# Authors: Ronan Perry, Sambit Panda, Haoyin Xu
# Adopted from: https://github.com/neurodata/honest-forests
from copy import deepcopy
import numpy as np
from sklearn.base import MetaEstimatorMixin
from sklearn.utils.multiclass import check_classification_targets
from sklearn.utils.validation import check_is_fitted, check_X_y
from sktree._lib.sklearn.tree import DecisionTreeClassifier
from sktree._lib.sklearn.tree._classes import BaseDecisionTree
[docs]class HonestTreeClassifier(MetaEstimatorMixin, BaseDecisionTree):
"""
A decision tree classifier with honest predictions.
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_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 : int, 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.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the tree 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 :term:`Glossary <random_state>` for details.
max_leaf_nodes : int, 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_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.
class_weight : dict, 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.
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. See
:ref:`minimal_cost_complexity_pruning` for details.
tree_estimator : object, default=None
Instatiated tree of type BaseDecisionTree.
If None, then DecisionTreeClassifier with default parameters will
be used.
honest_fraction : float, default=0.5
Fraction of training samples used for estimates in the leaves. The
remaining samples will be used to learn the tree structure. A larger
fraction creates shallower trees with lower variance estimates.
honest_prior : {"ignore", "uniform", "empirical"}, default="empirical"
Method for dealing with empty leaves during evaluation of a test
sample. If "ignore", returns numpy.nan.
If "uniform", the prior tree posterior is 1/(number of
classes). If "empirical", the prior tree posterior is the relative
class frequency in the voting subsample.
Attributes
----------
estimator_ : object
The child tree estimator template used to create the collection
of fitted sub-estimators.
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,)
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 [4]_.
Warning: impurity-based feature importances can be misleading for
high cardinality features (many unique values). See
:func:`sklearn.inspection.permutation_importance` as an alternative.
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 :term:`fit`.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`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 and
:ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
for basic usage of these attributes.
empirical_prior_ : float
Proportion of each class in the training labels y
structure_indices_ : numpy.ndarray, shape=(n_structure,)
Indices of training samples used to learn the structure
honest_indices_ : numpy.ndarray, shape=(n_honest,)
Indices of training samples used to learn leaf estimates
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 :meth:`predict` method operates using the :func:`numpy.argmax`
function on the outputs of :meth:`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 :term:`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
.. [5] S. Athey, J. Tibshirani, and S. Wager. "Generalized
Random Forests", Annals of Statistics, 2019.
Examples
--------
>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import cross_val_score
>>> from honest_forests import HonestTreeClassifier
>>> clf = HonestTreeClassifier(random_state=0)
>>> iris = load_iris()
>>> cross_val_score(clf, iris.data, iris.target, cv=10)
... # doctest: +SKIP
...
array([0.93333333, 0.93333333, 1. , 1. , 0.93333333,
0.8 , 0.8 , 0.93333333, 1. , 1. ])
"""
def __init__(
self,
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,
ccp_alpha=0.0,
tree_estimator=None,
honest_fraction=0.5,
honest_prior="empirical",
):
self.tree_estimator = tree_estimator
self.criterion = criterion
self.splitter = splitter
self.max_depth = max_depth
self.min_samples_split = min_samples_split
self.min_samples_leaf = min_samples_leaf
self.min_weight_fraction_leaf = min_weight_fraction_leaf
self.max_features = max_features
self.max_leaf_nodes = max_leaf_nodes
self.class_weight = class_weight
self.random_state = random_state
self.min_impurity_decrease = min_impurity_decrease
self.ccp_alpha = ccp_alpha
self.honest_fraction = honest_fraction
self.honest_prior = honest_prior
[docs] def fit(self, X, y, sample_weight=None, check_input=True):
"""Build an honest 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``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels) as integers or strings.
sample_weight : array-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_input : bool, default=True
Allow to bypass several input checking.
Don't use this parameter unless you know what you do.
Returns
-------
self : HonestTreeClassifier
Fitted tree estimator.
"""
rng = np.random.default_rng(self.random_state)
if check_input:
X, y = check_X_y(X, y)
# Account for bootstrapping too
if sample_weight is None:
_sample_weight = np.ones((X.shape[0],), dtype=np.float64)
else:
_sample_weight = np.array(sample_weight)
nonzero_indices = np.where(_sample_weight > 0)[0]
self.structure_indices_ = rng.choice(
nonzero_indices,
int((1 - self.honest_fraction) * len(nonzero_indices)),
replace=False,
)
self.honest_indices_ = np.setdiff1d(nonzero_indices, self.structure_indices_)
_sample_weight[self.honest_indices_] = 0
if not self.tree_estimator:
self.estimator_ = DecisionTreeClassifier(
criterion=self.criterion,
splitter=self.splitter,
max_depth=self.max_depth,
min_samples_split=self.min_samples_split,
min_samples_leaf=self.min_samples_leaf,
min_weight_fraction_leaf=self.min_weight_fraction_leaf,
max_features=self.max_features,
max_leaf_nodes=self.max_leaf_nodes,
class_weight=self.class_weight,
random_state=self.random_state,
min_impurity_decrease=self.min_impurity_decrease,
ccp_alpha=self.ccp_alpha,
)
else:
# XXX: maybe error out if the tree_estimator is already fitted
self.estimator_ = deepcopy(self.tree_estimator)
# Learn structure on subsample
self.estimator_.fit(
X,
y,
sample_weight=_sample_weight,
check_input=check_input,
)
self._inherit_estimator_attributes()
# update the number of classes, unsplit
if y.ndim == 1:
