Abstract
Large-scale sequencing has revealed extraordinary diversity among biological sequences, produced over the course of evolution and within the lifetime of individual organisms. Existing methods for building statistical models of sequences often pre-process the data using multiple sequence alignment, an unreliable approach for many genetic elements (antibodies, disordered proteins, etc.) that is subject to fundamental statistical pathologies. Here we introduce a structured emission distribution (the MuE distribution) that accounts for mutational variability (substitutions and indels) and use it to construct generative and predictive hierarchical Bayesian models (H-MuE models). Our framework enables the application of arbitrary continuous-space vector models (e.g. linear regression, factor models, image neural-networks) to unaligned sequence data. Theoretically, we show that the MuE generalizes classic probabilistic alignment models. Empirically, we show that H-MuE models can infer latent representations and features for immune repertoires, predict functional unobserved members of disordered protein families, and forecast the future evolution of pathogens.
Competing Interest Statement
The authors have declared no competing interest.
