Repeated Observations for Classification
This addresses classification problems where repeated measurements are available, offering improved error rates, but it appears incremental as it builds on existing nonparametric methods.
The paper tackles nonparametric classification with repeated observations, where instead of a single feature vector, multiple repeated vectors are available, and presents simple classification rules that achieve exponential convergence rates in error probabilities as the number of observations increases.
We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size $n$ and relatively low dimension $d$, this paper deals with the situation, when instead of observing a single feature vector $\bX$ we are given $t$ repeated feature vectors $\bV_1,\dots ,\bV_t $. Some simple classification rules are presented such that the conditional error probabilities have exponential convergence rate of convergence as $t\to\infty$. In the analysis, we investigate particular models like robust detection by nominal densities, prototype classification, linear transformation, linear classification, scaling.