  Data taking values on discrete sample spaces are the embodiment of modern
biological research. "Omics" experiments produce millions of symbolic outcomes
in the form of reads (i.e., DNA sequences of a few dozens to a few hundred
nucleotides). Unfortunately, these intrinsically non-numerical datasets are
often highly contaminated, and the possible sources of contamination are
usually poorly characterized. This contrasts with numerical datasets where
Gaussian-type noise is often well-justified. To overcome this hurdle, we
introduce the notion of latent weight, which measures the largest expected
fraction of samples from a contaminated probabilistic source that conform to a
model in a well-structured class of desired models. We examine various
properties of latent weights, which we specialize to the class of exchangeable
probability distributions. As proof of concept, we analyze DNA methylation data
from the 22 human autosome pairs. Contrary to what it is usually assumed, we
provide strong evidence that highly specific methylation patterns are
overrepresented at some genomic locations when contamination is taken into
account.
