pysindy.optimizers.MIOSR

class pysindy.optimizers.MIOSR(target_sparsity=5, group_sparsity=None, alpha=0.01, regression_timeout=10, constraint_lhs=None, constraint_rhs=None, constraint_order='target', normalize_columns=False, copy_X=True, initial_guess=None, verbose=False, unbias=False)[source]

Mixed-Integer Optimized Sparse Regression.

Solves the sparsity constrained regression problem to provable optimality .. math:

\|y-Xw\|^2_2 + \lambda R(u)
\[\text{subject to } \|w\|_0 \leq k\]

by using type-1 specially ordered sets (SOS1) to encode the support of the coefficients. Can optionally add additional constraints on the coefficients or access the gurobi model directly for advanced usage. See the following reference for additional details:

Bertsimas, D. and Gurnee, W., 2022. Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization. arXiv preprint arXiv:2206.00176.

Parameters:

  • target_sparsity (int, optional (default 5)) – The maximum number of nonzero coefficients across all dimensions. If set, the model will fit all dimensions jointly, potentially reducing statistical efficiency.

  • group_sparsity (int tuple, optional (default None)) – Tuple of length n_targets constraining the number of nonzero coefficients for each target dimension.

  • alpha (float, optional (default 0.01)) – Optional L2 (ridge) regularization on the weight vector.

  • regression_timeout (int, optional (default 10)) – The timeout (in seconds) of the gurobi optimizer to solve and prove optimality (either per dimension or jointly depending on the above sparsity settings).

  • constraint_lhs (numpy ndarray, optional (default None)) – Shape should be (n_constraints, n_features * n_targets), The left hand side matrix C of Cw <= d. There should be one row per constraint.

  • constraint_rhs (numpy ndarray, shape (n_constraints,), optional (default None)) – The right hand side vector d of Cw <= d.

  • constraint_order (string, optional (default "target")) – The format in which the constraints constraint_lhs were passed. Must be one of “target” or “feature”. “target” indicates that the constraints are grouped by target: i.e. the first n_features columns correspond to constraint coefficients on the library features for the first target (variable), the next n_features columns to the library features for the second target (variable), and so on. “feature” indicates that the constraints are grouped by library feature: the first n_targets columns correspond to the first library feature, the next n_targets columns to the second library feature, and so on.

  • 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. Note that this parameter is incompatible with the constraints!

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

  • initial_guess (np.ndarray, shape (n_features) or (n_targets, n_features), optional (default None)) – Initial guess for coefficients coef_ to warmstart the optimizer.

  • verbose (bool, optional (default False)) – If True, prints out the Gurobi solver log.

  • unbias (bool) – Required to be false, maintained for supertype compatibility

Attributes:

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

  • ind_ (array, shape (n_features,) or (n_targets, n_features)) – Array of 0s and 1s indicating which coefficients of the weight vector have not been masked out, i.e. the support of self.coef_.

  • model (gurobipy.model) – The raw gurobi model being solved.

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

complexity

max_iter

normalize_columns

initial_guess

copy_X

unbias

coef_

intercept_

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

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 = '$UNCHANGED$') → MIOSR

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