We obtain error approximation bounds between expected suprema of canonical processes that are generated by random vectors with independent coordinates and expected suprema of Gaussian processes. In particular, we obtain a sharper proximity estimate for Rademacher and Gaussian complexities. Our estimates are dimension-free, and depend only on the geometric parameters and the numerical complexity of the underlying index set.

翻译：我们获得了由具有独立坐标的随机向量生成的典型过程的期望上确界与高斯过程的期望上确界之间的误差逼近界。特别地，我们得到了Rademacher复杂度与高斯复杂度之间更精确的邻近性估计。我们的估计是维数无关的，仅依赖于底层指标集的几何参数和数值复杂度。