gpmp.kernel parameter selection

Likelihood objectives and parameter-selection wrappers operate on gpmp.core.Model objects and backend-native arrays. Selection procedures modify model.covparam and return (model, info_ret).

Likelihood objectives

The following functions return negative log-likelihood or negative restricted log-likelihood values. They are objective functions to minimize over covariance parameters.

negative_log_likelihood_zero_mean

gpmp.kernel.negative_log_likelihood_zero_mean(model, covparam, xi, zi)[source]

Evaluate the negative log-likelihood for a zero-mean GP model.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • covparam (array_like) – Covariance parameter vector.

  • xi (array_like) – Observation points and observed values.

  • zi (array_like) – Observation points and observed values.

Returns:

Negative log-likelihood value.

Return type:

scalar

negative_log_likelihood

gpmp.kernel.negative_log_likelihood(model, meanparam, covparam, xi, zi)[source]

Evaluate the negative log-likelihood for a GP model with mean parameters.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • meanparam (array_like) – Mean-function parameter vector.

  • covparam (array_like) – Covariance parameter vector.

  • xi (array_like) – Observation points and observed values.

  • zi (array_like) – Observation points and observed values.

Returns:

Negative log-likelihood value.

Return type:

scalar

negative_log_restricted_likelihood

gpmp.kernel.negative_log_restricted_likelihood(model, covparam, xi, zi)[source]

Evaluate the negative restricted log-likelihood (REML criterion).

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • covparam (array_like) – Covariance parameter vector.

  • xi (array_like) – Observation points and observed values.

  • zi (array_like) – Observation points and observed values.

Returns:

Negative restricted log-likelihood value.

Return type:

scalar

Generic selection helpers

These helpers build criterion callables, connect them to SciPy optimizers, and provide generic selection/update procedures for custom criteria.

make_selection_criterion_with_gradient

gpmp.kernel.make_selection_criterion_with_gradient(model, selection_criterion, xi=None, zi=None, dataloader=None, batches_per_eval=0, parameterized_mean=False, meanparam_len=1)[source]

Build criterion wrappers for value/gradient optimization and diagnostics.

Parameters:

  • model (gpmp.core.Model) – GP model instance passed to selection_criterion.

  • selection_criterion (callable) – Criterion function. When parameterized_mean is False, the expected signature is f(model, covparam, xi, zi). When parameterized_mean is True, the expected signature is f(model, meanparam, covparam, xi, zi).

  • xi (array_like, optional) – Observation arrays used for criterion evaluation.

  • zi (array_like, optional) – Observation arrays used for criterion evaluation.

  • dataloader (iterable, optional) – Batch loader used instead of xi, zi. Batches must be yielded as (xb, zb).

  • batches_per_eval (int, default=0) – Number of batches used per criterion call when dataloader is provided. Use 0 to iterate over the full loader at each evaluation. Use a positive value to evaluate exactly that many batches per call; the iterator cycles when needed.

  • parameterized_mean (bool, default=False) – Whether the criterion depends on explicit mean parameters.

  • meanparam_len (int, default=1) – Number of leading parameters in the optimization vector assigned to the mean model.

Returns:

  • evaluate (callable) – Value function with gradient-enabled behavior from backend wrapper.

  • evaluate_pre_grad (callable) – Value function intended to be called just before gradient in optimization loops.

  • evaluate_no_grad (callable) – Criterion evaluation function without gradient tracking.

  • gradient (callable) – Gradient function with respect to optimization parameters.

Notes

Exactly one data source must be provided: either observation arrays (xi, zi) or dataloader.

Internally, this function wraps selection_criterion into an adapter accepting either covariance parameters only or concatenated [meanparam, covparam] parameters.

For array data it uses gnp.DifferentiableSelectionCriterion. For loader data it uses gnp.BatchDifferentiableSelectionCriterion.

The four returned callables are complementary. evaluate and evaluate_pre_grad are used for optimizer value calls, gradient is used for optimizer gradient calls, and evaluate_no_grad is used for diagnostics and sampling paths where gradients are not required.

autoselect_parameters

gpmp.kernel.autoselect_parameters(p0, criterion, gradient, bounds=None, bounds_auto=True, bounds_delta=10.0, silent=True, info=False, method='SLSQP', method_options=None)[source]

Minimize a scalar selection criterion with SciPy.

