Compression-based inference of network motif sets
Fig 3
Performance of compression-based motif inference on numerically generated networks.
(A-D) Number of spurious motifs inferred using our compression-based method with MDL-based model selection and using hypothesis testing with four different null models in random networks generated from the same four null models: (A) the Erdős-Rényi model (ER); (B) the configuration model (CM); (C) the reciprocal ER model (RER); and (D) the reciprocal CM (RCM). The x-axis labels indicate which method was used for motif inference: our method (MDL) or classic hypothesis testing with each of the four null models as reference. The corresponding generative model is highlighted in boldface. To make hypothesis testing as conservative as possible, we applied a Bonferroni correction, which multiplies the raw p-values by |Γ| = 9576 and we set the uncorrected significance threshold to 0.01. The random networks in (A-D) are all generated by fixing the values of each null model’s parameters to those of the Drosophila larva right MB connectome (e.g., N = 198 and E = 6499 for the ER model). (E-H) Ability of our method to correctly identify a placed graphlet as a motif as a function of the number of times it is repeated, mα. We show results for two selected 5-node graphlets: an hourglass structure (top row) and a clique (bottom row). The clique is the densest graphlet and is totally symmetric (the number of orientations, i.e., the number of non-automorphic node permutations, is equal to one). The hourglass has intermediary density, ρα = 2/5, and symmetry, with 60 non-automorphic orientations within a possible range of 1 to 5! = 120. The generated networks in (E-H) contain N = 300 nodes and an edge density of either ρ = E/N(N − 1) = 0.025 (E,G) or ρ = 0.1 (F,H). Each point is an average over five independently generated graphs. (E,F) The discovery rate is the estimated probability that the planted motif belongs to the inferred motif set, i.e., 〈1 − δ(mα, 0)〉. (G,H) Average inferred number of repetitions of the planted motif, 〈mα〉.