the bounded differences condition: changing any single input
x
i
changes
f
by at most
c
i
. Which of the following functions does NOT satisfy this condition for
X
i
∈
[
0
,
1
]
?
Hide and think first
A.
The exponential sum
f
=
e
∑
i
x
i
with a claimed uniform bound
c
i
=
e
−
1
for all
i
B.
The function
exp
(
n
x
ˉ
)
with a claimed bound
c
i
=
e
−
1
that is independent of
n
C.
The sum of squares
f
=
∑
i
x
i
2
with claimed
c
i
=
1
, since each coordinate lies in
[
0
,
1
]
D.
The product
f
=
∏
i
x
i
with claimed
c
i
=
1
, since each
x
i
∈
[
0
,
1
]
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