More details and discussion about Table 1 can be found in Appendix A.

Sampling from a continuous distribution in high dimensions is a fundamental problem in algorithm design. As sampling serves as a key subroutine in a variety of tasks in machine learning [AdFDJ03], statistical methods [RC99], and scientific computing [Liu01], it is an important undertaking to understand the complexity of sampling from families of distributions arising in applications. The more restricted problem of sampling from a particular family of distributions, which we call "well-conditioned distributions," has garnered a substantial amount of recent research effort from the algorithmic learning and statistics communities. This specific family is interesting for a number of reasons. First of all, it is practically relevant: Bayesian methods have found increasing use in machine learning applications [Bar12], and many distributions arising from these methods are well-conditioned, such as multivariate Gaussians, mixture models with small separation, and densities arising from Bayesian logistic regression with a Gaussian prior [DCWY18].

The more restricted problem of sampling from a particular distribution family we call "well-conditioned" has garnered a substantial amount of recent research effort from the algorithmic learning

While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs.

Hamiltonian Monte Carlo (HMC) has emerged as a powerful Markov Chain Monte Carlo (MCMC) method to sample from complex continuous distributions.