Several approaches to predictive uncertainty quantification have been introduced in recent years, considering uncertainty inaBayesian sense [2,7,18]aswell asfrom afrequentist'spoint ofview [15,5,34].

In machine learning, given a finite set of samples, there are usually multiple solutions that can perfectly fit the training data, but theinductive biasof a learning algorithm selects and prioritizes those solutions that agree with itsaprioriassumptions [1,2].

Algorithmic stability is a key characteristic of an algorithm regarding its sensitivity to perturbations of input samples. In this paper,we propose an innovativeunsupervised feature selection algorithm attaining this stability with provable guarantees.