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Symmetrization Inequality
Symmetrization Inequality
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The standard proof of the symmetrization inequality introduces an independent "ghost sample"
X
1
′
,
…
,
X
n
′
drawn from the same distribution. Why is this step necessary?
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A.
The ghost sample introduces additional noise that acts as a regularizer in the uniform-convergence bound
B.
The ghost sample replaces the unknown population expectation with an empirical sample mean, which is then symmetrized using Rademacher signs
C.
The ghost sample breaks the correlation between
X
i
and
f
in the supremum, restoring independence needed for Markov's inequality
D.
The ghost sample doubles the effective sample size, which improves the concentration rate by a factor of
2
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