  Genomic datasets contain the effects of various unobserved biological
variables in addition to the variable of primary interest. These latent
variables often affect a large number of features (e.g., genes) and thus give
rise to dense latent variation, which presents both challenges and
opportunities for classification. Some of these latent variables may be
partially correlated with the phenotype of interest and therefore helpful,
while others may be uncorrelated and thus merely contribute additional noise.
Moreover, whether potentially helpful or not, these latent variables may
obscure weaker effects that impact only a small number of features but more
directly capture the signal of primary interest. We propose the
cross-residualization classifier to better account for the latent variables in
genomic data. Through an adjustment and ensemble procedure, the
cross-residualization classifier essentially estimates the latent variables and
residualizes out their effects, trains a classifier on the residuals, and then
re-integrates the the latent variables in a final ensemble classifier. Thus,
the latent variables are accounted for without discarding any potentially
predictive information that they may contribute. We apply the method to
simulated data as well as a variety of genomic datasets from multiple
platforms. In general, we find that the cross-residualization classifier
performs well relative to existing classifiers and sometimes offers substantial
gains.
