High-Dimensional Gaussian Process Regression with Soft Kernel Interpolation

• URL: http://arxiv.org/abs/2410.21419v1
• Date: Mon, 28 Oct 2024 18:13:56 GMT
• Title: High-Dimensional Gaussian Process Regression with Soft Kernel Interpolation
• Authors: Chris Camaño, Daniel Huang,
• Abstract summary: We introduce Soft Kernel Interpolation (SoftKI) designed for scalable Process (GP) regression on high-dimensional datasets. Inspired by Structured Interpolation (SKI), which approximates a GP kernel via a structured lattice, SoftKI approximates a kernel via softmax from a smaller number of learned points. By abandoning the lattice structure used in SKI-based methods, SoftKI separates the cost of forming an approximate GP kernel from the dimensionality of the data, making it well-suited for high-dimensional datasets.
• Score: 0.8057006406834466
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• Abstract: We introduce Soft Kernel Interpolation (SoftKI) designed for scalable Gaussian Process (GP) regression on high-dimensional datasets. Inspired by Structured Kernel Interpolation (SKI), which approximates a GP kernel via interpolation from a structured lattice, SoftKI approximates a kernel via softmax interpolation from a smaller number of learned interpolation (i.e, inducing) points. By abandoning the lattice structure used in SKI-based methods, SoftKI separates the cost of forming an approximate GP kernel from the dimensionality of the data, making it well-suited for high-dimensional datasets. We demonstrate the effectiveness of SoftKI across various examples, and demonstrate that its accuracy exceeds that of other scalable GP methods when the data dimensionality is modest (around $10$).

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