# reshape is necessary to preserve the data contiguity against vs
# [:, np.newaxis] that does not.
y = np.reshape(y, (-1, 1))
check_classification_targets(y)
y = np.copy(y).astype(int)
# Normally called by super
X = self.estimator_._validate_X_predict(X, True)
# Fit leaves using other subsample
honest_leaves = self.tree_.apply(X[self.honest_indices_])
# preserve from underlying tree
# https://github.com/scikit-learn/scikit-learn/blob/1.0.X/sklearn/tree/_classes.py#L202
self._tree_classes_ = self.classes_
self._tree_n_classes_ = self.n_classes_
self.classes_ = []
self.n_classes_ = []
self.empirical_prior_ = []
y_encoded = np.zeros(y.shape, dtype=int)
for k in range(self.n_outputs_):
classes_k, y_encoded[:, k] = np.unique(y[:, k], return_inverse=True)
self.classes_.append(classes_k)
self.n_classes_.append(classes_k.shape[0])
self.empirical_prior_.append(
np.bincount(y_encoded[:, k], minlength=classes_k.shape[0]) / y.shape[0]
)
y = y_encoded
# y-encoded ensures that y values match the indices of the classes
self._set_leaf_nodes(honest_leaves, y)
self.n_classes_ = np.array(self.n_classes_, dtype=np.intp)
if self.n_outputs_ == 1:
self.n_classes_ = self.n_classes_[0]
self.classes_ = self.classes_[0]
self.empirical_prior_ = self.empirical_prior_[0]
y = y[:, 0]
return self
def _set_leaf_nodes(self, leaf_ids, y):
"""Traverse the already built tree with X and set leaf nodes with y.
tree_.value has shape (n_nodes, n_outputs, max_n_classes), where
n_nodes are the number of nodes in the tree (each node is either a split,
or leaf node), n_outputs is the number of outputs (1 for classification,
n for regression), and max_n_classes is the maximum number of classes
across all outputs. For classification with n_classes classes, the
classes are ordered by their index in the tree_.value array.
"""
self.tree_.value[:, :, :] = 0
for leaf_id, yval in zip(leaf_ids, y[self.honest_indices_, :]):
self.tree_.value[leaf_id][:, yval] += 1
def _inherit_estimator_attributes(self):
"""Initialize necessary attributes from the provided tree estimator"""
self.classes_ = self.estimator_.classes_
self.max_features_ = self.estimator_.max_features_
self.n_classes_ = self.estimator_.n_classes_
self.n_features_in_ = self.estimator_.n_features_in_
self.n_outputs_ = self.estimator_.n_outputs_
self.tree_ = self.estimator_.tree_
def _empty_leaf_correction(self, proba, pos=0):
"""Leaves with empty posteriors are assigned values.
The posteriors are corrected according to the honest prior.
In multi-output cases, the posterior corrections only correspond
to the respective y dimension, indicated by the position param pos.
"""
zero_mask = proba.sum(axis=1) == 0.0
# For multi-output cases
if self.n_outputs_ > 1:
if self.honest_prior == "empirical":
proba[zero_mask] = self.empirical_prior_[pos]
elif self.honest_prior == "uniform":
proba[zero_mask] = 1 / self.n_classes_[pos]
elif self.honest_prior == "ignore":
proba[zero_mask] = np.nan
else:
raise ValueError(f"honest_prior {self.honest_prior} not a valid input.")
else:
if self.honest_prior == "empirical":
proba[zero_mask] = self.empirical_prior_
elif self.honest_prior == "uniform":
proba[zero_mask] = 1 / self.n_classes_
elif self.honest_prior == "ignore":
proba[zero_mask] = np.nan
else:
raise ValueError(f"honest_prior {self.honest_prior} not a valid input.")
return proba
[docs] def predict_proba(self, 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_input : bool, default=True
Allow to bypass several input checking.
Don't use this parameter unless you know what you do.
Returns
-------
proba : ndarray 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 :term:`classes_`.
"""
check_is_fitted(self)
X = self.estimator_._validate_X_predict(X, check_input)
proba = self.tree_.predict(X)
if self.n_outputs_ == 1:
proba = proba[:, : self._tree_n_classes_]
normalizer = proba.sum(axis=1)[:, np.newaxis]
normalizer[normalizer == 0.0] = 1.0
proba /= normalizer
proba = self._empty_leaf_correction(proba)
return proba
else:
all_proba = []
for k in range(self.n_outputs_):
proba_k = proba[:, k, : self._tree_n_classes_[k]]
normalizer = proba_k.sum(axis=1)[:, np.newaxis]
normalizer[normalizer == 0.0] = 1.0
proba_k /= normalizer
proba_k = self._empty_leaf_correction(proba_k, k)
all_proba.append(proba_k)
return all_proba
[docs] def predict(self, X, check_input=True):
"""Predict class for X.
For a classification model, the predicted class for each sample in 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_input : bool, default=True
Allow to bypass several input checking.
Don't use this parameter unless you know what you're doing.
Returns
-------
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The predicted classes, or the predict values.
"""
X = self._validate_X_predict(X, check_input)
return self.estimator_.predict(X, False)