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Function-on-Function Gaussian Process with Application in Robust Parameter Design
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DOI：10.1287/ijoc.2024.0751.png)
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Abstract
En 中文
As data sensing technology advances, functional data have become increasingly popular in complex systems. Function-on-function regression models, where both input and output variables are functional data, have attracted increasing attention in research. However, all the existing models have limitations that cannot qualify prediction uncertainty. To fill this gap, we propose a novel function-on-function Gaussian process (FFGP). It employs a detachable structure based on the operator-valued kernel to represent the covariance between functional inputs and output. Compared with existing Gaussian process models, FFGP can model functional data directly in the continuous space, and a scalar-valued operator-covariance is defined to qualify the output uncertainty. We further apply FFGP to robust parameter design by proposing an expected loss function to measure the functional output bias and uncertainty given a functional input. Then, an effective and scalable functional gradient descent algorithm (FRGD) is proposed to identify the optimal functional input that minimizes the loss function. Some theoretical properties of FFGP and its corresponding robust parameter optimization via FRGD are discussed.
Keywords:
functional data
Gaussian process
operator-valued kernel
robust parameter design
functional gradient descent
Journal
I
IF:
2.1
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86
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3.2K
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