  Constant (naive) imputation is still widely used in practice as this is a
first easy-to-use technique to deal with missing data. Yet, this simple method
could be expected to induce a large bias for prediction purposes, as the
imputed input may strongly differ from the true underlying data. However,
recent works suggest that this bias is low in the context of high-dimensional
linear predictors when data is supposed to be missing completely at random
(MCAR). This paper completes the picture for linear predictors by confirming
the intuition that the bias is negligible and that surprisingly naive
imputation also remains relevant in very low dimension.To this aim, we consider
a unique underlying random features model, which offers a rigorous framework
for studying predictive performances, whilst the dimension of the observed
features varies.Building on these theoretical results, we establish
finite-sample bounds on stochastic gradient (SGD) predictors applied to
zero-imputed data, a strategy particularly well suited for large-scale
learning.If the MCAR assumption appears to be strong, we show that similar
favorable behaviors occur for more complex missing data scenarios.
