Data-driven polynomial chaos expansion for machine learning regression
This work provides a data-driven regression method with uncertainty quantification for machine learning practitioners, though it is incremental as it adapts an existing technique to a new context.
The paper tackled regression problems by applying polynomial chaos expansion (PCE), a technique from uncertainty quantification, to machine learning, showing it yields pointwise prediction accuracy comparable to neural networks and support vector machines on benchmark datasets, with additional benefits like robustness to noise and good performance for small training sets.
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.