О классификации разреженных наблюдений в случае двух нормальных классов

In this talk, we consider the problem of classifying an observation coming from one of two distinct $p$-variate normal populations based on training samples of size $n$ from these populations. We assume that $p$ can be very large and that $n$ is much smaller than $p$. Under the sparsity assumption on the underlying distributions, we propose new classification procedures that first separate the data that are ‘useful’ for classification from the rest of the sample, and then apply standard classification rules to the cleaned data. The proposed classification procedures are shown to have their maximum classification errors tending to zero as $p$ tends to infinity. The obtained results, that augment previous work in this area, are illustrated numerically. This is joint work with Tatjana Pavlenko (KTH Royal Institute of Technology) and Lee Thompson (a former MSc student at Carleton University).