  We consider the classic supervised learning problem, where a continuous
non-negative random label $Y$ (i.e. a random duration) is to be predicted based
upon observing a random vector $X$ valued in $\mathbb{R}^d$ with $d\geq 1$ by
means of a regression rule with minimum least square error. In various
applications, ranging from industrial quality control to public health through
credit risk analysis for instance, training observations can be right censored,
meaning that, rather than on independent copies of $(X,Y)$, statistical
learning relies on a collection of $n\geq 1$ independent realizations of the
triplet $(X, \; \min\{Y,\; C\},\; \delta)$, where $C$ is a nonnegative r.v.
with unknown distribution, modeling censorship and $\delta=\mathbb{I}\{Y\leq
C\}$ indicates whether the duration is right censored or not. As ignoring
censorship in the risk computation may clearly lead to a severe underestimation
of the target duration and jeopardize prediction, we propose to consider a
plug-in estimate of the true risk based on a Kaplan-Meier estimator of the
conditional survival function of the censorship $C$ given $X$, referred to as
Kaplan-Meier risk, in order to perform empirical risk minimization. It is
established, under mild conditions, that the learning rate of minimizers of
this biased/weighted empirical risk functional is of order
$O_{\mathbb{P}}(\sqrt{\log(n)/n})$ when ignoring model bias issues inherent to
plug-in estimation, as can be attained in absence of censorship. Beyond
theoretical results, numerical experiments are presented in order to illustrate
the relevance of the approach developed.