Parameters:

  • p0 (array_like) – Initial parameter vector.

  • criterion (callable) – Objective function criterion(p) -> scalar.

  • gradient (callable) – Gradient function gradient(p) -> array_like.

  • bounds (sequence of tuple, optional) – Bounds passed to SciPy in normalized parameter space.

  • bounds_auto (bool, default=True) – If True and bounds is None, construct local bounds around p0 using bounds_delta and internal safety limits.

  • bounds_delta (float, default=10.0) – Half-width used for automatic local bounds.

  • silent (bool, default=True) – If False, enable solver output.

  • info (bool, default=False) – If True, return the full SciPy result object.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Additional options passed to SciPy minimize.

Returns:

  • p_opt (array_like) – Best parameter vector found.

  • info_ret (scipy.optimize.OptimizeResult or None) – Optimization diagnostics if info=True, else None.

Notes

Optimization wrapper behavior:

  1. Builds SciPy options from method-specific defaults and user method_options.

  2. Tracks full optimization history (parameter vectors and criterion values).

  3. If the final SciPy result is worse than the best visited point, replaces the returned solution by the best seen one and sets best_value_returned=False in the result object.

Exception handling: criterion evaluation exceptions caused by linear-algebra failures are mapped to +inf inside criterion_with_history so optimization can continue. Other exceptions are re-raised.

Added fields in returned OptimizeResult (when info=True): history_params, history_criterion, initial_params, final_params, bounds, selection_criterion, total_time, and best_value_returned.

select_parameters_with_criterion

gpmp.kernel.select_parameters_with_criterion(model, criterion, xi=None, zi=None, dataloader=None, meanparam0=None, covparam0=None, parameterized_mean=False, meanparam_len=1, info=False, verbosity=0, *, bounds=None, bounds_auto=True, bounds_delta=10.0, batches_per_eval=0, method='SLSQP', method_options=None)[source]

Optimize model parameters using a user-supplied selection criterion.

Parameters:

  • model (gpmp.core.Model) – GP model whose parameters are optimized.

  • criterion (callable) –

    Criterion minimized by SciPy.

    Expected signatures:

    • criterion(model, covparam, xi, zi) when parameterized_mean=False

    • criterion(model, meanparam, covparam, xi, zi) when parameterized_mean=True.

  • xi (array_like, optional) – Dataset arrays. Must be provided together unless dataloader is used instead.

  • zi (array_like, optional) – Dataset arrays. Must be provided together unless dataloader is used instead.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi. Must yield batches (xb, zb) compatible with criterion.

  • meanparam0 (array_like, optional) – Initial parameters in normalized space. If covparam0 is None, an anisotropic initial guess is computed from the provided data source.

  • covparam0 (array_like, optional) – Initial parameters in normalized space. If covparam0 is None, an anisotropic initial guess is computed from the provided data source.

  • parameterized_mean (bool, default False) – If True, optimize both mean and covariance parameters jointly using the concatenated vector [meanparam, covparam].

  • meanparam_len (int, default 1) – Number of leading entries in the concatenated vector corresponding to mean parameters.

  • info (bool, default False) – If True, return optimization diagnostics.

  • verbosity (int, default 0) – 0: silent, 1: short progress message, 2: SciPy solver output.

  • bounds – Bounds configuration in normalized parameter space, forwarded to autoselect_parameters.

  • bounds_auto – Bounds configuration in normalized parameter space, forwarded to autoselect_parameters.

  • bounds_delta – Bounds configuration in normalized parameter space, forwarded to autoselect_parameters.

  • batches_per_eval (int, default 0) – Number of loader batches per objective call when using dataloader. 0 means one full pass over loader per criterion evaluation. >0 means evaluate on exactly that many batches (with iterator cycling).

  • method (str, default "SLSQP") – Optimization method (“SLSQP” or “L-BFGS-B”).

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Model with updated parameters.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

Notes

Data source contract: exactly one of (xi, zi) or dataloader must be provided.

Internally, this function constructs four complementary criterion callables from make_selection_criterion_with_gradient required by optimization and diagnostics, then optimizes with autoselect_parameters.

