Fig. 8

Boxplot of logarithms of squared errors of different predictors, demonstrating superiority of our proposed algorithm to other methods. For each of 100 Monte Carlo samples, a random dot product graph with \(n=750\) nodes is generated for which the i-th latent position is given by \({\textbf{x}}_i=\frac{1}{\sqrt{2}}(cos(t_i),sin(t_i),cos(t_i),sin(t_i))\), \(t_i \sim ^{iid} U(0,1)\). Based upon the responses from the first \(s=5\) nodes, the response at the 6-th node is predicted. The red box corresponds to the predicted responses based on the true regressors, and the orange box corresponds to the predicted responses obtained from our proposed algorithm. The green box corresponds to the predicted responses obtained from a nonparametric local linear regression model linking the responses with the adjacency spectral estimates of the latent positions. The blue box corresponds to the predicted responses obtained from nearest neighbour regression on the adjacency spectral estimates of the latent positions