# Data-driven sparse polynomial chaos expansion for models with dependent inputs

arXiv: https://arxiv.org/abs/2101.07997 · HTML: https://mlsanity.com/paper/2101.07997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 20 Jan 2021.

## Builds on (most cited first, 6 of 6)

- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models](https://mlsanity.com/paper/1909.01648/) (2019)
- [Global sensitivity analysis in the context of imprecise probabilities (p-boxes) using sparse polynomial chaos expansions](https://mlsanity.com/paper/1705.10061/) (2017)
- [The basic reproduction number as a predictor for epidemic outbreaks in temporal networks](https://mlsanity.com/paper/1407.6598/) (2014)
- [Data-Driven Sensitivity Indices for Models With Dependent Inputs Using the Polynomial Chaos Expansion](https://mlsanity.com/paper/1803.10978/) (2018)
- [Identifying the Influential Inputs for Network Output Variance Using Sparse Polynomial Chaos Expansion](https://mlsanity.com/paper/1907.04266/) (2019)

## Abstract (arXiv)

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram-Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm.