ExtraTreesQuantileRegressor#

class quantile_forest.ExtraTreesQuantileRegressor(n_estimators=100, *, default_quantiles=0.5, criterion='squared_error', max_depth=None, min_samples_split=2, min_samples_leaf=1, max_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features=1.0, max_leaf_nodes=None, min_impurity_decrease=0.0, bootstrap=False, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, ccp_alpha=0.0, max_samples=None, monotonic_cst=None)#

An extra-trees regressor that provides quantile estimates.

A quantile extra trees regressor is a meta estimator that fits a number of randomized decision trees (a.k.a. extra-trees) on various sub-samples of the dataset, keeps the values of samples that reach each node, and assesses the conditional distribution based on this information [1]. The leaf-sample size is controlled with the max_samples_leaf parameter.

Parameters:

n_estimatorsint, default=100

The number of trees in the forest.

default_quantilesfloat, list, or “mean”, default=0.5

The default quantile or list of quantiles that the model tries to predict. Each quantile must be strictly between 0 and 1. If “mean”, the model predicts the mean.

Added in version 1.2.

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_depthint, 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_splitint 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_leafint 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.

max_samples_leafint, float or None, default=1

The maximum number of samples permitted to be at a leaf node.

If int, then consider max_samples_leaf as the maximum number.
If float, then max_samples_leaf is a fraction and ceil(max_samples_leaf * n_samples) are the maximum number of samples for each node.
If None, then unlimited number of leaf samples.

min_weight_fraction_leaffloat, 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.

Changed in scikit-learn version 1.1: The default of max_features changed from "auto" to 1.0.

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_nodesint, 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_decreasefloat, 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.

bootstrapbool, default=False

Whether bootstrap samples are used when building trees. If False, the whole dataset is used to build each tree.

oob_scorebool or callable, default=False

Whether to use out-of-bag samples to estimate the generalization score. By default, 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_jobsint, 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_stateint, RandomState instance or None, default=None

Controls 3 sources of randomness:

the bootstrapping of the samples used when building trees (if bootstrap=True)
the sampling of the features to consider when looking for the best split at each node (if max_features < n_features)
the draw of the splits for each of the max_features

verboseint, default=0

Controls the verbosity when fitting and predicting.

warm_startbool, 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_alphanon-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.

max_samplesint 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_samples * X.shape[0] samples. Thus, max_samples should be in the interval (0.0, 1.0].

monotonic_cstarray-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:

multioutput regressions (i.e. when n_outputs_ > 1),
regressions trained on data with missing values,
trees with multi-sample leaves (i.e. when max_samples_leaf > 1).

Attributes:

estimator_ExtraTreeRegressor: The child estimator template used to create the collection of fitted sub-estimators.
estimators_list of DecisionTreeRegressor: The collection of fitted sub-estimators.
feature_importances_ndarray of shape (n_features,): The impurity-based feature importances.
n_features_in_int: Number of features seen during fit.
feature_names_in_ndarray of shape (n_features_in_,): Names of features seen during fit. Defined only when X has feature names that are all strings.
n_outputs_int: The number of outputs.
oob_score_float: Score of the training dataset obtained using an out-of-bag estimate. This attribute exists only when oob_score is True.
oob_prediction_ndarray of shape (n_samples,) or (n_samples, n_outputs): Prediction computed with out-of-bag estimate on the training set. This attribute exists only when oob_score is True.
estimators_samples_list of arrays: The subset of drawn samples for each base estimator.

See also

RandomForestQuantileRegressor: Quantile ensemble regressor using trees.

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

References

[1]

N. Meinshausen, “Quantile Regression Forests”, Journal of Machine Learning Research, 7(Jun), 983-999, 2006. http://www.jmlr.org/papers/volume7/meinshausen06a/meinshausen06a.pdf

[2]

P. Geurts, D. Ernst., and L. Wehenkel, “Extremely Randomized Trees”, Machine Learning, 63(1), 3-42, 2006.

Examples

>>> from quantile_forest import ExtraTreesQuantileRegressor
>>> from sklearn.datasets import fetch_california_housing
>>> X, y = fetch_california_housing(return_X_y=True)
>>> qrf = ExtraTreesQuantileRegressor(random_state=0)
>>> qrf.fit(X[:1000], y[:1000])
ExtraTreesQuantileRegressor(random_state=0)
>>> qrf.score(X, y, quantiles=0.5)
0.3...

