# Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines

arXiv: https://arxiv.org/abs/1912.11029 · HTML: https://mlsanity.com/paper/1912.11029/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Sparse Bayesian Learning for Complex-Valued Rational Approximations](https://mlsanity.com/paper/2206.02523/) (2022)
- [Conformal prediction for full and sparse polynomial chaos expansions](https://mlsanity.com/paper/2601.16636/) (2026)

## Abstract (arXiv)

The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series representation through retaining only the most important basis terms. In this work, we present a novel sparse Bayesian learning technique for obtaining sparse Polynomial Chaos expansions which is based on a Relevance Vector Machine model and is trained using Variational Inference. The methodology shows great potential in high-dimensional data-driven settings using relatively few data points and achieves user-controlled sparse levels that are comparable to other methods such as compressive sensing. The proposed approach is illustrated on two numerical examples, a synthetic response function that is explored for validation purposes and a low-carbon steel plate with random Young's modulus and random loading, which is modeled by stochastic finite element with 38 input random variables.