Data taking values on discrete sample spaces are the embodiment of modern biological research. ``Omics'' experiments produce millions to billions of symbolic outcomes in the form of reads (i.e., DNA sequences of a few dozen 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. The latter contrasts with continuous datasets, where it is often well-justified to assume that the distribution of contaminating samples is Gaussian.

To overcome these hurdles, we introduce the new notion of ``latent weight,'' which measures the largest expected fraction of samples from a contaminated probabilistic source that conforms to a model in a well-structured class of desired models.

We examine various properties of latent weights in general and then specialize the discussion to the mathematical and statistical properties of latent weights of several specially-structured classes of interest. These include the exchangeable distributions, models with independent marginals, as well as models with independent and identically distributed (i.i.d.) marginals. As proof of concept, we use latent weights to analyze DNA methylation data and probabilistic graphical models of infection.