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[, sample_weight, sparse_pickle])	Build a forest from the training set (X, y).
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X[, quantiles, interpolation, ...])	Predict quantiles for X.
`proximity_counts`(X[, max_proximities, ...])	Return training proximity counts for input samples.
`quantile_ranks`(X, y[, kind, ...])	Return quantile ranks for X with scores y.
`score`(X, y[, quantiles, sample_weight])	Return the coefficient of determination R^2 of the prediction.
`set_fit_request`(*[, sample_weight, ...])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.
`set_predict_request`(*[, ...])	Request metadata passed to the `predict` method.
`set_score_request`(*[, quantiles, sample_weight])	Request metadata passed to the `score` method.

apply(X)#

Apply trees in the forest to X, return leaf indices.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, its dtype will be converted to dtype=np.float32. If a sparse matrix is provided, it will be converted into a sparse csr_matrix.

Returns:

X_leavesndarray of shape (n_samples, n_estimators): For each datapoint x in X and for each tree in the forest, return the index of the leaf x ends up in.

decision_path(X)#

Return the decision path in the forest.

Added in version 0.18.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, its dtype will be converted to dtype=np.float32. If a sparse matrix is provided, it will be converted into a sparse csr_matrix.

Returns:

indicatorsparse matrix of shape (n_samples, n_nodes): Return a node indicator matrix where non zero elements indicates that the samples goes through the nodes. The matrix is of CSR format.
n_nodes_ptrndarray of shape (n_estimators + 1,): The columns from indicator[n_nodes_ptr[i]:n_nodes_ptr[i+1]] gives the indicator value for the i-th estimator.

property estimators_samples_#

The subset of drawn samples for each base estimator.

Returns a dynamically generated list of indices identifying the samples used for fitting each member of the ensemble, i.e., the in-bag samples.

Note: the list is re-created at each call to the property in order to reduce the object memory footprint by not storing the sampling data. Thus fetching the property may be slower than expected.

property 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.

Returns:

feature_importances_ndarray of shape (n_features,): The values of this array sum to 1, unless all trees are single node trees consisting of only the root node, in which case it will be an array of zeros.

fit(X, y, sample_weight=None, sparse_pickle=False)#

Build a forest from the training set (X, y).

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The training input samples. Internally, its dtype will be converted to dtype=np.float32. If a sparse matrix is provided, it will be converted into a sparse csc_matrix.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): The target values (real numbers).
sample_weightarray-like of shape (n_samples,), default=None: Sample weights. If None, then samples are equally weighted. Splits that would create child nodes with net zero or negative weight are ignored while searching for a split in each node.
sparse_picklebool, default=False: Pickle the underlying data structure using a SciPy sparse matrix.

Returns:

selfobject: Fitted estimator.

get_metadata_routing()#

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)#

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(X, quantiles=None, interpolation='linear', weighted_quantile=True, weighted_leaves=False, aggregate_leaves_first=True, oob_score=False, indices=None, duplicates=None)#

Predict quantiles for X.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

The input samples. Internally, its dtype will be converted to dtype=np.float32. If a sparse matrix is provided, it will be converted into a sparse csr_matrix.

quantilesfloat, list, or “mean”, default=None

The quantile or list of quantiles that the model tries to predict. Each quantile must be strictly between 0 and 1. If “mean”, the model predicts the mean. If None, the model uses the value of default_quantiles.

interpolation{“linear”, “lower”, “higher”, “midpoint”, “nearest”}, default=”linear”

Specifies the interpolation method to use when the desired quantile lies between two data points i < j:

If “linear”, then i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.
If “lower”, then i.
If “higher”, then j.
If “nearest”, then i or j, whichever is nearest.
If “midpoint”, then (i + j) / 2.

Note

When max_samples_leaf=1, the specific interpolation options will depend on those available in the NumPy quantile and nanquantile methods.

weighted_quantilebool, default=True

Calculate a weighted quantile. Weighted quantiles are computed by assigning weights to each training sample, while unweighted quantiles are computed by aggregating sibling samples. When the number of training samples relative to siblings is small, weighted quantiles can be more efficient to compute than unweighted ones.

weighted_leavesbool, default=False

Weight samples inversely to the size of their leaf node. Only used if weighted_quantile=True and max_samples_leaf!=1.

aggregate_leaves_firstbool, default=True

Calculate predictions using aggregated leaf values. If True, a single prediction is calculated over the aggregated leaf values. If False, a prediction is calculated for each leaf and aggregated.

oob_scorebool, default=False

Only use out-of-bag (OOB) samples to predict quantiles.

