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We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant.
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K. Makarychev, W. Schudy and M. Sviridenko, Concentration Inequalities for Nonlinear Matroid Intersection, to appear in SODA2012
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M. Dudik, D. Hsu, S. Kale, N. Karampatziakis, J. Langford, L. Reyzin and T. Zhang, Efficient Optimal Learning for Contextual Bandits, in Proceedings of UAI 2011
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