[Paper Review] DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets

Lazar Atanackovic, Alexander Tong+4 more|arXiv (Cornell University)|Feb 8, 2023

Gene Regulatory Network AnalysisBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

DynGFN proposes a Bayesian structure learning framework for gene regulatory networks (GRNs) that jointly models cyclic dependencies and epistemic uncertainty using RNA velocity data. By framing GRN inference as sparse identification of a dynamical system and leveraging GFlowNets to estimate complex posterior distributions over cyclic graphs, DynGFN outperforms state-of-the-art methods in capturing uncertainty, achieving lower KL divergence and Bayes-SHD on synthetic and single-cell data.

ABSTRACT

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.

Motivation & Objective

• To address the dual challenges of modeling cyclic feedback loops and capturing uncertainty in gene regulatory network (GRN) inference from noisy, limited single-cell data.
• To develop a fully differentiable, end-to-end framework for Bayesian dynamic structure learning that jointly estimates posterior distributions over graph structures and system parameters.
• To enable robust causal discovery in settings where experimental perturbations are costly by modeling a distribution over plausible GRN structures rather than a single best graph.
• To overcome limitations of existing methods that either assume acyclic structures (DAGs) or fail to model complex uncertainty in cyclic systems.
• To demonstrate the method’s efficacy on synthetic systems and real single-cell RNA-seq data, particularly in capturing posterior distributions over cyclic GRNs.

Proposed method

• DynGFN models the posterior over GRN structures using a GFlowNet, which learns a sequential policy to sample sparse, cyclic graphs from the combinatorial space of possible dependencies.
• It leverages RNA velocity data to estimate gene expression velocity (dx/dt), treating GRN inference as a sparse identification problem of a dynamical system with drift function modeling regulatory interactions.
• A HyperNetwork is used to model the posterior over system parameters (θ) conditioned on the inferred graph structure G, enabling end-to-end differentiability.
• The method jointly optimizes graph structure and parameter posteriors via a score function that evaluates how well G and θ explain the observed dynamic data (x, dx).
• The framework avoids restrictive parametric assumptions on the posterior by using GFlowNets, which naturally model complex, discrete distributions over combinatorial structures.
• The architecture is trained via reinforcement learning with a reward signal based on data fit (e.g., negative log-likelihood), enabling scalable posterior estimation over large equivalence classes of graphs.

Experimental results

Research questions

• RQ1 Can a Bayesian structure learning framework effectively model uncertainty over cyclic gene regulatory networks when data is noisy and limited?
• RQ2 Can RNA velocity data be leveraged to improve the identifiability of cyclic regulatory structures in GRN inference?
• RQ3 Does using GFlowNets for posterior estimation over discrete, cyclic graph structures lead to better uncertainty quantification than existing DAG-based Bayesian methods?
• RQ4 How does DynGFN compare to state-of-the-art baselines in capturing the true posterior distribution over GRN structures in synthetic and real single-cell data?
• RQ5 To what extent does the method scale to realistic biological systems, and what are the key bottlenecks in its current implementation?

Key findings

• On a 5-dimensional synthetic dynamical system with 81 admissible graphs, ℓ-DynGFN achieved a Bayes-SHD of 3.3 ± 0.4 and a KL divergence of 44.98 ± 18.60, significantly outperforming ℓ-DynBCD (Bayes-SHD: 2.6 ± 0.1, KL: 321.95 ± 3.34) in uncertainty modeling despite similar structure recovery.
• h-DynGFN achieved the lowest KL divergence (39.82 ± 28.05) and moderate Bayes-SHD (5.1 ± 1.2) among all models, indicating superior posterior approximation while maintaining good data fit.
• The method demonstrated improved AUC (0.58–0.59) and lower NLL compared to baselines like h-DynDiBS and h-DynBCD, indicating better generalization and calibration of the posterior.
• In a single-cell fibroblast dataset, DynGFN captured higher correlation between genes over cell cycle time, suggesting better modeling of latent biological dynamics and reduced noise impact.
• The results show that DynGFN better encapsulates the true posterior distribution over cyclic structures than DAG-focused Bayesian baselines, which often converge to a single graph despite high uncertainty.
• Despite its performance, DynGFN faces scalability limitations due to exponential growth in the graph search space, restricting it to low-dimensional systems (5–20 variables) for now.