CoverForestRegressor

class coverforest.CoverForestRegressor(n_estimators=5, *, method='cv', cv=5, alpha_default=None, n_forests_per_fold=1, resample_n_estimators=True, criterion='squared_error', max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features='sqrt', max_leaf_nodes=None, min_impurity_decrease=0.0, max_samples=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, ccp_alpha=0.0, monotonic_cst=None)

A conformal random forest regressor.

This class provides an implementation of conformal random forest for prediction intervals that contain the true target value with probability above 1-alpha, where alpha is a user-specified error rate.

The class supports three subsampling methods for out-of-sample calibration:

• ‘cv’: Uses K-fold cross-validation to split the training set. This method is referred to as CV+.

• ‘bootstrap’: Uses bootstrap subsampling on the training set. This method is referred to as Jackknife+-after-Bootstrap.

• ‘split’: Uses train-test split on the training set. This method is referred to as split conformal.

The Jackknife+-after-bootstrap implementation (method='bootstrap') follows [5] Specifically, before fitting, the number of sub-estimators is resampled from the binomial distribution: Binomial(n_estimators / p, p) where

p = 1 / (1 - n_samples)**max_samples.

To fit the model with exactly n_estimators number of sub-estimators, initiate the model with resample_n_estimators=False.

Parameters:

• n_estimators (int, default=10) – The number of sklearn.tree.DecisionTreeClassifier in the forest.

• method ({'cv', 'bootstrap', 'split'}, default='cv') –

  The conformal prediction method to use:

  • ’cv’: Uses CV+ for conformal prediction

  • ’bootstrap’: Uses Jackknife+-after-Bootstrap

  • ’split’: Uses split conformal prediction

• cv (int or cross-validation generator, default=5) – Used when method='cv'. If an integer is provided, then it is the number of folds used. See the module sklearn.model_selection module for the list of possible cross-validation objects.

• alpha_default (float, default=None) – The default value of miscoverage rate alpha that will be passed to predict() whenever it is called indirectly i.e. via scikit-learn’s GridSearchCV.

• n_forests_per_fold (int, default=1) – Used when method='cv'. The number of the forests to be fitted on each combination of K-1 folds.

• resample_n_estimators (bool, default=True) – Used when method='bootstrap'. If True, resample the value of n_estimators following the procedure in Kim, Xu & Barber (2020). Specifically, a new number of estimators is sampled from Binomial(n_estimators / p, p) where p = 1 / (1 - n_samples)**max_samples.

• criterion ({"squared_error", "absolute_error", "friedman_mse", "poisson"}, default="squared_error") – The function to measure the quality of a split. Supported criteria are “squared_error” for the mean squared error, which is equal to variance reduction as feature selection criterion and minimizes the L2 loss using the mean of each terminal node, “friedman_mse”, which uses mean squared error with Friedman’s improvement score for potential splits, “absolute_error” for the mean absolute error, which minimizes the L1 loss using the median of each terminal node, and “poisson” which uses reduction in Poisson deviance to find splits. Training using “absolute_error” is significantly slower than when using “squared_error”.

• max_depth (int, default=None) – The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.

• min_samples_split (int or float, default=2) –

  The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.

  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

• min_samples_leaf (int or float, default=1) –

  The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.

  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

• min_weight_fraction_leaf (float, default=0.0) – The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.

• max_features ({"sqrt", "log2", None}, int or float, default=1.0) –

  The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.

  • If float, then max_features is a fraction and max(1, int(max_features * n_features_in_)) features are considered at each split.

  • If “sqrt”, then max_features=sqrt(n_features).

  • If “log2”, then max_features=log2(n_features).

  • If None or 1.0, then max_features=n_features.

  Note

  The default of 1.0 is equivalent to bagged trees and more randomness can be achieved by setting smaller values, e.g. 0.3.

  Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

• max_leaf_nodes (int, default=None) – Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.

• min_impurity_decrease (float, default=0.0) –

  A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

  The weighted impurity decrease equation is the following:

  N_t / N * (impurity - N_t_R / N_t * right_impurity
                      - N_t_L / N_t * left_impurity)
  

  where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

  N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

• max_samples (int or float, default=None) –

  If bootstrap is True, the number of samples to draw from X to train each base estimator.

  • If None (default), then draw X.shape[0] samples.

  • If int, then draw max_samples samples.

  • If float, then draw max(round(n_samples * max_samples), 1) samples.

  Thus, max_samples should be in the interval (0.0, 1.0]. When method='cv', the value will be passed on to the FastRandomForestClassifier sub-estimators.

• bootstrap (bool, default=True) – Whether bootstrap samples are used when building trees. If False, the whole dataset is used to build each tree. When method='cv', the value will be passed on to the FastRandomForestClassifier sub-estimators.

• oob_score (bool or callable, default=False) – Whether to use out-of-bag samples to estimate the generalization score. By default, sklearn.metrics.r2_score is used. Provide a callable with signature metric(y_true, y_pred) to use a custom metric. Only available if bootstrap=True.

• n_jobs (int, default=None) – The number of jobs to run in parallel. fit, predict, decision_path and apply are all parallelized over the trees. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors.

