Transformed Optimizers#

Single-task optimizers that fit a Gaussian process to observations after a fixed output transform (link function), and use :py:meth:gpcam.GPOptimizer.evaluate_posterior to push the latent Gaussian posterior back through the inverse link to the original observation space.

Use :py:class:gpcam.LogGPOptimizer for strictly positive observations in (0, inf) — predictions and credible intervals are guaranteed positive, and the original-scale mean/std are available in closed form (lognormal).

Use :py:class:gpcam.LogitGPOptimizer for observations bounded in [0, 1] — predictions and credible intervals are guaranteed inside (0, 1); the original-scale mean/std are estimated by Monte Carlo (logistic-normal has no closed form). Observations are clipped to [eps, 1 - eps] because logit(0)/logit(1) are infinite.

The inherited :py:meth:posterior_mean / :py:meth:posterior_covariance operate in the GP’s modeling space (log / logit); use :py:meth:evaluate_posterior to obtain a posterior on the original scale.

LogGPOptimizer#

class gpcam.gp_optimizer.LogGPOptimizer(x_data=None, y_data=None, init_hyperparameters=None, noise_variances=None, compute_device='cpu', kernel_function=None, kernel_function_grad=None, noise_function=None, noise_function_grad=None, prior_mean_function=None, prior_mean_function_grad=None, gp2Scale=False, dask_client=None, gp2Scale_batch_size=10000, linalg_mode=None, ram_economy=False, cost_function=None, logging=False, args=None)[source]#

A single-task GPOptimizer for strictly positive observations in (0, inf).

Observations are modeled in log-space (the GP sees log(y)), and posterior predictions are mapped back to the original scale with exp via evaluate_posterior(), which guarantees strictly positive predictions and credible intervals. exp of a Gaussian is lognormal, so the original-scale mean and standard deviation are available in closed form.

All constructor arguments are identical to GPOptimizer. Note that the inherited posterior_mean() / posterior_covariance() operate in log-space; use evaluate_posterior() for the original (positive) scale.

Acquisition functions: ask() optimizes the GP in log-space. Because log is monotone increasing, ranking acquisitions (variance, ucb, lcb, maximum, minimum) still identify the same locations as on the original scale. For target probability, pass bounds already in log-space (np.log(a), np.log(b)).

LogitGPOptimizer#

class gpcam.gp_optimizer.LogitGPOptimizer(x_data=None, y_data=None, eps=1e-06, n_samples=10000, range=(0.0, 1.0), **kwargs)[source]#

A single-task GPOptimizer for observations bounded in a closed interval [lower, upper] (default [0, 1]).

Observations are linearly rescaled to [0, 1] and modeled in logit (log-odds) space (the GP sees logit((y - lower) / (upper - lower))). Posterior predictions are mapped back to [lower, upper] via the inverse (affine ∘ sigmoid) through evaluate_posterior(), which guarantees predictions and credible intervals stay inside (lower, upper). Because logit(0) / logit(1) are infinite, normalized observations are clipped to [eps, 1 - eps] (a warning is emitted when clipping occurs). The logistic-normal distribution has no closed-form moments, so the original-scale mean and standard deviation are estimated by Monte-Carlo.

Parameters:

  • eps (float, optional) – Clipping margin for the open interval; normalized observations are clipped to [eps, 1 - eps] before the logit transform. The default is 1e-6.

  • n_samples (int, optional) – Number of Monte-Carlo samples used to estimate the original-scale mean/std in evaluate_posterior(). The default is 10000.

  • range (tuple of float, optional) – (lower, upper) bounds of the observation domain. Observations are linearly rescaled to [0, 1] before the logit transform, and posterior predictions are mapped back to [lower, upper]. The default is (0.0, 1.0).

Notes

All other constructor arguments are identical to GPOptimizer. The inherited posterior_mean() / posterior_covariance() operate in logit-space (on the rescaled [0, 1] data); use evaluate_posterior() for the original [lower, upper] scale. The acquisition-function note for LogGPOptimizer applies here too (pass target probability bounds in logit-space, where they refer to the rescaled [0, 1] data).