IsotonicRegression

classsklearn.isotonic.IsotonicRegression(*, y_min=None, y_max=None, increasing=True, out_of_bounds='nan')[source]

Isotonic regression model.

Read more in the User Guide.

Added in version 0.13.

Parameters:

y_minfloat, default=None

Lower bound on the lowest predicted value (the minimum value may still be higher). If not set, defaults to -inf.

y_maxfloat, default=None

Upper bound on the highest predicted value (the maximum may still be lower). If not set, defaults to +inf.

increasingbool or ‘auto’, default=True

Determines whether the predictions should be constrained to increase or decrease with X. ‘auto’ will decide based on the Spearman correlation estimate’s sign.

out_of_bounds{‘nan’, ‘clip’, ‘raise’}, default=’nan’

Handles how X values outside of the training domain are handled during prediction.

• ‘nan’, predictions will be NaN.
• ‘clip’, predictions will be set to the value corresponding to the nearest train interval endpoint.
• ‘raise’, a ValueError is raised.

Attributes:

X_min_float

Minimum value of input array X_ for left bound.

X_max_float

Maximum value of input array X_ for right bound.

X_thresholds_ndarray of shape (n_thresholds,)

Unique ascending X values used to interpolate the y = f(X) monotonic function.

Added in version 0.24.

y_thresholds_ndarray of shape (n_thresholds,)

De-duplicated y values suitable to interpolate the y = f(X) monotonic function.

Added in version 0.24.

f_function

The stepwise interpolating function that covers the input domain X.

increasing_bool

Inferred value for increasing.

See also

sklearn.linear_model.LinearRegression

Ordinary least squares Linear Regression.

sklearn.ensemble.HistGradientBoostingRegressor

Gradient boosting that is a non-parametric model accepting monotonicity constraints.

isotonic_regression

Function to solve the isotonic regression model.

Notes

Ties are broken using the secondary method from de Leeuw, 1977.

References

Isotonic Median Regression: A Linear Programming Approach Nilotpal Chakravarti Mathematics of Operations Research Vol. 14, No. 2 (May, 1989), pp. 303-308

Isotone Optimization in R : Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods de Leeuw, Hornik, Mair Journal of Statistical Software 2009

Correctness of Kruskal’s algorithms for monotone regression with ties de Leeuw, Psychometrica, 1977

Examples

>>> from sklearn.datasets import make_regression
>>> from sklearn.isotonic import IsotonicRegression
>>> X, y = make_regression(n_samples=10, n_features=1, random_state=41)
>>> iso_reg = IsotonicRegression().fit(X, y)
>>> iso_reg.predict([.1, .2])
array([1.8628..., 3.7256...])

fit(X, y, sample_weight=None)[source]

Fit the model using X, y as training data.

Parameters:

Xarray-like of shape (n_samples,) or (n_samples, 1)

Training data.

Changed in version 0.24: Also accepts 2d array with 1 feature.

yarray-like of shape (n_samples,)

Training target.

sample_weightarray-like of shape (n_samples,), default=None

Weights. If set to None, all weights will be set to 1 (equal weights).

Returns:

selfobject

Returns an instance of self.

Notes

X is stored for future use, as transform needs X to interpolate new input data.

fit_transform(X, y=None, **fit_params)[source]

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns:

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

get_feature_names_out(input_features=None)[source]

Get output feature names for transformation.

Parameters:

input_featuresarray-like of str or None, default=None

Ignored.

Returns:

feature_names_outndarray of str objects

An ndarray with one string i.e. [“isotonicregression0”].

get_metadata_routing()[source]

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

predict(T)[source]

Predict new data by linear interpolation.

Parameters:

Tarray-like of shape (n_samples,) or (n_samples, 1)

Data to transform.

Returns:

y_predndarray of shape (n_samples,)

Transformed data.

score(X, y, sample_weight=None)[source]

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:

Xarray-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.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:

scorefloat

\(R^2\) of self.predict(X) w.r.t. y.

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_fit_request(*, sample_weight:bool|None|str='$UNCHANGED$') → IsotonicRegression[source]

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see 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.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in fit.

Returns:

selfobject

The updated object.

set_output(*, transform=None)[source]

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:

transform{“default”, “pandas”, “polars”}, default=None

Configure output of transform and fit_transform.

• "default": Default output format of a transformer
• "pandas": DataFrame output
• "polars": Polars output
• None: Transform configuration is unchanged

Added in version 1.4: "polars" option was added.

Returns:

selfestimator instance

Estimator instance.

set_params(**params)[source]

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:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

set_score_request(*, sample_weight:bool|None|str='$UNCHANGED$') → IsotonicRegression[source]

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see 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.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in score.

Returns:

selfobject

The updated object.

transform(T)[source]

Transform new data by linear interpolation.

Parameters:

Tarray-like of shape (n_samples,) or (n_samples, 1)

Data to transform.

Changed in version 0.24: Also accepts 2d array with 1 feature.

Returns:

y_predndarray of shape (n_samples,)

The transformed data.

Gallery examples

Isotonic Regression