When info=True, the returned diagnostics include optimization metadata (history, timing, parameters) and both callable criteria: selection_criterion and selection_criterion_nograd.

update_parameters_with_criterion

gpmp.kernel.update_parameters_with_criterion(model, criterion, xi=None, zi=None, dataloader=None, parameterized_mean=False, meanparam_len=1, info=False, *, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Update model parameters using current model parameters as initialization.

Parameters:

  • model (gpmp.core.Model) – GP model instance to update.

  • criterion (callable) – Selection criterion to minimize.

  • xi (array_like, optional) – Dataset arrays.

  • zi (array_like, optional) – Dataset arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • parameterized_mean (bool, default=False) – Whether mean parameters are optimized jointly.

  • meanparam_len (int, default=1) – Number of mean parameters in concatenated vectors.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • bounds – Bounds configuration in normalized parameter space.

  • bounds_auto – Bounds configuration in normalized parameter space.

  • bounds_delta – Bounds configuration in normalized parameter space.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

Specific selection procedures

These are the main public procedures for common criteria. select_* uses an explicit initial covariance vector when provided. update_* starts from the current model.covparam when it exists.

select_parameters_with_reml

gpmp.kernel.select_parameters_with_reml(model, xi=None, zi=None, dataloader=None, covparam0=None, info=False, verbosity=0, *, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Select covariance parameters with REML.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Dataset arrays.

  • zi (array_like, optional) – Dataset arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • covparam0 (array_like, optional) – Initial covariance parameters. If None, an anisotropic initial guess is computed.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to generic criterion selection.

  • bounds – Bounds configuration in normalized parameter space.

  • bounds_auto – Bounds configuration in normalized parameter space.

  • bounds_delta – Bounds configuration in normalized parameter space.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

update_parameters_with_reml

gpmp.kernel.update_parameters_with_reml(model, xi=None, zi=None, dataloader=None, info=False, *, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Update covariance parameters with REML from current model parameters.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • bounds – Bounds configuration in normalized parameter space.

  • bounds_auto – Bounds configuration in normalized parameter space.

  • bounds_delta – Bounds configuration in normalized parameter space.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

select_parameters_with_remap

gpmp.kernel.select_parameters_with_remap(model, xi=None, zi=None, dataloader=None, covparam0=None, covparam0_init=None, info=False, verbosity=0, **kwargs)[source]

Alias of select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • covparam0 (array_like, optional) – Covariance parameters used to anchor prior hyperparameters.

  • covparam0_init (array_like, optional) – Initial covariance parameters for the optimizer. If None, covparam0 is used.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to the target function.

  • **kwargs – Additional keyword arguments forwarded to select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

update_parameters_with_remap

gpmp.kernel.update_parameters_with_remap(model, xi=None, zi=None, dataloader=None, info=False, verbosity=0, **kwargs)[source]

Alias of update_parameters_with_remap_gaussian_logsigma2_and_logrho_prior.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to the target function.

  • **kwargs – Additional keyword arguments forwarded to update_parameters_with_remap_gaussian_logsigma2_and_logrho_prior.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

select_parameters_with_remap_gaussian_logsigma2

gpmp.kernel.select_parameters_with_remap_gaussian_logsigma2(model, xi=None, zi=None, dataloader=None, covparam0=None, info=False, verbosity=0, *, covparam0_prior=None, prior_gamma=None, prior_sigma2_coverage=None, covparam0_init=None, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Select covariance parameters with REMAP and Gaussian prior on log(sigma^2).

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • covparam0 (array_like, optional) – Shared fallback covariance parameters. Used when one of covparam0_prior or covparam0_init is not provided.

  • covparam0_prior (array_like, optional) – Covariance parameters used to define the prior center prior_log_sigma2_0. If None, an anisotropic initial guess is computed.

  • covparam0_init (array_like, optional) – Initial covariance parameters for optimization. If None, covparam0 is used when provided; otherwise an anisotropic initial guess is computed.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to generic criterion selection.

  • prior_gamma (float, optional) – Multiplicative factor around sigma2_0 used for prior calibration. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • prior_sigma2_coverage (float, optional) – Central Gaussian probability mass assigned to [sigma2_0 / prior_gamma, sigma2_0 * prior_gamma]. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • bounds – Bounds configuration in normalized parameter space.

