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

翻译：为了解决Tikhonov的正规化(TR)和图表上的内插问题,建议了蒙得洛新估计器。这些估计器基于随机的横贯森林(RSF),其理论特性可以分析估计器的理论平均值和差异。我们还展示了如何对这些基于RSF的估测器进行超参数调。最后,TR或内插是几种算法的构件之一,我们展示了如何轻而易举地调整拟议的估计器,以避免在众所周知的算法中出现昂贵的中间步骤,如普遍的半监督学习、标签传播、牛顿方法和迭代重标定最小平方形。在实验中,我们介绍了关于若干问题的拟议方法,并提供了运行时间的观察结果,这些观察与最新技术相当。