Analytical Extraction of Conditional Sobol' Indices via Basis Decomposition of Polynomial Chaos Expansions

The key contribution is not just speed: by working analytically through the PCE basis rather than running Monte Carlo samples, researchers can extract how model outputs respond to subsets of inputs while holding others fixed, without re-running the underlying simulation at all. That matters most in expensive physical or engineering models where each forward pass has real cost.

This connects most directly to the ORCA paper from mid-April ('Structural interpretability in SVMs with truncated orthogonal polynomial kernels'), which also used orthogonal polynomial decompositions to quantify feature contributions and interaction orders without retraining. Both papers are working in the same mathematical territory: expanding model behavior in polynomial bases to make sensitivity or importance measures tractable. The broader thread across recent Modelwire coverage, including SegWithU's single-pass uncertainty quantification, is a push toward post-hoc analysis methods that extract interpretability or uncertainty estimates cheaply, without additional inference overhead.

The practical test is whether this analytical approach holds up when the PCE approximation error is non-negligible, specifically whether conditional Sobol' indices computed this way remain reliable as input dimensionality grows past the truncation order used during the original expansion. Benchmark comparisons against Monte Carlo estimates on high-dimensional test cases would settle that question.