Nonparametric Combinatorial Sequence Models

This work considers biological sequences that exhibit combinatorial structures in their composition: groups of positions of the aligned sequences are "linked" and covary as one unit across sequences. If multiple such groups exist, complex interactions can emerge between them. Sequences of this kind arise frequently in biology but methodologies for analyzing them are still being developed. This article presents a nonparametric prior on sequences which allows combinatorial structures to emerge and which induces a posterior distribution over factorized sequence representations. We carry out experiments on three biological sequence families which indicate that combinatorial structures are indeed present and that combinatorial sequence models can more succinctly describe them than simpler mixture models. We conclude with an application to MHC binding prediction which highlights the utility of the posterior distribution over sequence representations induced by the prior. By integrating out the posterior, our method compares favorably to leading binding predictors.