Fig. 4

True Positive and False Positive Rates for several test methods on ER graphs of two different levels of sparsity. Erdős-Rényi (ER) graphs with triangles for a 50 nodes graph with strong sparsity due to \(p = 0.04\), and the x’s for 50 nodes ER graphs with due to denser \(p = 0.1\). The magenta lines represent GLASSO, the blue lines represent the Poisson oMII, the red lines represent the Gaussian oMII, and the green lines represent the KNN oMII. In a the true positive rate (TPR) is shown for different sample sizes, each point is averaged over 50 realizations of the network dynamics. In b the false positive rate (FPR) is shown. Clearly GLASSO finds more true edges, but at the expense of a significantly higher false positives. In fact, for the highly sparse ER network GLASSO finds 3 times as many edges as actually exist in the network with 1000 data points. The FPR increases with data set. As can be seen the Gaussian oMII performs as well as Poisson oMII in TPR with the KNN performing poorly, but the Poisson oMII significantly outperforms all other methods in terms of FPR. It appears that the Poisson oMII is the only method that converges to the true network structure with increasing sample size. c Comparing TPR between GLASSO, the hybrid method and Poisson oCSE. The hybrid method has an increased TPR relative to Poisson oCSE. d The FPR increases slightly for the hybrid method, but is substantially lower than GLASSO