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Squared RKHS norm of a kernel expansion

Source: R/rkhsn.R
Rkhsnorm.Rd

Formula: ||f||_H^2 = sum_i sum_j beta_i beta_j K(x_i, x_j) = beta' K beta

Usage

Rkhsnorm(beta, K)

Arguments

beta

Kernel expansion coefficients, length n.

K

Gram matrix.

Value

List with norm2, norm, n.

References

Montesinos Lopez, Montesinos Lopez and Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, doi:10.1007/978-3-030-89010-0. Chapter 8, Eq. (8.2) p. 254: the squared norm of f in the reproducing kernel Hilbert space is beta'K beta. Read from the chapter PDF, not recalled.

Examples

Rkhsnorm(beta = 0.5, K = 5L)
#> $norm2
#> [1] 1.25
#> 
#> $norm
#> [1] 1.118034
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "Squared RKHS norm, MVSML Eq. (8.2)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"