class STLSQ¶

class deeptime.sindy.STLSQ(threshold=0.1, alpha=0.05, max_iter=20, ridge_kw=None, normalize=False, fit_intercept=False, copy_X=True)¶

Sequentially thresholded least squares algorithm.

Attempts to minimize the objective function \(\|y - Xw\|^2_2 + \alpha \|w\|^2_2\) by iteratively performing least squares and masking out elements of the weight that are below a given threshold.

See this paper for more details [1].

Parameters:

threshold (float, optional, default=0.1) – Minimum magnitude for a coefficient in the weight vector. Coefficients with magnitude below the threshold are set to zero.
alpha (float, optional, default=0.05) – Optional L2 (ridge) regularization on the weight vector.
max_iter (int, optional, default=20) – Maximum iterations of the optimization algorithm.
ridge_kw (dict, optional, default=None) – Optional keyword arguments to pass to the ridge regression.
fit_intercept (boolean, optional, default=False) – Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations.
normalize (boolean, optional, default=False) – This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm.
copy_X (boolean, optional, default=True) – If True, X will be copied; else, it may be overwritten.

References

Methods

`fit`(x_, y)	Fit to the data.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X)	Predict using the linear model.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

fit(x_, y)¶

Fit to the data.

Parameters:

x (array-like, shape (n_samples, n_features)) – Training data (\(X\) in the above equation).
y (array-like, shape (n_samples,) or (n_samples, n_targets)) – Target values (\(y\) in the above equation).

Returns:

self – Reference to self

Return type:

STLSQ

get_params(deep=True)¶

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

predict(X)¶

Predict using the linear model.

Parameters:: X (array-like or sparse matrix, shape (n_samples, n_features)) – Samples.
Returns:: C – Returns predicted values.
Return type:: array, shape (n_samples,)

score(X, y, sample_weight=None)¶

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters:

X (array-like of shape (n_samples, n_features)) – Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.
sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns:

score – \(R^2\) of self.predict(X) wrt. y.

Return type:

float

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params)¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance