  We obtain a denoising loss bound of the recently proposed neural network
based universal discrete denoiser, Neural DUDE, which can adaptively learn its
parameters solely from the noise-corrupted data, by minimizing the
\emph{empirical estimated loss}. The resulting bound resembles the
generalization error bound of the standard empirical risk minimizers (ERM) in
supervised learning, and we show that the well-known bias-variance tradeoff
also exists in our loss bound. The key tool we develop is the concentration of
the unbiased estimated loss on the true denoising loss, which is shown to hold
\emph{uniformly} for \emph{all} bounded network parameters and \emph{all}
underlying clean sequences. For proving our main results, we make a novel
application of the tools from the statistical learning theory. Finally, we show
that the hyperparameters of Neural DUDE can be chosen from a small validation
set to significantly improve the denoising performance, as predicted by the
theoretical result of this paper.
