提出SoftKI方法，让高维数据上的高斯过程回归更高效稳定。
High-Dimensional Gaussian Process Regression with Soft Kernel Interpolation
- 用软最大化插值动态学习关键点，兼顾精度与计算效率。
- 在10维左右数据上表现媲美其他近似高斯过程方法。
- 适合需要灵活适应数据分布的高维回归任务。
我们提出软核插值（SoftKI），结合结构化核插值（SKI）和变分诱导点方法的优点，实现高维数据上的可扩展高斯过程（GP）回归。SoftKI通过优化软核边缘对数似然（MLL）及必要时的近似MLL，利用更少的插值点进行软最大化插值来逼近核函数。该方法克服了传统SKI在密集静态网格下难以应对维度增长的问题，同时保留了变分方法可根据数据自适应调整诱导点的灵活性。我们在多个实验中验证了SoftKI的有效性，当数据维度约为10时，其性能与其他近似GP方法相当。
原文摘要 · Abstract (English)
We introduce Soft Kernel Interpolation (SoftKI), a method that combines aspects of Structured Kernel Interpolation (SKI) and variational inducing point methods, to achieve scalable Gaussian Process (GP) regression on high-dimensional datasets. SoftKI approximates a kernel via softmax interpolation from a smaller number of interpolation points learned by optimizing a combination of the SoftKI marginal log-likelihood (MLL), and when needed, an approximate MLL for improved numerical stability. Consequently, it can overcome the dimensionality scaling challenges that SKI faces when interpolating from a dense and static lattice while retaining the flexibility of variational methods to adapt inducing points to the dataset. We demonstrate the effectiveness of SoftKI across various examples and show that it is competitive with other approximated GP methods when the data dimensionality is modest (around 10).
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