Systematic evaluation of continuous optimization approaches for causal discovery of gene regulatory networks

Abstract

Continuous optimization-based structure learning for Directed Acyclic Graphs (DAGs) is increasingly popular. They are used to infer the structure of graphs from high volumes of data. However, previously it has been shown that these methods are often not usable for causal discovery because of inherent algorithmic biases. The main problem stems from their sensitivity to variance in the data. In other words, they are not scaleinvariant. This leads to variables with lower variance having more outgoing edges while variables with higher variance tend to have more incoming edges. In this paper, we test five of these methods (NOTEARS, NOTEARS-MLP, GOLEM-EV, GOLEM-NV, and DAG-NoCurl) on their performance and their robustness to variance in the data. We evaluate our findings on transcriptomic data to construct gene regulatory networks. These networks can uncover the hidden mechanisms of gene expressions. The use of scalable algorithms is well-motivated in the field. We use bootstrapping to evaluate the uncertainty of the found edges and quantify the bias of the methods. To quantify the bias, we calculate the posterior probability of a vertex being more likely to be a parent than a child and vice-versa.