Spherical Random Features for Polynomial Kernels

By Jeffrey Pennington, Felix X. Yu, Sanjiv Kumar. 2015

78 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Representation & Self-Supervised Learning

In Statistical Learning Theory

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Ramdas et al. (2015a) also demonstrates that the power of the kernel-based tests degrades with dimension.”
Orthogonal Random Features (2016, background): “2 Related Works Explicit nonlinear random feature maps have been constructed for many types of kernels, such as intersection kernels [15], generalized RBF kernels [22], skewed multiplicative histogram kernels [14], additive kernels [24], and polynomial kernels [11, 18].”
SGD Learns the Conjugate Kernel Class of the Network (2017, background): “earn in polynomial time. Connection to kernels. As mentioned earlier, our paper builds on Daniely et al. [13], who developed the association of kernels to NN which we rely on. Several previous papers [24, 10,28,27,25,32,18,26,6,5,16,2] investigated such associations, but in a more restricted setting”
Differentially Private Mixture of Generative Neural Networks (2017, background): “˘with only d= O(m˘ 2 log˘ 2) dimensions [38]. Explicit nonlinear feature maps have already been proposed for shift-invariant kernels (e.g., generalized RBF kernels) [50] as well as polynomial kernels [37] among others. 3.4Differential Privacy (DP) Differential Privacy allows a party to privately rel”
A Survey of Modern Questions and Challenges in Feature Extraction (2015, background): “One novel work that attacks this problem is Pennington et al. (2015), where they show that a simple normalization of input data to a unit l2 sphere and the use of spherical random Fourier features achieves an accurate kernel approximation with many fewer random features.”
Sampled Softmax with Random Fourier Features (2019, background): “However, due to rank deficiency of the produced features, it requires large D in order to achieve small mean squared error [23, 24].”