  Importance sampling (IS) is a Monte Carlo methodology that allows for
approximation of a target distribution using weighted samples generated from
another proposal distribution. Adaptive importance sampling (AIS) implements an
iterative version of IS which adapts the parameters of the proposal
distribution in order to improve estimation of the target. While the adaptation
of the location (mean) of the proposals has been largely studied, an important
challenge of AIS relates to the difficulty of adapting the scale parameter
(covariance matrix). In the case of weight degeneracy, adapting the covariance
matrix using the empirical covariance results in a singular matrix, which leads
to poor performance in subsequent iterations of the algorithm. In this paper,
we propose a novel scheme which exploits recent advances in the IS literature
to prevent the so-called weight degeneracy. The method efficiently adapts the
covariance matrix of a population of proposal distributions and achieves a
significant performance improvement in high-dimensional scenarios. We validate
the new method through computer simulations.