  • bounds_auto – Bounds configuration in normalized parameter space.

  • bounds_delta – Bounds configuration in normalized parameter space.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

Notes

The Gaussian prior center prior_log_sigma2_0 is taken from covparam0_prior[0].

update_parameters_with_remap_gaussian_logsigma2

gpmp.kernel.update_parameters_with_remap_gaussian_logsigma2(model, xi=None, zi=None, dataloader=None, info=False, verbosity=0, *, covparam0=None, covparam0_prior=None, covparam0_init=None, prior_gamma=None, prior_sigma2_coverage=None, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Update covariance parameters with REMAP and Gaussian prior on log(sigma^2).

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • covparam0 (array_like, optional) – Shared fallback covariance parameters. If provided without covparam0_prior, it is reused as prior anchor and a warning is emitted.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to the selector function.

  • covparam0_prior (array_like, optional) – Covariance parameters used to anchor prior hyperparameters. If None, covparam0 is used when provided; otherwise model.covparam is used when available; otherwise an anisotropic initial guess is used.

  • covparam0_init (array_like, optional) – Initial covariance parameters for optimization. If None, uses covparam0 when provided; otherwise falls back to model.covparam then an anisotropic initial guess.

  • prior_gamma (float, optional) – Multiplicative factor around sigma2_0 used for prior calibration. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • prior_sigma2_coverage (float, optional) – Central Gaussian probability mass assigned to [sigma2_0 / prior_gamma, sigma2_0 * prior_gamma]. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • bounds – Bounds configuration in normalized parameter space.

  • bounds_auto – Bounds configuration in normalized parameter space.

  • bounds_delta – Bounds configuration in normalized parameter space.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior

gpmp.kernel.select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior(model, xi=None, zi=None, dataloader=None, covparam0=None, info=False, verbosity=0, *, covparam0_prior=None, prior_gamma=None, prior_sigma2_coverage=None, prior_rho_min_range_factor=None, prior_logrho_min=None, prior_log_sigma2_0=None, prior_logrho_0=None, prior_alpha=None, covparam0_init=None, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Select covariance parameters with REMAP and priors on log(sigma^2) and logrho.

The optimized objective is a regularized REML criterion:

\[J(\theta) = -\log p(z \mid x, \theta)_{\mathrm{REML}} - \log p_{\sigma^2}(\theta) - \log p_{\rho}(\theta),\]

where theta = covparam, log(sigma^2)=covparam[0] and logrho=-covparam[1:].

log p_{\sigma^2} is Gaussian in log(sigma^2) and centered at prior_log_sigma2_0 inferred from covparam0_prior (or overridden by prior_log_sigma2_0 when provided). Its log-space standard deviation is calibrated from prior_gamma and prior_sigma2_coverage so that P(sigma2_0 / prior_gamma <= sigma^2 <= sigma2_0 * prior_gamma) = prior_sigma2_coverage.

log p_{\rho} is a barrier + linear-tail prior in logrho: componentwise support is logrho > prior_logrho_min, the minimum is at prior_logrho_0, and prior_alpha controls the right-tail linear slope.

When prior_logrho_min is not provided, it is inferred from observation points by combining a minimum-gap bound and a range-based safeguard controlled by prior_rho_min_range_factor.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • covparam0 (array_like, optional) – Shared fallback covariance parameters. Used when one of covparam0_prior or covparam0_init is not provided.

  • covparam0_prior (array_like, optional) – Covariance parameters used to anchor prior hyperparameters. If None, an anisotropic initial guess is computed.

  • covparam0_init (array_like, optional) – Initial covariance parameters for optimization. If None, covparam0 is used when provided; otherwise an anisotropic initial guess is computed.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to generic criterion selection.

  • prior_gamma (float, optional) – Multiplicative factor around sigma2_0 used for prior calibration. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • prior_sigma2_coverage (float, optional) – Central Gaussian probability mass assigned to [sigma2_0 / prior_gamma, sigma2_0 * prior_gamma]. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • prior_rho_min_range_factor (float, optional) – Safeguard factor used when prior_logrho_min is inferred from data. It defines the range-based candidate lower bound log(range(x[:, j]) * prior_rho_min_range_factor) is applied in addition to the minimum-gap bound. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • prior_logrho_min (array_like, optional) – Lower bounds for logrho prior support.

