The huge volume of data that are available today requires data-
selective processing approaches that avoid the costs in computa-
tional complexity via appropriately treating the non-innovative data.
In this paper, extensions of the well-known adaptive filtering LMS-
Newton and LMS-Quasi-Newton Algorithms are developed that
enable data selection while also addressing the censorship of out-
liers that emerge due to high measurement errors. The proposed
solutions allow the prescription of how often the acquired data are
expected to be incorporated into the learning process based on some
a priori information regarding the environment. Simulation results
on both synthetic and real-world data verify the effectiveness of
the proposed algorithms that may achieve significant reductions in
computational costs without sacrificing estimation accuracy due to
the selection of the data.