alpha = (K + lambda I)^-1 y with K_ij = k((x_i - x_j) / h) for the smoothing
kernels (gaussian is the normal density) and f(x0) = sum_i alpha_i k((x0 -
x_i) / h) (ESL eq 5.55).
Usage
kernel_ridge_regression(
X,
y,
kernel = "gaussian",
lam = 1,
x_eval = NULL,
bandwidth = NULL
)
Arguments
- X
Predictor.
- y
Response.
- kernel
"gaussian", "epanechnikov" or "uniform".
- lam
Ridge penalty, > 0.
- x_eval
Evaluation points (default X).
- bandwidth
Bandwidth; Silverman's rule when NULL.
Value
Named list: x_eval, y_hat, alpha, bandwidth, penalty, n_obs.
References
Hastie, Tibshirani & Friedman (2009), sec. 5.8.
Examples
x <- (1:25) / 25
kernel_ridge_regression(x, sin(6 * x), lam = 0.1, bandwidth = 0.2, x_eval = c(0.3, 0.6))$y_hat
#> [1] 0.9313952 -0.4340773
