Estimation Class#

class regmmd.estimation.MMDEstimator(model, par_v=None, par_c=None, kernel='Gaussian', bandwidth='auto', solver=None, random_state=None)[source]#

Bases: BaseEstimator

Estimator using the Maximum Mean Discrepancy criterion.

Maximum Mean Discrepancy (MMD) is a kernel-based statistical test used to compare two probability distributions. This estimator fits a parametric model by minimizing the MMD between the empirical distribution of the observed data and the model distribution.

Depending on the type of model provided, the estimator will use either an exact gradient descent procedure (for GaussianLoc) or a stochastic gradient descent approach for general models.

Parameters:

  • model (EstimationModel) – The parametric estimation model to be fitted, provided as an instance of EstimationModel. This model defines the distributional form assumed for the data and exposes an _init_params method used to initialise parameters before optimisation.

  • par_v (float, optional) – Initial value for the variable parameters of the model. If None, it will be initialised automatically by the model’s _init_params method when fit() is called.

  • par_c (float, optional) – Initial value for the constant parameters of the model. If None, it will be initialised automatically by the model’s _init_params method when fit() is called.

  • kernel (str, default="Gaussian") – The kernel function used to compute the MMD. Currently supports "Gaussian", "Laplace" or "Cauchy".

  • bandwidth (str or float, default="auto") – The bandwidth of the kernel. If set to "auto", the bandwidth is selected automatically using a heuristic method such as the median heuristic.

  • solver (dict, optional) –

    A dictionary specifying the solver parameters for the optimisation procedure. Expected keys are:

    • "burnin" (int): Number of burn-in steps before recording results.

    • "n_step" (int): Total number of optimisation steps.

    • "stepsize" (float): Learning rate for gradient updates.

    • "epsilon" (float): Convergence tolerance or regularisation term.

    If None, solver settings must be provided before calling fit().

  • random_state (int, optional) – random seed to be passed to the model and any sampler used in the SGD optimizers.

par_v[source]#

The variable parameter, updated with the optimised value after fitting.

Type:

float

par_c[source]#

The constant parameter, not updated with the optimised value after fitting.

Type:

float

Notes

  • For GaussianLoc models, an exact gradient descent routine (_gd_gaussian_loc_exact_estimation) can be used, when the kernel is "Gaussian" as wellduring fitting.

  • For all other models, a stochastic gradient descent routine (_sgd_estimation) is applied instead.

fit(X)[source]#

Fit the MMD estimation model according to the given training data.

Parameters:

X (np.ndarray, shape (n_samples, n_features)) – Training input samples.

Returns:

res – A dictionary containing the results of the optimization process, including the estimated parameters and the optimization trajectory.

Return type:

MMDResult