A convex regularized loss function is minimized respective to a prediction tensor of order K to generate an optimized prediction tensor of order K where K>2. The convex regularized loss function comprises a linear combination of (i) a loss function comparing the prediction tensor and an observation tensor of order K representing a set of observations and (ii) a regularization parameter including a K-th order matrix norm decomposition of the tensor trace norm of the prediction tensor. In some such embodiments, the observation tensor of order K represents a set of social network observations and includes at least dimensions corresponding to (1) users, (2) items, and (3) tags. The optimized prediction tensor of order K is suitably used to perform inference operations.