pysindy.optimizers.SSR

class pysindy.optimizers.SSR(alpha=0.05, max_iter=20, ridge_kw=None, normalize_columns=False, copy_X=True, criteria='coefficient_value', kappa=None, verbose=False, unbias=True)[source]

Stepwise sparse regression (SSR) greedy algorithm.

Attempts to minimize the objective function \(\|y - Xw\|^2_2 + \alpha \|w\|^2_2\) by iteratively eliminating the smallest coefficient

See the following reference for more details:

Boninsegna, Lorenzo, Feliks Nüske, and Cecilia Clementi. “Sparse learning of stochastic dynamical equations.” The Journal of chemical physics 148.24 (2018): 241723.

Parameters:

  • max_iter (int, optional (default 20)) – Maximum iterations of the optimization algorithm.

  • normalize_columns (boolean, optional (default False)) – Normalize the columns of x (the SINDy library terms) before regression by dividing by the L2-norm. Note that the ‘normalize’ option in sklearn is deprecated in sklearn versions >= 1.0 and will be removed.

  • copy_X (boolean, optional (default True)) – If True, X will be copied; else, it may be overwritten.

  • kappa (float, optional (default None)) – If passed, compute the MSE errors with an extra L0 term with strength equal to kappa times the condition number of Theta.

  • criteria (string, optional (default "coefficient_value")) – The criteria to use for truncating a coefficient each iteration. Must be “coefficient_value” or “model_residual”. “coefficient_value”: zero out the smallest coefficient). “model_residual”: choose the N-1 term model with the smallest residual error.

  • alpha (float, optional (default 0.05)) – Optional L2 (ridge) regularization on the weight vector.

  • ridge_kw (dict, optional (default None)) – Optional keyword arguments to pass to the ridge regression.

  • verbose (bool, optional (default False)) – If True, prints out the different error terms every iteration.

Attributes:

  • coef_ (array, shape (n_features,) or (n_targets, n_features)) – Weight vector(s).

  • history_ (list) – History of coef_. history_[k] contains the values of coef_ at iteration k of SSR

  • err_history_ (list) – History of coef_. history_[k] contains the MSE of each coef_ at iteration k of SSR

Examples

>>> import numpy as np
>>> from scipy.integrate import odeint
>>> from pysindy import SINDy
>>> from pysindy.optimizers import SSR
>>> lorenz = lambda z,t : [10 * (z[1] - z[0]),
>>>                        z[0] * (28 - z[2]) - z[1],
>>>                        z[0] * z[1] - 8 / 3 * z[2]]
>>> t = np.arange(0, 2, .002)
>>> x = odeint(lorenz, [-8, 8, 27], t)
>>> opt = SSR(alpha=.5)
>>> model = SINDy(optimizer=opt)
>>> model.fit(x, t=t[1] - t[0])
>>> model.print()
x0' = -9.999 1 + 9.999 x0
x1' = 27.984 1 + -0.996 x0 + -1.000 1 x1
x2' = -2.666 x1 + 1.000 1 x0

Methods

set_fit_request

Configure whether metadata should be requested to be passed to the fit method.

set_score_request

Configure whether metadata should be requested to be passed to the score method.

Attributes

max_iter

normalize_columns

initial_guess

copy_X

unbias

coef_

intercept_

set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$', x_: bool | None | str = '$UNCHANGED$') → SSR

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to fit.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

  • sample_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in fit.

  • x (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for x_ parameter in fit.

Returns:

self – The updated object.

Return type:

object

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → SSR

Configure whether metadata should be requested to be passed to the score method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to score.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

sample_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in score.

Returns:

self – The updated object.

Return type:

object