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].

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.

Wealso provide improvedregret bounds when theothers' maximum bid exhibits the further structure of sparsity.

Multivariate time-series forecasting plays a crucial role in many real-world applications.

Multivariate time-series forecasting plays a crucial role in many real-world applications.

Markov chain Monte Carlo (MCMC) is an inference mechanism that approximates a target probability distribution by a sequence of states (a.k.a.

In this section, we review some key results on the Wasserstein distance. Wpp Rπ(t,θi),Rρ(t,θi), (4) where the approximation comes from using Monte-Carlo integration by samplingθi uniformly in SD 1 [2]. M,M is the number of points used to approximate the integral. Calculating the Wasserstein distance with the empirical distribution function is computationally attractive. To do that, we first sortxms in an ascending order, such thatxi[m] xi[m+1], where i[m]istheindexofthesortedxms. Hamiltonian Monte Carlo (HMC)[24]isahighly-efficient MarkovChain Monte Carlo (MCMC) method used to generate samples from the posteriorw p(w|y).

The bottleneck introduced by the low-dimensional latent space is what characterizes the compression and representation learning capabilities ofautoencoders.