Model containers

ModelContainer manages one or more independent gpmp.core.Model objects, one per output. It stores the mean and covariance callables, initial-guess procedure, selection criterion, selected parameter object, optimizer report, and underlying gpmp model for each output.

Per-output access

Use model[k] to inspect output k. The entry is an attribute-access dictionary. Main keys are:

• model[k]["model"]: underlying gpmp.core.Model.

• model[k]["param"] or model[k].get_param(): readable Param object.

• model[k]["selection_criterion"]: selection criterion used by optimization.

• model[k]["info"]: optimizer and criterion information after select_params.

• model[k]["prior"]: resolved prior object for classes using REMAP selection with priors.

Core object

class ModelContainer(name, output_dim, parameterized_mean, mean_specification, covariance_specification, initial_guess_procedures=None, selection_criteria=None)

Container for one or more gpmp.core.Model objects.

Direct construction requires mean specifications, covariance specifications, and usually subclass methods for building initial guesses, selection criteria, and parameter objects. Applications usually instantiate one of the provided Matérn container classes, such as Model_ConstantMean_Maternp_REML or Model_ConstantMean_Maternp_REMAP.

select_params(xi, zi, *, force_param_initial_guess=True, param0=None, use_bounds_from_param_obj=True, bounds=None, bounds_factory=None, bounds_delta=None, method='SLSQP', method_options=None, rebuild_selection_criterion=None)

Select parameters independently for each output.

xi has shape (n, d). zi has shape (n,) for one output or (n, output_dim) for several outputs. If param0 is provided, it is used as the optimizer start and force_param_initial_guess is ignored. If param0 is not provided, the method uses the configured initial guess procedure when force_param_initial_guess is true or when current parameters are missing.

Bounds are selected in this order: explicit bounds, then bounds_factory, then bounds from the parameter object when use_bounds_from_param_obj is true. bounds_delta intersects the chosen bounds with a local box around the optimizer start.

Stores, for each output k:

• model[k]["model"].covparam.

• model[k]["model"].meanparam when the mean is parameterized.

• model[k]["param"], a readable gpmp.parameter.Param object.

• model[k]["info"], the optimizer report and criterion callables.

• model[k]["prior"] for classes using REMAP selection with priors.

Raises ValueError for incompatible shapes, invalid bounds, missing observation data when a REMAP criterion needs observations, or missing per-output initialization values.

predict(xi, zi, xt, convert_in=True, convert_out=True)

Compute posterior means and variances at xt for all outputs. xi has shape (n, d), zi has shape (n,) or (n, output_dim), and xt has shape (m, d). Returns (zpm, zpv) with shape (m, output_dim). With convert_out=True, returned arrays are NumPy arrays. With convert_out=False, they are backend objects.

loo(xi, zi, convert_in=True, convert_out=True)

Compute leave-one-out predictions for all outputs. Returns (zloo, sigma2loo, eloo), each with shape (n, output_dim).

run_diagnosis(xi, zi)

Print per-output parameter-selection status, parameter values, and data summaries through gpmp.modeldiagnosis. Raises ValueError if select_params has not populated model[k]["info"].

run_perf(xi, zi, *, output_ind=None, loo=True, loo_res=None, xtzt=None, zpmzpv=None, convert_in=True)

Print prediction-performance summaries through gpmp.modeldiagnosis. If output_ind is None, reports all outputs. Otherwise, reports only the selected output.

loo=True enables leave-one-out metrics. loo_res may provide precomputed (zloom, zloov, eloo) arrays. xtzt provides test points and reference values as (xt, zt). zpmzpv may provide precomputed predictions as (zpm, zpv). For multi-output arrays, run_perf slices the second dimension for each output.

The printed metrics are tss, press, rss, rmse, rmse/std(z), Q2, and R2. Their definitions are given in Diagnostics and inspection.

compute_conditional_simulations(xi, zi, xt, n_samplepaths=1)

Draw conditional sample paths at xt. Returns shape (nt, n_samplepaths) for one output and (nt, n_samplepaths, output_dim) for several outputs.

sample_parameters(method='nuts', model_indices=None, init_box=None, sampling_box=None, **kwargs)

Sample covariance parameters from the stored selection criterion. Implemented public methods are "mh", "hmc", "nuts", and "smc". init_box initializes random starts or particles. sampling_box truncates the sampling domain. Points outside the box get log-probability -inf.

Requires select_params first, because the sampler uses model[k]["info"]. init_box is mandatory for method="smc". Returns a dictionary keyed by output index:

• "mh": {"samples", "mh", "criterion_values"}.

• "hmc" and "nuts": {"samples", "hmc"} or {"samples", "nuts"}.

• "smc": {"particles", "smc"}.

Backend conventions

ModelContainer converts inputs with gpmp.num.asarray when convert_in=True. Prediction, LOO, and conditional-simulation methods return NumPy arrays when convert_out=True and backend objects when convert_out=False. Optimizer reports and stored model parameters use backend objects.

Supporting objects

Gaussian Process Model Container

This module defines a ModelContainer object as a wrapper around the Model object in gpmp, simplifying the creation and management of Gaussian Process models. It provides tools for choosing the mean and covariance functions, and accommodates multiple outputs. The module supports parameter selection using user-provided methods (ML, REML…). It is used by SequentialPrediction and SequentialStrategy.

Author: Emmanuel Vazquez <emmanuel.vazquez@centralesupelec.fr> Copyright: 2022-2026, CentraleSupelec License: GPLv3 (refer to LICENSE file)

class gpmpcontrib.modelcontainer.AttrDict

Bases: dict

Dict with attribute access to keys (d.k <-> d[‘k’]).

Missing keys raise AttributeError.

class gpmpcontrib.modelcontainer.SelectionCriterionBuildContext(model, xi=None, zi=None)

Bases: object

Context passed when building a per-output selection criterion.

Parameters:

• model (object)

• xi (object)

• zi (object)

gpmpcontrib.modelcontainer.mean_linpred_constant(x, param)

Constant mean function for Gaussian Process models, linear predictor type. :param x: Input data points in dimension d. :type x: ndarray(n, d) :param param: Parameters of the mean function (unused in constant mean). :type param: ndarray

Returns:

Array of ones with shape (n, 1).

Return type:

ndarray

gpmpcontrib.modelcontainer.mean_linpred_linear(x, param)

Linear mean function for Gaussian Process models, linear predictor type. :param x: Input data points in dimension d. :type x: ndarray(n, d) :param param: Parameters of the mean function (unused in linear mean). :type param: ndarray

Returns:

Matrix [1, x_[1,1], …, x_[1, d]

1, x_[2,1], …, x_[2, d] … 1, x_[n,1], …, x_[n, d]] ]

Return type:

ndarray