Abstract
Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in recent years due to their improved approximation accuracy and better calibrated uncertainty estimates compared to Random Fourier Feature (RFF) methods. However, a key limitation of QFF is that its performance can suffer from well-known pathologies related to highly oscillatory quadrature, resulting in mediocre approximation with limited features. We address this critical issue via a new Trigonometric Quadrature Fourier Feature (TQFF) method, which uses a novel non-Gaussian quadrature rule specifically tailored for the desired Fourier transform. We derive an exact quadrature rule for TQFF, along with kernel approximation error bounds for the resulting feature map. We then demonstrate the improved performance of our method over RFF and Gaussian QFF in a suite of numerical experiments and applications, and show the TQFF enjoys accurate GP approximations over a broad range of length-scales using fewer features.
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Kevin Li
PhD Student Statistical Science
Hello! I’m a 3rd Year Statistical Science PhD student at Duke University. I work on computational and statistical methods for modeling complex phenomenon and quantifying uncertainty under limited information. I’m particularly interested in applying these models for downstream decisionmaking tasks such as causal inference and adaptive experimentation. My research applications have included retail forecasting, emulation of engineering and physics experiments, neuro-computation, and genetic sequencing. Before my PhD I developed credit authorization systems with the Risk and Decision Sciences team at American Express.