Classification With Repeated Observations

We study the problem of nonparametric classification with repeated observations. Let
${\mathbf {X}}$
be the
$d$
dimensional feature vector and let
$Y$
denote the label taking values in
$\lbrace 1,\ldots, M\rbrace$
. In contrast to usual setup with large sample size
$n$
and relatively low dimension
$d$
, this letter deals with the situation, when instead of observing a single feature vector
${\mathbf {X}}$
we are given
$t$
repeated feature vectors
${\mathbf {V}}_{1},\ldots, {\mathbf {V}}_{t}$
. Some simple classification rules are presented such that the conditional error probabilities have exponential rate of convergence as
$t\to \infty$
.