ARGFlows: Amortized Posterior Sampling of Ancestral Recombination Graphs with GFlowNets

Ancestral recombination graphs (ARGs) describe the genealogical and recombi- nation history of sampled genomes, underpinning inference of demography, selec- tion, and mutation age. Despite decades of work, posterior inference over ARGs remains challenging. The space combines a variable number of discrete events with continuous event times and is sharply multimodal because structurally dif- ferent histories can explain the same sequence data almost equally well. In this paper we adopt generative flow networks (GFlowNets) to tackle Bayesian infer- ence over ARGs. Because GFlowNets sample combinatorial structures in pro- portion to reward, they are a natural choice for a posterior whose mass is spread across many distinct histories, and where posterior sampling requires sustained exploration of alternative histories. Across three simulated datasets spanning dif- ferent recombination rates, ARGFlow achieves competitive reconstruction against ARGInfer and SINGER while representing uncertainty in coalescence times and local genealogical structure.