  We explore the effect of applying a non-linear transformation to the
Lyman-$\alpha$ forest transmitted flux $F=e^{-\tau}$ and the ability of
analytic models to predict the resulting clustering amplitude. Both the
large-scale bias of the transformed field (signal) and the amplitude of small
scale fluctuations (noise) can be arbitrarily modified, but we were unable to
find a transformation that increases significantly the signal-to-noise ratio on
large scales using Taylor expansion up to third order. In particular, however,
we achieve a 33% improvement in signal to noise for Gaussianized field in
transverse direction. On the other hand, we explore an analytic model for the
large-scale biasing of the Ly$\alpha$ forest, and present an extension of this
model to describe the biasing of the transformed fields. Using hydrodynamic
simulations we show that the model works best to describe the biasing with
respect to velocity gradients, but is less successful in predicting the biasing
with respect to large-scale density fluctuations, especially for very nonlinear
transformations.
