  In this paper we investigate the problem of learning an unknown bounded
function. We be emphasize special cases where it is possible to provide very
simple (in terms of computation) estimates enjoying in addition the property of
being universal : their construction does not depend on a priori knowledge on
regularity conditions on the unknown object and still they have almost optimal
properties for a whole bunch of functions spaces. These estimates are
constructed using a thresholding schema, which has proven in the last decade in
statistics to have very good properties for recovering signals with
inhomogeneous smoothness but has not been extensively developed in Learning
Theory. We will basically consider two particular situations. In the first
case, we consider the RKHS situation. In this case, we produce a new algorithm
and investigate its performances in $L\_2(\hat\rho\_X)$. The exponential rates
of convergences are proved to be almost optimal, and the regularity assumptions
are expressed in simple terms. The second case considers a more specified
situation where the $X\_i$'s are one dimensional and the estimator is a wavelet
thresholding estimate. The results are comparable in this setting to those
obtained in the RKHS situation as concern the critical value and the
exponential rates. The advantage here is that we are able to state the results
in the $L\_2(\rho\_X)$ norm and the regularity conditions are expressed in
terms of standard H\"older spaces.
