Inference error versus number of random invalid edges. The proportional error (i.e., inference error) denotes the minimal cross-validation error divided by the minimal least-squares error of the linear regression without any regularization terms and averaged over five random networks. The blue, green and red curves represent 0, 5 and 20 random valid edges, respectively. 4 and 2 observations are considered in (A) and (B), respectively. When there are more valid edges (e.g., valid = 20), the errors are generally smaller as a whole. When only a few observations are available, the valid edges appear to be even more important. The cross-validation errors are in a large scale (i.e., 105) in (B), because they are divided by the least-squares errors, while fewer observations are easier to be over fitted with small least-squares errors (e.g., 10-6 ~ 10-4).