  We present a regression technique for data-driven problems based on
polynomial chaos expansion (PCE). PCE is a popular technique in the field of
uncertainty quantification (UQ), where it is typically used to replace a
runnable but expensive computational model subject to random inputs with an
inexpensive-to-evaluate polynomial function. The metamodel obtained enables a
reliable estimation of the statistics of the output, provided that a suitable
probabilistic model of the input is available. Machine learning (ML) regression
is a research field that focuses on providing purely data-driven input-output
maps, with the focus on pointwise prediction accuracy. We show that a PCE
metamodel purely trained on data can yield pointwise predictions whose accuracy
is comparable to that of other ML regression models, such as neural networks
and support vector machines. The comparisons are performed on benchmark
datasets available from the literature. The methodology also enables the
quantification of the output uncertainties, and is robust to noise.
Furthermore, it enjoys additional desirable properties, such as good
performance for small training sets and simplicity of construction, with only
little parameter tuning required.
