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@@ -69,7 +69,7 @@ which we call the Fourier $\ell _ { 1 }$ -norm of $f$ . Fourier $\ell _ { 1 }$ -
 
 # 4 A FOURIER-BASED GENERALIZATION BOUND
 
-Consider a supervised learning task with n training samples xi, yi
ni=1 and function space $\mathcal { F }$ . We are interested in uniform convergence bounds on the generalization risk. A standard approach to bound the generalization risk is based on the notion of Rademacher complexity. Given samples $\left( \mathbf { x } _ { i } , y _ { i } \right) _ { i = 1 } ^ { n }$ , the empirical Rademacher complexity of $\mathcal { F }$ is defined as
+Consider a supervised learning task with n training samples xi, yi
ni=1 and function space $\mathcal { F }$ . We are interested in uniform convergence bounds on the generalization risk. A standard approach to bound the generalization risk is based on the notion of Rademacher complexity. Given samples $\left( \mathbf { x } _ { i } , y _ { i } \right) _ { i = 1 } ^ { n }$ , the empirical Rademacher complexity of $\mathcal { F }$ is defined as
 
 $$
 \mathcal { R } _ { n } ^ { \mathrm { e m p } } ( \mathcal { F } ) : = \mathbb { E } _ { \pmb { \sigma } } \bigg [ \operatorname* { s u p } _ { f \in \mathcal { F } } \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \sigma _ { i } f ( \mathbf { x } _ { i } ) \bigg ]