# Lemma needed for my machine learning research [closed]

Say $\sigma_1, \sigma_2, \dots, \sigma_m$ are i.i.d distributed $\pm1$ variables. How do I show that for any choice of $S_1, S_2, \dots, S_d$ subsets of $\{1, 2, \dots, m\}$, the expectation of the supremum over $S_i$ of the absolute value of the sum of the $\sigma$'s with indices in $S_i$ is bounded above by $\sqrt{2m \log d}$?

## closed as off-topic by Kaveh, Lev Reyzin♦Jun 5 '15 at 20:58

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