listAmkatKernelFunctions: List Available Kernel Functions In the AMKAT Package

In brianpatrickneal/AMKAT: AMKAT: An Adaptive Multivariate Kernel-based Association Test

List Available Kernel Functions In the AMKAT Package

Description

Returns a vector containing the character strings that identify each of the kernel functions included in the AMKAT package.

Usage

listAmkatKernelFunctions()

Details

The main function amkat includes an argument candidate_kernels that specifies the candidate kernel functions to consider during kernel selection. Its value must be a subset of the character vector returned by listAmkatKernelFunctions.

The function generateKernelMatrix in the AMKAT package includes an argument kernel_function that specifies the kernel function used to generate the empirical kernel matrix. The value of kernel_function must be a character string matching one of the entries in the value returned by listAmkatKernelFunctions.

Five kernel functions are available as of the current version: linear, quadratic, Gaussian, exponential, and Identical-by-State. Details on the individual kernel functions can be found below. For kernel functions that include a tuning parameter, the value of the parameter is set at p, the dimension of each of the kernel function's arguments (i.e., the column dimension of the argument x in the function amkat). Please note that the IBS kernel is only applicable to very specific types of data.

Value

A character vector containing the following components, listed along with a description of the kernel function corresponding to each one:

"lin"	Linear kernel, defined as f(x_1, x_2) = x_1^T x_2 / p for two p-dimensional column vectors x_1 and x_2.
"quad"	Quadratic kernel, defined as f(x_1, x_2) = (x_1^T x_2 / p + 1)^2 for two p-dimensional column vectors x_1 and x_2.
"gau"	Gaussian kernel, defined as f(x_1, x_2) = exp(-|| x_1 - x_2 ||^2 / p) for two p-dimensional column vectors x_1 and x_2, where || x_1 - x_2 || is the Euclidean distance.
"exp"	Exponential kernel, defined as f(x_1, x_2) = exp(-(|| x_1 ||^2 + 3|| x_1 - x_2 ||^2 + || x_2 ||^2) / p) for two p -dimensional column vectors x_1 and x_2, where || . || is the Euclidean norm.
"IBS"	Identical-by-State kernel, defined as (2p)^(-1) ∑{k=1 to k=p} (2 - |x_{1,k} - x_{2,k}|) for two p-dimensional column vectors x_1 and x_2 written as x_1 = (x_{1,1}, x_{1,2}, …, x_{1,p})^T and x_2 = (x_{2,1}, x_{2,2}, …, x_{2,p})^T. Only applicable when the entries of x_1 and x_2 take on values in the set {0, 1, 2}, e.g., for additively-encoded single-nucleotide polymorphism (SNP) genotype data.

Author(s)

Brian Neal

References

Neal, Brian and He, Tao. “An adaptive multivariate kernel-based test for association with multiple quantitative traits in high-dimensional data.” Genetic Epidemiology (not yet submitted).

brianpatrickneal/AMKAT documentation built on June 15, 2022, 8:47 a.m.