On latent idealized models in symbolic datasets: unveiling signals in noisy sequencing data

Data taking values on discrete sample spaces are the embodiment of modern biological research. "Omics" experiments based on high-throughput sequencing 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 often deviate dramatically from natural assumptions a practitioner might make, and the possible sources of this deviation are usually poorly characterized. This contrasts with numerical datasets where Gaussian-type errors are often well-justified. To overcome this hurdle, we introduce the notion of latent weight, which measures the largest expected fraction of samples from a probabilistic source that conform to a model in a class of idealized 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 is usually assumed in the literature, we provide strong evidence that highly specific methylation patterns are overrepresented at some genomic locations when latent weights are taken into account.