  • prior_log_sigma2_0 (float, optional) – Override for the Gaussian prior center on log(sigma^2). If None, covparam0_prior[0] is used.

  • prior_logrho_0 (array_like, optional) – Override reference values for logrho prior. If None, -covparam0_prior[1:] is used.

  • prior_alpha (float, optional) – Linear right-tail slope of the logrho barrier-linear prior. If None, the default configured in gpmp.kernel.prior_defaults is used.

  • bounds – Bounds configuration in normalized parameter space.

  • bounds_auto – Bounds configuration in normalized parameter space.

  • bounds_delta – Bounds configuration in normalized parameter space.

  • method ({"SLSQP", "L-BFGS-B"}, default="SLSQP") – Optimization method.

  • method_options (dict, optional) – Extra options passed to SciPy minimize.

Returns:

  • model (gpmp.core.Model) – Updated model.

  • info_ret (dict | None) – Diagnostics dictionary if info=True, else None.

Notes

covparam0 anchors prior hyperparameters by default. This behavior can be overridden by passing prior_log_sigma2_0 and/or prior_logrho_0 explicitly.

If prior_logrho_min is None, this function uses: - xi if provided, else - dataloader.dataset.x_list (when available). The inferred bound is the componentwise maximum of: log(min_nonzero_gap) and log(range * prior_rho_min_range_factor).

update_parameters_with_remap_gaussian_logsigma2_and_logrho_prior

gpmp.kernel.update_parameters_with_remap_gaussian_logsigma2_and_logrho_prior(model, xi=None, zi=None, dataloader=None, info=False, verbosity=0, *, covparam0=None, covparam0_prior=None, covparam0_init=None, prior_gamma=None, prior_sigma2_coverage=None, prior_rho_min_range_factor=None, prior_logrho_min=None, prior_log_sigma2_0=None, prior_logrho_0=None, prior_alpha=None, bounds=None, bounds_auto=True, bounds_delta=10.0, method='SLSQP', method_options=None)[source]

Update covariance parameters with REMAP and priors on log(sigma^2) and logrho.

Parameters:

  • model (gpmp.core.Model) – GP model instance.

  • xi (array_like, optional) – Observation arrays.

  • zi (array_like, optional) – Observation arrays.

  • dataloader (iterable, optional) – Batch loader alternative to xi, zi.

  • covparam0 (array_like, optional) – Shared fallback covariance parameters. If provided without covparam0_prior, it is reused as prior anchor and a warning is emitted.

  • info (bool, default=False) – If True, return optimization diagnostics.

  • verbosity (int, default=0) – Verbosity level forwarded to the selector function.

  • covparam0_prior (array_like, optional) – Covariance parameters used to anchor prior hyperparameters. If None, covparam0 is used when provided; otherwise model.covparam is used when available; otherwise an anisotropic initial guess is used.

  • covparam0_init (array_like, optional) – Initial covariance parameters for optimization. If None, uses covparam0 when provided; otherwise falls back to model.covparam then an anisotropic initial guess.

  • prior_gamma – Prior hyperparameters forwarded to select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior. Missing values are resolved from gpmp.kernel.prior_defaults.

  • prior_sigma2_coverage – Prior hyperparameters forwarded to select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior. Missing values are resolved from gpmp.kernel.prior_defaults.

  • prior_rho_min_range_factor – Prior hyperparameters forwarded to select_parameters_with_remap_gaussian_logsigma2_and_logrho_prior. Missing values are resolved from gpmp.kernel.prior_defaults.

  • prior_logrho_min – Optional prior overrides forwarded to the selector function.

  • prior_log_sigma2_0 – Optional prior overrides forwarded to the selector function.

  • prior_logrho_0 – Optional prior overrides forwarded to the selector function.

  • prior_alpha – Optional prior overrides forwarded to the selector function.

  • bounds – Optimization settings forwarded to the selector function.

  • bounds_auto – Optimization settings forwarded to the selector function.

  • bounds_delta – Optimization settings forwarded to the selector function.

  • method – Optimization settings forwarded to the selector function.

  • method_options – Optimization settings forwarded to the selector function.