Title: Data-driven polynomial chaos expansion for machine learning regression,
Abstract: 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.
In classical machine learning (ML) regression settings, however, the system
is only known through observations of its inputs and output, and the interest
lies in obtaining accurate pointwise predictions of the latter. Here, 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. In the presence of statistically dependent
inputs, we investigate two ways to build the PCE, and show through simulations
that one approach is superior to the other in the stated settings.