Returns:

y_predarray of shape (n_samples,) or (n_samples, n_quantiles) or (n_samples, n_outputs, n_quantiles): If quantiles is set to ‘mean’, then return E(Y | X). Else, for all quantiles, return y at q for which F(Y=y|x) = q, where q is the quantile.

Other Parameters:

indiceslist, default=None: List of training indices that correspond to X indices. An index of -1 can be used to specify rows omitted from the training set. By default, assumes all X indices correspond to all training indices. Only used if oob_score=True.
duplicateslist of lists, default=None: List of sets of functionally identical indices. Only used if oob_score=True.

proximity_counts(X, max_proximities=None, return_sorted=True, oob_score=False, indices=None, duplicates=None)#

Return training proximity counts for input samples.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, its dtype will be converted to dtype=np.float32. If a sparse matrix is provided, it will be converted into a sparse csr_matrix.
max_proximitiesint, default=None: Maximum number of proximities to return for each scoring sample, prioritized by proximity count. By default, return all proximity counts for each sample.
return_sortedbool, default=True: For each sample, sort its proximity counts in descending order. If False, the proximities will be returned in arbitrary order.
oob_scorebool, default=False: Only use out-of-bag (OOB) samples to generate proximity counts.

Returns:

proximitieslist of tuples, length = n_samples: List of tuples mapping training sample indices to proximity counts.

Other Parameters:

indiceslist, default=None: List of training indices that correspond to X indices. An index of -1 can be used to specify rows omitted from the training set. By default, assumes all X indices correspond to all training indices. Only used if oob_score=True.
duplicateslist of lists, default=None: List of sets of functionally identical indices. Only used if oob_score=True.

Notes

For details on the calculation and use of random forest proximities:

https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm#prox

quantile_ranks(X, y, kind='rank', aggregate_leaves_first=True, oob_score=False, indices=None, duplicates=None)#

Return quantile ranks for X with scores y.

A quantile rank of, for example, 0.8 means that 80% of the scores in the frequency distribution of the inputs are below the given score.

In the case of gaps or ties, the exact definition depends on the optional keyword kind.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

The input samples. Internally, its dtype will be converted to dtype=np.float32. If a sparse matrix is provided, it will be converted into a sparse csr_matrix.

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

The target values for which to calculate ranks.

kind{“rank”, “weak”, “strict”, “mean”}, default=”rank”

Specifies the interpretation of the resulting score:

If “rank”, then average percentage ranking of score. If multiple matches, average the percentage rankings of all matching scores.
If “weak”, then only values that are less than or equal to the provided score are counted. Corresponds to the definition of a cumulative distribution function.
If “strict”, then similar to “weak”, except that only values that are strictly less than the provided score are counted.
If “mean”, then the average of the “weak” and “strict” scores.

aggregate_leaves_firstbool, default=True

Calculate quantile ranks using aggregated leaf values. If True, a single rank is calculated over the aggregated leaf values. If False, a rank is calculated for each leaf and aggregated.

oob_scorebool, default=False

Only use out-of-bag (OOB) samples to predict quantile ranks.

Returns:

y_ranksarray of shape (n_samples,) or (n_samples, n_outputs): Quantile ranks in range [0, 1].

Other Parameters:

indiceslist, default=None: List of training indices that correspond to X indices. An index of -1 can be used to specify rows omitted from the training set. By default, assumes all X indices correspond to all training indices. Only used if oob_score=True.
duplicateslist, default=None: List of sets of functionally identical indices. Only used if oob_score=True.

score(X, y, quantiles=0.5, sample_weight=None)#

Return the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - 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.
quantilesfloat or list, default=0.5: The quantile or list of quantiles that the model tries to predict.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns:

scorefloat: $R^2$ of self.predict(X) wrt. y.

set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$', sparse_pickle: bool | None | str = '$UNCHANGED$') → ExtraTreesQuantileRegressor#

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.
sparse_picklestr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sparse_pickle parameter in fit.

Returns:

selfobject: The updated object.

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:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

Request metadata passed to the predict 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 predict 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 predict.
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:

aggregate_leaves_firststr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for aggregate_leaves_first parameter in predict.
duplicatesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for duplicates parameter in predict.
indicesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for indices parameter in predict.
interpolationstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for interpolation parameter in predict.
oob_scorestr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for oob_score parameter in predict.
quantilesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for quantiles parameter in predict.
weighted_leavesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for weighted_leaves parameter in predict.
weighted_quantilestr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for weighted_quantile parameter in predict.

Returns:

selfobject: The updated object.

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

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:

quantilesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for quantiles parameter in score.
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.