  In this paper, we study classification and regression error bounds for
inhomogenous data that are independent but not necessarily identically
distributed. First, we consider classification of data in the presence of
non-stationary noise and establish ergodic type sufficient conditions that
guarantee the achievability of the Bayes error bound, using universal rules. We
then perform a similar analysis for $k$-nearest neighbour regression and obtain
optimal error bounds for the same. Finally, we illustrate applications of our
results in the context of wireless networks.
