The paper introduces the Polynomial Chaos Expanded Gaussian Process (PCEGP), a novel machine learning approach that combines Gaussian processes (GPs) and polynomial chaos expansion (PCE) to model complex, nonlinear processes.
The key aspects of the PCEGP are:
Nonstationary Covariance Functions: The PCEGP uses PCE to calculate input-dependent lengthscale parameters for the GP's covariance functions, allowing the model to adapt to varying degrees of smoothness and training data densities across the input space.
Heteroscedastic Noise Estimation: The PCEGP also employs PCE to model the heteroscedastic noise variance as a function of the input data, enabling more accurate representation of the underlying data characteristics.
Transparent and Interpretable: The PCEGP provides a mathematically interpretable method, as the PCE-based hyperparameters are expressed as analytical polynomials, enhancing the transparency and traceability of the model.
The performance of the PCEGP is evaluated on several regression benchmark datasets, including the Boston Housing, Energy Efficiency, and Concrete Compressive Strength datasets. The results demonstrate that the PCEGP often outperforms or matches the performance of previous state-of-the-art methods, while offering the key advantage of increased interpretability.
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by Domi... às arxiv.org 05-03-2024
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