Formula: min over f in H of {(1/n) sum_i L(y_i, f(x_i)) + lambda ||f||_H^2}
(eq. 8.1), the penalized empirical risk in a reproducing kernel Hilbert
space, where L is minus the conditional log-likelihood for the response type
and ||f||_H^2 measures model complexity. The objective is evaluated at a
given (eta_0, beta).
Usage
Msm123(K, y, beta, eta0 = 0, lam = 1, loss = "squared")
Arguments
- K
Kernel matrix.
- y
Response vector.
- beta
Representer coefficients.
- eta0
Intercept on the latent scale.
- lam
Complexity weight.
- loss
One of "squared", "logistic" or "hinge".
Value
List with estimate, objective, empirical_risk, rkhs_norm2, method.
References
Montesinos Lopez, Montesinos Lopez & Crossa (2022),
Multivariate Statistical Machine Learning Methods for Genomic Prediction,
Springer, eq. (8.1) p.254. DOI 10.1007/978-3-030-89010-0.
Examples
set.seed(19)
xx <- seq(0, 1, length.out = 8)
K <- exp(-outer(xx, xx, "-")^2 / 0.1)
y <- sin(2 * pi * xx)
Msm123(K, y, beta = rep(0, 8), lam = 0.1)$estimate
#> [1] 0.4375
