Two processes: one for the mean, one for the LOG noise variance, so the noise level is itself a smooth function of the input and cannot go negative. The alternation is the deterministic analogue of the paper's sampler: fit the mean GP under the current noise, form the log squared residuals, smooth them with the second GP, exponentiate, refit. Zero iterations leaves the plain homoscedastic GP exactly.
Usage
Gphtr(
X,
y,
X_test = NULL,
lengthscale = 1,
variance = 1,
noise0 = 0.1,
noise_lengthscale = 1,
iters = 3,
floor = 1e-06
)Arguments
- X
Training inputs.
- y
Training responses.
- X_test
Test inputs; the training inputs by default.
- lengthscale, variance
Mean-process hyperparameters.
- noise0
Starting noise variance.
- noise_lengthscale
Lengthscale of the log-variance process.
- iters
Alternations; zero gives the homoscedastic GP.
- floor
Lower bound on a squared residual before its logarithm.
References
Goldberg, Williams and Bishop (1998), Regression with input-dependent noise: a Gaussian process treatment, NIPS 10.
Examples
V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Gphtr(V, V)
#> $estimate
#> [1] 0.9999997
#>
#> $mean
#> [1] 0.9999997 1.9999987 2.9999988 3.9999863 4.9999615 5.9996741 7.0000221
#> [8] 7.7881334
#>
#> $variance
#> [1] 1.711233e-06 1.171769e-06 1.678085e-06 5.860203e-06 4.807558e-05
#> [6] 7.562480e-05 1.247672e-04 2.743539e-02
#>
#> $noise
#> [1] 1.711239e-06 1.171774e-06 1.678098e-06 5.860374e-06 4.808708e-05
#> [6] 7.565129e-05 1.248248e-04 2.901199e-02
#>
#> $noise_test
#> [1] 2.505620e-06 1.551685e-06 2.210735e-06 7.558225e-06 3.970447e-05
#> [6] 5.676765e-05 2.438285e-04 5.352347e-03
#>
#> $loglik
#> [1] -55.65461
#>
#> $n
#> [1] 8
#>
#> $method
#> [1] "alternating mean GP and log-variance GP, Goldberg, Williams & Bishop (1998)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"