`treeple.tree`.ObliqueDecisionTreeClassifier#

class treeple.tree.ObliqueDecisionTreeClassifier(*, criterion='gini', splitter='best', max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features=None, random_state=None, max_leaf_nodes=None, min_impurity_decrease=0.0, class_weight=None, feature_combinations=None, ccp_alpha=0.0, store_leaf_values=False, monotonic_cst=None)[source]#

An oblique decision tree classifier.

Read more in the User Guide. The implementation follows that of [1] and [2].

Parameters:

criterion{“gini”, “entropy”}, default=”gini”

The function to measure the quality of a split. Supported criteria are “gini” for the Gini impurity and “entropy” for the information gain.

splitter{“best”, “random”}, default=”best”

The strategy used to choose the split at each node. Supported strategies are “best” to choose the best split and “random” to choose the best random split.

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_featuresint, float or {“auto”, “sqrt”, “log2”}, default=None

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 int(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.

Note: Compared to axis-aligned Random Forests, one can set max_features to a number greater then n_features.

random_stateint, RandomState instance or None, default=None

Controls the randomness of the estimator. The features are always randomly permuted at each split, even if splitter is set to "best". When max_features < n_features, the algorithm will select max_features at random at each split before finding the best split among them. But the best found split may vary across different runs, even if max_features=n_features. That is the case, if the improvement of the criterion is identical for several splits and one split has to be selected at random. To obtain a deterministic behaviour during fitting, random_state has to be fixed to an integer. See Glossary for details.

max_leaf_nodesint, default=None

Grow a tree 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.

class_weightdict, list of dict or “balanced”, default=None

Weights associated with classes in the form {class_label: weight}. If None, all classes are supposed to have weight one. For multi-output problems, a list of dicts can be provided in the same order as the columns of y.

Note that for multioutput (including multilabel) weights should be defined for each class of every column in its own dict. For example, for four-class multilabel classification weights should be [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of [{1:1}, {2:5}, {3:1}, {4:1}].

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))

For multi-output, the weights of each column of y will be multiplied.

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

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.

ccp_alphanon-negative float, default=0.0

Not used.

store_leaf_valuesbool, default=False

Whether to store the leaf values.

monotonic_cstarray_like of int of shape (n_features), default=None

Indicates the monotonicity constraint to enforce on each feature.

1: monotonic increase
0: no constraint
-1: monotonic decrease

Not used.

Attributes:

classes_ndarray of shape (n_classes,) or list of ndarray: The classes labels (single output problem), or a list of arrays of class labels (multi-output problem).
feature_importances_ndarray of shape (n_features,): Return the feature importances.
max_features_int: The inferred value of max_features.
n_classes_int or list of int: The number of classes (for single output problems), or a list containing the number of classes for each output (for multi-output problems).
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.
tree_Tree instance: The underlying Tree object. Please refer to help(sklearn.tree._tree.Tree) for attributes of Tree object.
feature_combinations_float: The number of feature combinations on average taken to fit the tree.

Methods

`apply`(X[, check_input])	Return the index of the leaf that each sample is predicted as.
`compute_similarity_matrix`(X)	Compute the similarity matrix of samples in X.
`cost_complexity_pruning_path`(X, y[, ...])	Compute the pruning path during Minimal Cost-Complexity Pruning.
`decision_path`(X[, check_input])	Return the decision path in the tree.
`fit`(X, y[, sample_weight, check_input, classes])	Build a decision tree classifier from the training set (X, y).
`get_depth`()	Return the depth of the decision tree.
`get_leaf_node_samples`(X[, check_input])	For each datapoint x in X, get the training samples in the leaf node.
`get_metadata_routing`()	Get metadata routing of this object.
`get_n_leaves`()	Return the number of leaves of the decision tree.
`get_params`([deep])	Get parameters for this estimator.
`partial_fit`(X, y[, sample_weight, ...])	Update a decision tree classifier from the training set (X, y).
`predict`(X[, check_input])	Predict class or regression value for X.
`predict_log_proba`(X)	Predict class log-probabilities of the input samples X.
`predict_proba`(X[, check_input])	Predict class probabilities of the input samples X.
`predict_quantiles`(X[, quantiles, method, ...])	Predict class or regression value for X at given quantiles.
`score`(X, y[, sample_weight])	Return the mean accuracy on the given test data and labels.
`set_fit_request`(*[, check_input, classes, ...])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.
`set_partial_fit_request`(*[, check_input, ...])	Request metadata passed to the `partial_fit` method.
`set_predict_proba_request`(*[, check_input])	Request metadata passed to the `predict_proba` method.
`set_predict_request`(*[, check_input])	Request metadata passed to the `predict` method.
`set_score_request`(*[, sample_weight])	Request metadata passed to the `score` method.

