  Uncertainty quantification (UQ) is an active area of research, and an
essential technique used in all fields of science and engineering. The most
common methods for UQ are Monte Carlo and surrogate-modelling. The former
method is dimensionality independent but has slow convergence, while the latter
method has been shown to yield large computational speedups with respect to
Monte Carlo. However, surrogate models suffer from the so-called curse of
dimensionality, and become costly to train for high-dimensional problems, where
UQ might become computationally prohibitive. In this paper we present a new
technique, Lasso Monte Carlo (LMC), which combines a Lasso surrogate model with
the multifidelity Monte Carlo technique, in order to perform UQ in
high-dimensional settings, at a reduced computational cost. We provide
mathematical guarantees for the unbiasedness of the method, and show that LMC
can be more accurate than simple Monte Carlo. The theory is numerically tested
with benchmarks on toy problems, as well as on a real example of UQ from the
field of nuclear engineering. In all presented examples LMC is more accurate
than simple Monte Carlo and other multifidelity methods. Thanks to LMC,
computational costs are reduced by more than a factor of 5 with respect to
simple MC, in relevant cases.
