Predictive variance of a Gaussian process

$$V_* = k_{**} - K_*(K+\sigma_n^2 I)^{-1}K_*^\top$$ Rasmussen & Williams (2006), eq. (2.24), (2.26). As the book notes, this does not depend on the observed targets at all.

Usage

Gpvar(X, X_star, kernel = NULL, sigma2 = 0)

Arguments

X

Training inputs, n x d.

X_star

Test inputs, m x d.

kernel

c(sf, l) or a function k(x1, x2).

sigma2

Observation noise VARIANCE (not the sd; the name follows the book).

Value

Named list with estimate, prior, n, method.

References

Rasmussen & Williams (2006), eq. (2.24).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Gpvar(V, V)
#> $estimate
#> [1] 0.000000e+00 0.000000e+00 0.000000e+00 2.220446e-16 1.110223e-16
#> [6] 1.110223e-16 0.000000e+00 0.000000e+00
#> 
#> $prior
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "GP predictive variance -- Rasmussen & Williams (2006) eq. (2.24)"
#>