`treeple`.ObliqueRandomForestRegressor#

class treeple.ObliqueRandomForestRegressor(n_estimators=100, *, criterion='squared_error', max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features=1.0, max_leaf_nodes=None, min_impurity_decrease=0.0, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, max_samples=None, feature_combinations=None)[source]#

An oblique random forest regressor.

A oblique random forest is a meta estimator similar to a random forest that fits a number of oblique decision tree regressor on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting.

The sub-sample size is controlled with the max_samples parameter if bootstrap=True (default), otherwise the whole dataset is used to build each tree.

Read more in the User Guide.

Parameters:

n_estimatorsint, default=100

The number of trees in the forest.

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.

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=”sqrt”

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 round(max_features * n_features) features are considered at each split.
If “auto”, then max_features=sqrt(n_features).
If “sqrt”, then max_features=sqrt(n_features).
If “log2”, then max_features=log2(n_features).
If None, then max_features=n_features.

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=True

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

oob_scorebool, default=False

Whether to use out-of-bag samples to estimate the generalization score. 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. See Glossary for more details.

random_stateint, 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). See Glossary for details.

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. See the Glossary.

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].

feature_combinationsfloat, default=None

The number of features to combine on average at each split of the decision trees. If None, then will default to the minimum of (1.5, n_features). This controls the number of non-zeros is the projection matrix. Setting the value to 1.0 is equivalent to a traditional decision-tree. feature_combinations * max_features gives the number of expected non-zeros in the projection matrix of shape (max_features, n_features). Thus this value must always be less than n_features in order to be valid.

Attributes:

estimators_list of ObliqueDecisionTreeRegressor: The collection of fitted sub-estimators.
n_features_int: The number of features when fit is performed.
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 when fit is performed.
feature_importances_ndarray of shape (n_features,): The impurity-based feature importances.
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_decision_function_ndarray of shape (n_samples, n_classes) or (n_samples, n_classes, n_outputs): Decision function computed with out-of-bag estimate on the training set. If n_estimators is small it might be possible that a data point was never left out during the bootstrap. In this case, oob_decision_function_ might contain NaN. This attribute exists only when oob_score is True.

Methods

`apply`(X)	Apply trees in the forest to X, return leaf indices.
`compute_similarity_matrix`(X)	Compute the similarity matrix of samples in X.
`decision_path`(X)	Return the decision path in the forest.
`fit`(X, y[, sample_weight, classes])	Build a forest of trees from the training set (X, y).
`get_leaf_node_samples`(X)	For each datapoint x in X, get the training samples in the leaf node.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X)	Predict regression target for X.
`predict_quantiles`(X[, quantiles, method])	Predict class or regression value for X at given quantiles.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_fit_request`(*[, classes, sample_weight])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.
`set_score_request`(*[, sample_weight])	Request metadata passed to the `score` method.

See also

treeple.tree.ObliqueDecisionTreeRegressor: An oblique decision tree regressor.
sklearn.ensemble.RandomForestRegressor: An axis-aligned decision forest regressor.

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.

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data, max_features=n_features and bootstrap=False, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, random_state has to be fixed.

References

[1]

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

[2]

Tomita, “Sparse Projection Oblique Randomer Forests”, Journal of Machine Learning Research, 21(104), 1-39, 2020.

Examples

>>> from treeple.ensemble import ObliqueRandomForestRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=4, n_informative=2,
...                        random_state=0, shuffle=False)
>>> regr = ObliqueRandomForestRegressor(max_depth=2, random_state=0)
>>> regr.fit(X, y)
ObliqueRandomForestRegressor(...)
>>> print(regr.predict([[0, 0, 0, 0]]))
[-5.86327109]

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.

compute_similarity_matrix(X)#

Compute the similarity matrix of samples in X.

Parameters:

Xarray_like of shape (n_samples, n_features): The input data.

Returns:

sim_matrixarray_like of shape (n_samples, n_samples): The similarity matrix among the samples.

decision_path(X)#

Return the decision path in the forest.

New 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.

fit(X, y, sample_weight=None, classes=None)#

Build a forest of trees 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 (class labels in classification, real numbers in regression).
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. In the case of classification, splits are also ignored if they would result in any single class carrying a negative weight in either child node.
classesarray_like of shape (n_classes,), default=None: List of all the classes that can possibly appear in the y vector.

Returns:

selfobject: Fitted estimator.

get_leaf_node_samples(X)#

For each datapoint x in X, get the training samples in the leaf node.

Parameters:

Xarray_like of shape (n_samples, n_features): Dataset to apply the forest to.

Returns:

leaf_node_samplesa list of array_like: Each sample is represented by the indices of the training samples that reached the leaf node. The n_leaf_node_samples may vary between samples, since the number of samples that fall in a leaf node is variable. Each array-like has shape (n_leaf_node_samples, n_outputs).

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)#

Predict regression target for X.

The predicted regression target of an input sample is computed as the mean predicted regression targets of the trees in the forest.

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:

yndarray of shape (n_samples,) or (n_samples, n_outputs): The predicted values.

predict_quantiles(X, quantiles=0.5, method='nearest')#

Predict class or regression value for X at given quantiles.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): Input data.
quantilesfloat, optional: The quantiles at which to evaluate, by default 0.5 (median).
methodstr, optional: The method to interpolate, by default ‘linear’. Can be any keyword argument accepted by numpy.quantile().

Returns:

yndarray of shape (n_samples, n_quantiles, [n_outputs]): The predicted values. The n_outputs dimension is present only for multi-output regressors.

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:

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(*, classes='$UNCHANGED$', sample_weight='$UNCHANGED$')#

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.

New 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:

classesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for classes parameter in fit.
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_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.

set_score_request(*, sample_weight='$UNCHANGED$')#

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.

New 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.

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.

property oob_samples_#

The sample indices that are out-of-bag.

Only utilized if bootstrap=True, otherwise, all samples are “in-bag”.

treeple.ObliqueRandomForestRegressor#

`treeple`.ObliqueRandomForestRegressor#