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. TR is a component in many well-known algorithms, and we show how the proposed estimators can be easily adapted to avoid expensive intermediate steps in generalized semi-supervised learning, label propagation, Newton's method and iteratively reweighted least squares. In the experiments, we illustrate the proposed methods on several problems and provide observations on their run time.

中文翻译：

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通过随机生成森林进行图吉洪诺夫正则化和插值


提出了新颖的蒙特卡洛估计器来解决吉洪诺夫正则化（TR）和图上的插值问题。这些估计量基于随机生成森林 (RSF)，其理论特性使得能够分析估计量的理论均值和方差。我们还展示了如何对这些基于 RSF 的估计器执行超参数调整。 TR 是许多著名算法中的一个组成部分，我们展示了如何轻松地调整所提出的估计器，以避免广义半监督学习、标签传播、牛顿法和迭代重新加权最小二乘中昂贵的中间步骤。在实验中，我们针对几个问题说明了所提出的方法，并提供了对其运行时间的观察。