# Effect Decomposition of Functional-Output Computer Experiments via Orthogonal Additive Gaussian Processes

arXiv: https://arxiv.org/abs/2506.12701 · HTML: https://mlsanity.com/paper/2506.12701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Vecchia approximations of Gaussian-process predictions](https://mlsanity.com/paper/1805.03309/) (2018)
- [Additive Gaussian Processes Revisited](https://mlsanity.com/paper/2206.09861/) (2022)
- [Modern Non-Linear Function-on-Function Regression](https://mlsanity.com/paper/2107.14151/) (2021)
- [Orthogonal Gaussian process models](https://mlsanity.com/paper/1611.00203/) (2016)
- [Efficient Spatio-Temporal Gaussian Regression via Kalman Filtering](https://mlsanity.com/paper/1705.01485/) (2017)
- [An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications](https://mlsanity.com/paper/2209.12565/) (2022)
- [Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments](https://mlsanity.com/paper/1709.07064/) (2017)
- [Computer Model Emulation with High-Dimensional Functional Output in Large-Scale Observing System Uncertainty Experiments](https://mlsanity.com/paper/1911.09274/) (2019)
- [Robust Functional ANOVA with Application to Additive Manufacturing](https://mlsanity.com/paper/2112.10643/) (2021)

## Abstract (arXiv)

Functional ANOVA (FANOVA) is a widely used variance-based sensitivity analysis tool. However, studies on functional-output FANOVA remain relatively scarce, especially for black-box computer experiments, which often involve complex and nonlinear functional-output relationships with unknown data distribution. Conventional approaches often rely on predefined basis functions or parametric structures that lack the flexibility to capture complex nonlinear relationships. Additionally, strong assumptions about the underlying data distributions further limit their ability to achieve a data-driven orthogonal effect decomposition. To address these challenges, this study proposes a functional-output orthogonal additive Gaussian process (FOAGP) to efficiently perform the data-driven orthogonal effect decomposition. By enforcing a conditional orthogonality constraint on the separable prior process, the proposed functional-output orthogonal additive kernel enables data-driven orthogonality without requiring prior distributional assumptions. The FOAGP framework also provides analytical formulations for local Sobol' indices and expected conditional variance sensitivity indices, enabling comprehensive sensitivity analysis by capturing both global and local effect significance. Validation through two simulation studies and a real case study on fuselage shape control confirms the model's effectiveness in orthogonal effect decomposition and variance decomposition, demonstrating its practical value in engineering applications.