• random_state (int, RandomState instance or None, default=None) – Controls both the randomness of the bootstrapping of the samples used when building trees (if bootstrap=True) and the sampling of the features to consider when looking for the best split at each node (if max_features < n_features).

• verbose (int, default=0) – Controls the verbosity when fitting and predicting.

• warm_start (bool, default=False) – When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest.

• ccp_alpha (non-negative float, default=0.0) – Complexity parameter used for Minimal Cost-Complexity Pruning. The subtree with the largest cost complexity that is smaller than ccp_alpha will be chosen. By default, no pruning is performed.

• monotonic_cst (array-like of int of shape (n_features), default=None) –

  Indicates the monotonicity constraint to enforce on each feature.

  • 1: monotonically increasing

  • 0: no constraint

  • -1: monotonically decreasing

  If monotonic_cst is None, no constraints are applied.

  Monotonicity constraints are not supported for regressions trained on data with missing values.

estimator_

The child estimator template used to create the collection of fitted sub-estimators. It will be a FastRandomForestClassifier if method='cv' and sklearn.tree.DecisionTreeRegressor otherwise.

Type:

FastRandomForestClassifier or sklearn.tree.DecisionTreeRegressor

estimators_

The collection of fitted sub-estimators. A list of FastRandomForestClassifier if method='cv' and a list of sklearn.tree.DecisionTreeRegressor otherwise.

Type:

list of FastRandomForestRegressor or sklearn.tree.DecisionTreeRegressor

oob_pred_

The out-of-bag predictions on the training data.

Type:

ndarray of shape (n_samples,)

residuals_

The out-of-bag residuals on the training data.

Type:

ndarray of shape (n_samples,)

feature_importances_

The impurity-based feature importances. The higher, the more important the feature. The importance of a feature is computed as the (normalized) total reduction of the criterion brought by that feature. It is also known as the Gini importance.

Warning: impurity-based feature importances can be misleading for high cardinality features (many unique values). See sklearn.inspection.permutation_importance() as an alternative.

Type:

ndarray of shape (n_features,)

n_features_in_

Number of features seen during fit.

Type:

int

feature_names_in_

Names of features seen during fit. Defined only when X has feature names that are all strings.

Type:

ndarray of shape (n_features_in_,)

n_outputs_

The number of outputs when fit is performed.

Type:

int

oob_score_

Score of the training dataset obtained using an out-of-bag estimate. This attribute exists only when oob_score is True.

Type:

float

oob_prediction_

Prediction computed with out-of-bag estimate on the training set. This attribute exists only when oob_score is True.

Type:

ndarray of shape (n_samples,) or (n_samples, n_outputs)

estimators_samples_

The subset of drawn samples (i.e., the in-bag samples) for each base estimator. Each subset is defined by an array of the indices selected.

Type:

list of arrays

See also

CoverForestClassifier

A conformal random forest for classification tasks.

sklearn.ensemble.RandomForestRegressor

The standard random forest regressor from scikit-learn.

Notes

The conformal prediction with K-fold cross-validation (CV+) method was proposed by Romano, Sesia & Candès (2020). The conformal prediction with bootstrap subsampling (Jackknife+-after-Bootstrap) was proposed by Kim, Xu & Barber (2020).

References

[1]

Leo Breiman, “Random Forests”, Machine Learning, 45(1), 5-32, 2001.

[2]

Vladimir Vovk, Ilia Nouretdinov, Valery Manokhin & Alexander Gammerman, “Cross-conformal predictive distributions”, 37-51, COPA 2018.

[3]

Rina Foygel Barber, Emmanuel J. Candès, Aaditya Ramdas & Ryan J. Tibshirani, “Predictive inference with the jackknife+”, Ann. Statist. 49 (1) 486-507, 2021.

[4]

Byol Kim, Chen Xu, Rina Foygel Barber, “Predictive inference is free with the jackknife+-after-bootstrap”, NeurIPS 2020.

Examples

>>> from coverforest import CoverForestRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_samples=200, n_features=4, n_informative=2,
...                        random_state=0, shuffle=False)
>>> regr = CoverForestRegressor(n_estimators=10, method='cv', random_state=0)
>>> regr.fit(X, y)
CoverForestRegressor(...)
>>> print(regr.predict([[0, 0, 0, 0]]))
(array([13.14530751]), array([[-44.87496872,  73.12034704]]))

Methods

apply(X)	Apply trees in the forest to X, return leaf indices.
decision_path(X)	Return the decision path in the forest.
fit(X, y[, alpha, calib_size, sample_weight])	Fit the conformal forest regressor.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
predict(X[, alpha, num_threads])	Predict regression values and prediction intervals for X.
score(X, y[, alpha, scoring, sample_weight])	Evaluate the prediction intervals on the given test data and labels.
set_fit_request(*[, alpha, calib_size, ...])	Request metadata passed to the fit method.
set_params(**params)	Set the parameters of this estimator.
set_predict_request(*[, alpha, num_threads])	Request metadata passed to the predict method.
set_score_request(*[, alpha, sample_weight, ...])	Request metadata passed to the score method.