Summary
The authors tackle the well-known problem of Gene Regulatory Network (GRN) inference from time series data. Starting from an estimate of RNA velocity, GRN inference is framed as a causal discovery task, with two specificities: the inferred graphs may be cyclic, and a probabilistic distribution over candidate graphs is sought rather than a point estimate, so as to account for the high amounts of noise inherently present in biological data. The method is articulated around two assumptions:
- a dynamic structural model $\frac{dx_i(t)}{dt} = f_i(\text{Pa}(x_i), \epsilon_i)$ for each gene. $\text{Pa}(x_i)$ is directly obtained from the regulatory graph $G$, and the structural causal model (SCM) $f_i$ is parametrized by $\theta$
- a factorisation of the joint distribution of the graph $G$, the structural causal model parameters $\theta$, and the observed data $\mathcal{D}$ as $p(G,\theta,\mathcal{D}) = p(\mathcal{D}|G,\theta)p(\theta|G)p(G)$. The graph sampler $p(G)$ is modeled as a GFlowNets. Next, since the parameters of the SCM depend on the graph structure, they are computed by a HyperNetwork, i.e. $p(\theta|G)$ is substituted to a neural network which takes as input a graph $G$ and outputs the structural equation model parameters $\theta$: $p(\theta|G) = \delta(\theta|G)$.
Next, the authors evaluate the proposed method, DynGFN, on several synthetic examples as well as a real-world one involving single-cell RNA velocity data. The authors introduce other baselines by using different approaches than a GFlowNets for the graph sampler $p(G)$. This being said, DynGFN offers substantial improvements when it comes to jointly recovering the ground truth structure while characterizing the uncertainty around it.
Strengths
The big picture of the method is well explained. The work described here is likely to have a significant impact for the GRN inference community, as I believe that not many probabilistic methods are available in this field. I also believe that DynGFN could be used as a starting point for the more general problem of physical/biological dynamical system discovery, where one is not only concerned with the graph adjacency matrix but with providing a mechanistic description of the structural causal model $f_i$ [1,2]
[1] Discovering governing equations from data by sparse identification of nonlinear dynamical systems, PNAS, 2016
[2] Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods, PLoS Comp. Biol., 2022
Weaknesses
- The paper builds on GFlowNets for the graph sampler $P(G)$ and Hypernetworks to generate the structural causal model parameters $\theta$ given a sampled graph $G$. I found it slightly difficult to understand everything $in$ $detail$ given that these tools are each introduced only in a small paragraph.
- Even though the method focuses on Bayesian Inference, it would have been interesting to assess DynGFN's performances compared to SOTA methods for GRN inference from time series data such as DynGENIE3 [1], BINGO [2] or others. Lastly, these methods use time-resolved gene expression data, from which one can get an estimate of the RNA velocity using for instance finite differences, which may be a quite rough estimate for sparsely sampled measurements. Do I understand right that the RNA velocity data employed in this submission somehow constitutes a ``more principled'' way to estimate the RNA velocity?
[1] dynGENIE3: dynamical GENIE3 for the inference of gene networks from time series expression data, Scientific Reports, 2018
[2] Gene regulatory network inference from sparsely sampled noisy data, Nature Communications, 2020
Questions
- Any insights on why $h$-DynGFN yields significantly better results than $\ell$-DynGFN on the linear system presented in table 1?
- In the single cell experiment, where does the ground truth network (used to compute AUC / Bayes-SHD) come from? Could you explain a little more what does "correlation over cell cycle time" means in Section 6.3?
I have read the rebuttal done by the authors.
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Limitations
The authors mention as main limitation the difficulties to scale to large gene regulatory networks due to the combinatorial explosion. Causal sufficiency is also assumed here, which means that all relevant variables are observed. This assumption hardly ever holds in real-world biological problems. This issue is also mentioned by the authors in the Appendix.