See also

sklearn.tree.DecisionTreeClassifier: An axis-aligned decision tree classifier.

Notes

Compared to DecisionTreeClassifier, oblique trees can sample more features then n_features, where n_features is the number of columns in X. This is controlled via the max_features parameter. In fact, sampling more times results in better trees with the caveat that there is an increased computation. It is always recommended to sample more if one is willing to spend the computational resources.

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 predict() method operates using the numpy.argmax() function on the outputs of predict_proba(). This means that in case the highest predicted probabilities are tied, the classifier will predict the tied class with the lowest index in classes_.

References

[1]

https://en.wikipedia.org/wiki/Decision_tree_learning

[2]

L. Breiman, J. Friedman, R. Olshen, and C. Stone, “Classification and Regression Trees”, Wadsworth, Belmont, CA, 1984.

[3]

T. Hastie, R. Tibshirani and J. Friedman. “Elements of Statistical Learning”, Springer, 2009.

[4]

L. Breiman, and A. Cutler, “Random Forests”, https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

Examples

>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import cross_val_score
>>> from treeple.tree import ObliqueDecisionTreeClassifier
>>> clf = ObliqueDecisionTreeClassifier(random_state=0)
>>> iris = load_iris()
>>> cross_val_score(clf, iris.data, iris.target, cv=10)
...                             
...
array([ 1.     ,  0.93...,  0.86...,  0.93...,  0.93...,
        0.93...,  0.93...,  1.     ,  0.93...,  1.      ])

apply(X, check_input=True)#

Return the index of the leaf that each sample is predicted as.

New in version 0.17.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.
check_inputbool, default=True: Allow to bypass several input checking. Don’t use this parameter unless you know what you’re doing.

Returns:

X_leavesarray_like of shape (n_samples,): For each datapoint x in X, return the index of the leaf x ends up in. Leaves are numbered within [0; self.tree_.node_count), possibly with gaps in the numbering.

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.

cost_complexity_pruning_path(X, y, sample_weight=None)#

Compute the pruning path during Minimal Cost-Complexity Pruning.

See Minimal Cost-Complexity Pruning for details on the pruning process.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The training input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csc_matrix.
yarray_like of shape (n_samples,) or (n_samples, n_outputs): The target values (class labels) as integers or strings.
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. Splits are also ignored if they would result in any single class carrying a negative weight in either child node.

Returns:

ccp_pathBunch

Dictionary-like object, with the following attributes.

ccp_alphasndarray: Effective alphas of subtree during pruning.
impuritiesndarray: Sum of the impurities of the subtree leaves for the corresponding alpha value in ccp_alphas.

decision_path(X, check_input=True)#

Return the decision path in the tree.

New in version 0.18.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.
check_inputbool, default=True: Allow to bypass several input checking. Don’t use this parameter unless you know what you’re doing.

Returns:

indicatorsparse matrix of shape (n_samples, n_nodes): Return a node indicator CSR matrix where non zero elements indicates that the samples goes through the nodes.

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

Build a decision tree classifier from the training set (X, y).

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The training input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csc_matrix.
yarray_like of shape (n_samples,) or (n_samples, n_outputs): The target values (class labels) as integers or strings.
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. Splits are also ignored if they would result in any single class carrying a negative weight in either child node.
check_inputbool, default=True: Allow to bypass several input checking. Don’t use this parameter unless you know what you’re doing.
classesarray_like of shape (n_classes,), default=None: List of all the classes that can possibly appear in the y vector.

Returns:

selfDecisionTreeClassifier: Fitted estimator.

get_depth()#

Return the depth of the decision tree.

