$$\bar{f}_* = K_*(K+\sigma_n^2 I)^{-1}y,\quad
V_* = k_{**} - K_*(K+\sigma_n^2 I)^{-1}K_*^\top$$
Rasmussen & Williams (2006), eq. (2.23)-(2.24), p. 16; the
squared-exponential covariance on p. 19. One linear solve, no
iteration.
Usage
Gpreg(X, y, X_test, kernel = NULL, noise = 0)
Arguments
- X
Training inputs, n x d.
- y
Training targets.
- X_test
Test inputs, m x d.
- kernel
c(sf, l) (default c(1, 1)) or a function k(x1, x2).
- noise
Observation noise standard deviation.
Value
Named list with estimate, variance, loglik, n, method.
References
Rasmussen & Williams (2006), eq. (2.23)-(2.24), (2.30).
Examples
Gpreg(matrix(c(0, 1, 2), 3, 1), c(0, 1, 0.5), matrix(c(0.5), 1, 1))$estimate
#> [1] 0.5992997
