Formula: min over (eta_0, beta) of {(1/n) sum_i L(y_i, eta_0 + k_i'beta)
(lambda/2) beta'K beta} (eq. 8.3), obtained by substituting the representer
form (8.2) into (8.1). beta'K beta is the empirical RKHS norm and lambda
controls the trade-off between goodness of fit and complexity; with the
squared-error loss the stationarity conditions are linear and are solved
directly.
Arguments
- K
Kernel matrix.
- y
Response vector.
- lam
Complexity weight.
Value
List with estimate, eta0, beta, fitted, objective, penalty, method.
References
Montesinos Lopez, Montesinos Lopez & Crossa (2022),
Multivariate Statistical Machine Learning Methods for Genomic Prediction,
Springer, eq. (8.3) p.254. DOI 10.1007/978-3-030-89010-0.
Examples
xx <- seq(0, 1, length.out = 8)
K <- exp(-outer(xx, xx, "-")^2 / 0.1)
f <- Msm128(K, sin(2 * pi * xx), lam = 0.1)
names(f)
#> [1] "estimate" "eta0" "beta" "fitted" "objective" "penalty"
#> [7] "method"
