Multiple Signed Graph Learning for Gene Regulatory Network Inference

Many real-world data are represented through the relations between data samples, i.e., a graph structure. Although many datasets come with a pre-existing graph, there is still a large number of applications where the graph structure is not readily available. An essential task for such cases is graph learning (GL), which infers the graph structure from a set of graph signals. Existing GL techniques mostly focus on learning a single graph structure; however, samples are usually connected in multiple different ways. Furthermore, existing works can only handle unsigned graphs, while contemporary tasks require inference of signed graphs, which are better at representing similarity and dissimilarity of samples. In this paper, we propose a framework (mvSGL) for joint estimation of multiple related signed graphs. mvSGL optimizes the total variation of graph signals with respect to graphs while ensuring that the graphs are similar to each other through a consensus graph. mvSGL is employed in the inference of multiple gene regulatory networks (GRN) from single cell datasets that include multiple cell types. Performance evaluation using simulated and real datasets demonstrates the effectiveness of mvSGL in the inference of multiple related GRNs.