DeepAI AI Chat
Log In Sign Up

Complex-to-Real Random Features for Polynomial Kernels

by   Jonas Wacker, et al.

Kernel methods are ubiquitous in statistical modeling due to their theoretical guarantees as well as their competitive empirical performance. Polynomial kernels are of particular importance as their feature maps model the interactions between the dimensions of the input data. However, the construction time of explicit feature maps scales exponentially with the polynomial degree and a naive application of the kernel trick does not scale to large datasets. In this work, we propose Complex-to-Real (CtR) random features for polynomial kernels that leverage intermediate complex random projections and can yield kernel estimates with much lower variances than their real-valued analogs. The resulting features are real-valued, simple to construct and have the following advantages over the state-of-the-art: 1) shorter construction times, 2) lower kernel approximation errors for commonly used degrees, 3) they enable us to obtain a closed-form expression for their variance.


A Unifying View of Explicit and Implicit Feature Maps for Structured Data: Systematic Studies of Graph Kernels

Non-linear kernel methods can be approximated by fast linear ones using ...

Improved Random Features for Dot Product Kernels

Dot product kernels, such as polynomial and exponential (softmax) kernel...

On the generalization of Tanimoto-type kernels to real valued functions

The Tanimoto kernel (Jaccard index) is a well known tool to describe the...

Low-dimensional Interpretable Kernels with Conic Discriminant Functions for Classification

Kernels are often developed and used as implicit mapping functions that ...

Tensor machines for learning target-specific polynomial features

Recent years have demonstrated that using random feature maps can signif...

Learning Bounds for Greedy Approximation with Explicit Feature Maps from Multiple Kernels

Nonlinear kernels can be approximated using finite-dimensional feature m...

Complex-Valued Kernel Methods for Regression

Usually, complex-valued RKHS are presented as an straightforward applica...