Optimize the hyperparameters of a time-series GP — optimize_time_series

Estimates the kernel parameters and the noise of a GP on ordered time-series observations by maximizing the log marginal likelihood, with the optimizer of optimize_gp().

Usage

optimize_time_series_gp(
  time,
  y,
  kernel,
  unit = "auto",
  method = c("exact", "state_space"),
  ...
)

Arguments

time: Numeric, Date, or POSIXt vector in strictly increasing order.
y: Numeric response vector.
kernel: Initial kernel specification.
unit: Time unit passed to gp_time_index().
method: "exact" conditions a Gaussian prior on the observations with fit_gp(). "state_space" computes the same posterior and log marginal likelihood in $O(n)$ time by Kalman filtering and smoothing; it needs a Matérn-1/2, 3/2, or 5/2 kernel, a sum of such kernels, or scaled versions of them (see State-space inference).
...: Additional arguments passed to optimize_gp(). With method = "state_space", the arguments noise_variance, mean, optimize_noise, n_starts, start_spread, lower, upper, and control apply, with the meanings and defaults of optimize_gp().

Value

A fitted model as returned by fit_time_series_gp(), with optimizer diagnostics in $optimization.

Details

With method = "state_space" each objective value is one Kalman filter pass, in $O(n)$ time (fit_time_series_gp() describes the method). Gradients are finite-difference approximations by L-BFGS-B (gradient = "numerical" in optimize_gp()); analytical sensitivity recursions are not implemented yet.

Stability

Experimental: this interface may change in a minor release, and every change is listed in NEWS. See gaussianprocesses-package for the policy.

Examples

set.seed(1)
time <- sort(runif(200, 0, 50))
y <- sin(time / 3) + rnorm(200, sd = 0.2)

model <- optimize_time_series_gp(time, y, matern52_kernel(),
  noise_variance = 0.1, n_starts = 1, method = "state_space")
model$optimization$optimized_parameters
#>       variance   length_scale noise_variance 
#>     1.55681386     8.20864673     0.03920353