  Rare event probability estimation is an important topic in reliability
analysis. Stochastic methods, such as importance sampling, have been developed
to estimate such probabilities but they often fail in high dimension. In this
paper, we propose a simple cross-entropy-based importance sampling algorithm to
improve rare event estimation in high dimension. We consider the cross-entropy
method with Gaussian auxiliary distributions and we suggest to update the
Gaussian covariance matrix only in a one-dimensional subspace. The idea is to
project in the one dimensional subspace spanned by the Gaussian mean, which
gives an influential direction for the variance estimation. This approach does
not require any additional simulation budget compared to the basic
cross-entropy algorithm and greatly improves its performance in high dimension,
as we show on different numerical test cases.
