Learning a smooth graph signal from partially observed data is a well-studied
task in graph-based machine learning. We consider this task from the
perspective of optimal recovery, a mathematical framework for learning a
function from observational data that adopts a worst-case perspective tied to
model assumptions on the function to be learned. Earlier work in the optimal
recovery literature has shown that minimizing a regularized objective produces
optimal solutions for a general class of problems, but did not fully identify
the regularization parameter. Our main contribution provides a way to compute
regularization parameters that are optimal or near-optimal (depending on the
setting), specifically for graph signal processing problems. Our results offer
a new interpretation for classical optimization techniques in graph-based
learning and also come with new insights for hyperparameter selection. We
illustrate the potential of our methods in numerical experiments on several
semi-synthetic graph signal processing datasets.

从优化恢复的角度考虑了图信号处理中部分观测数据的平滑处理问题，并提出了一种计算最优或接近最优正则化参数的方法，在半合成图信号处理数据集的数值实验中取得了良好效果。