Graph Tikhonov Regularization and Interpolation Via Random Spanning Forests

Novel Monte Carlo estimators are proposed to solve both the Tikhonov regularization (TR) and interpolation problems on graphs. These based random spanning forests (RSF), theoretical properties of which enable analyze estimators' mean variance. We also show how perform hyperparameter tuning for these RSF-based estimators. TR is a component in many well-known algorithms, we can be easily adapted avoid expensive intermediate steps generalized semi-supervised learning, label propagation, Newton's method iteratively reweighted least squares. In experiments, illustrate methods several provide observations their run time.