  One of the grand challenges of cell biology is inferring the gene regulatory
network (GRN) which describes interactions between genes and their products
that control gene expression and cellular function. We can treat this as a
causal discovery problem but with two non-standard challenges: (1) regulatory
networks are inherently cyclic so we should not model a GRN as a directed
acyclic graph (DAG), and (2) observations have significant measurement noise,
so for typical sample sizes there will always be a large equivalence class of
graphs that are likely given the data, and we want methods that capture this
uncertainty. Existing methods either focus on challenge (1), identifying cyclic
structure from dynamics, or on challenge (2) learning complex Bayesian
posteriors over DAGs, but not both. In this paper we leverage the fact that it
is possible to estimate the "velocity" of gene expression with RNA velocity
techniques to develop an approach that addresses both challenges. Because we
have access to velocity information, we can treat the Bayesian structure
learning problem as a problem of sparse identification of a dynamical system,
capturing cyclic feedback loops through time. Since our objective is to model
uncertainty over discrete structures, we leverage Generative Flow Networks
(GFlowNets) to estimate the posterior distribution over the combinatorial space
of possible sparse dependencies. Our results indicate that our method learns
posteriors that better encapsulate the distributions of cyclic structures
compared to counterpart state-of-the-art Bayesian structure learning
approaches.
