  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.