The depth of a tree is the maximum distance between the root and any leaf.

Returns:

self.tree_.max_depthint: The maximum depth of the tree.

get_leaf_node_samples(X, check_input=True)#

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.
check_inputbool, default=True: Allow to bypass several input checking.

Returns:

leaf_nodes_samplesa list of array_like of length (n_samples,): 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 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_n_leaves()#

Return the number of leaves of the decision tree.

Returns:

self.tree_.n_leavesint: Number of leaves.

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.

partial_fit(X, y, sample_weight=None, check_input=True, classes=None)#

Update a decision tree classifier from the training set (X, y).

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The training input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csc_matrix.
yarray_like of shape (n_samples,) or (n_samples, n_outputs): The target values (class labels) as integers or strings.
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. Splits are also ignored if they would result in any single class carrying a negative weight in either child node.
check_inputbool, default=True: Allow to bypass several input checking. Don’t use this parameter unless you know what you do.
classesarray_like of shape (n_classes,), default=None: List of all the classes that can possibly appear in the y vector. Must be provided at the first call to partial_fit, can be omitted in subsequent calls.

Returns:

selfDecisionTreeClassifier: Fitted estimator.

predict(X, check_input=True)#

Predict class or regression value for X.

For a classification model, the predicted class for each sample in X is returned. For a regression model, the predicted value based on X is returned.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.
check_inputbool, default=True: Allow to bypass several input checking. Don’t use this parameter unless you know what you’re doing.

Returns:

yarray_like of shape (n_samples,) or (n_samples, n_outputs): The predicted classes, or the predict values.

predict_log_proba(X)#

Predict class log-probabilities of the input samples X.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.

Returns:

probandarray of shape (n_samples, n_classes) or list of n_outputs such arrays if n_outputs > 1: The class log-probabilities of the input samples. The order of the classes corresponds to that in the attribute classes_.

predict_proba(X, check_input=True)#

Predict class probabilities of the input samples X.

The predicted class probability is the fraction of samples of the same class in a leaf.

Parameters:

X{array_like, sparse matrix} of shape (n_samples, n_features): The input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csr_matrix.
check_inputbool, default=True: Allow to bypass several input checking. Don’t use this parameter unless you know what you’re doing.

Returns:

probandarray of shape (n_samples, n_classes) or list of n_outputs such arrays if n_outputs > 1: The class probabilities of the input samples. The order of the classes corresponds to that in the attribute classes_.

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

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().
check_inputbool, optional: Whether or not to check input, by default True.

Returns:

predictionsarray_like of shape (n_samples, n_outputs, len(quantiles)): The predicted quantiles.

score(X, y, sample_weight=None)#

Return the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters:

Xarray_like of shape (n_samples, n_features): Test samples.
yarray_like of shape (n_samples,) or (n_samples, n_outputs): True labels for X.
sample_weightarray_like of shape (n_samples,), default=None: Sample weights.

Returns:

scorefloat: Mean accuracy of self.predict(X) w.r.t. y.

set_fit_request(*, check_input='$UNCHANGED$', 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:

check_inputstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for check_input parameter in fit.
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_partial_fit_request(*, check_input='$UNCHANGED$', classes='$UNCHANGED$', sample_weight='$UNCHANGED$')#

Request metadata passed to the partial_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 partial_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 partial_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:

check_inputstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for check_input parameter in partial_fit.
classesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for classes parameter in partial_fit.
sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weight parameter in partial_fit.

Returns:

selfobject: The updated object.

set_predict_proba_request(*, check_input='$UNCHANGED$')#

Request metadata passed to the predict_proba 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_proba 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_proba.
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:

check_inputstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for check_input parameter in predict_proba.

Returns:

selfobject: The updated object.

set_predict_request(*, check_input='$UNCHANGED$')#

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.

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:

check_inputstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for check_input parameter in predict.

Returns:

selfobject: The updated object.

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 feature_importances_#

Return the feature importances.

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,): Normalized total reduction of criteria by feature (Gini importance).

treeple.tree.ObliqueDecisionTreeClassifier#

`treeple.tree`.ObliqueDecisionTreeClassifier#