Low-Precision Random Fourier Features for Memory-Constrained Kernel Approximation
This addresses memory efficiency for kernel methods in machine learning, offering a practical solution for resource-constrained applications, though it is incremental as it builds on existing RFF techniques.
The paper tackles the problem of training kernel approximation methods that generalize well under memory constraints by proposing low-precision random Fourier features (LP-RFFs), which achieve performance matching full-precision RFFs and the Nyström method with 3x-10x and 50x-460x less memory, respectively, across four benchmark datasets.
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical generalization performance of kernel approximation methods than conventional metrics. An important consequence of this definition is that a kernel approximation matrix must be high rank to attain close approximation. Because storing a high-rank approximation is memory intensive, we propose using a low-precision quantization of random Fourier features (LP-RFFs) to build a high-rank approximation under a memory budget. Theoretically, we show quantization has a negligible effect on generalization performance in important settings. Empirically, we demonstrate across four benchmark datasets that LP-RFFs can match the performance of full-precision RFFs and the Nyström method, with 3x-10x and 50x-460x less memory, respectively.