752 lines
28 KiB
Python
752 lines
28 KiB
Python
"""
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This module gathers tree-based methods, including decision, regression and
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randomized trees. Single and multi-output problems are both handled.
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"""
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# Code is originally adapted from MILK: Machine Learning Toolkit
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# Copyright (C) 2008-2011, Luis Pedro Coelho <luis@luispedro.org>
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# License: MIT. See COPYING.MIT file in the milk distribution
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# Authors: Brian Holt,
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# Peter Prettenhofer,
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# Satrajit Ghosh,
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# Gilles Louppe,
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# Noel Dawe
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# License: BSD 3 clause
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from __future__ import division
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import numbers
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import numpy as np
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from abc import ABCMeta, abstractmethod
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from warnings import warn
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from ..base import BaseEstimator, ClassifierMixin, RegressorMixin
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from ..externals import six
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from ..externals.six.moves import xrange
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from ..feature_selection.from_model import _LearntSelectorMixin
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from ..utils import array2d, check_random_state
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from ..utils.validation import check_arrays
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from . import _tree
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__all__ = ["DecisionTreeClassifier",
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"DecisionTreeRegressor",
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"ExtraTreeClassifier",
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"ExtraTreeRegressor"]
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DTYPE = _tree.DTYPE
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DOUBLE = _tree.DOUBLE
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CLASSIFICATION = {
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"gini": _tree.Gini,
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"entropy": _tree.Entropy,
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}
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REGRESSION = {
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"mse": _tree.MSE,
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}
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class BaseDecisionTree(six.with_metaclass(ABCMeta, BaseEstimator,
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_LearntSelectorMixin)):
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"""Base class for decision trees.
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Warning: This class should not be used directly.
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Use derived classes instead.
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"""
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@abstractmethod
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def __init__(self,
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criterion,
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max_depth,
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min_samples_split,
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min_samples_leaf,
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min_density,
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max_features,
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compute_importances,
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random_state):
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self.criterion = criterion
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self.max_depth = max_depth
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self.min_samples_split = min_samples_split
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self.min_samples_leaf = min_samples_leaf
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self.min_density = min_density
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self.max_features = max_features
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if compute_importances:
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warn("Setting compute_importances=True is no longer "
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"required. Variable importances are now computed on the fly "
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"when accessing the feature_importances_ attribute. This "
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"parameter will be removed in 0.15.", DeprecationWarning)
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self.compute_importances = compute_importances
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self.random_state = random_state
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self.n_features_ = None
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self.n_outputs_ = None
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self.classes_ = None
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self.n_classes_ = None
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self.find_split_ = _tree.TREE_SPLIT_BEST
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self.tree_ = None
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def fit(self, X, y,
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sample_mask=None, X_argsorted=None,
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check_input=True, sample_weight=None):
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"""Build a decision tree from the training set (X, y).
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Parameters
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----------
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X : array-like, shape = [n_samples, n_features]
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The training input samples. Use ``dtype=np.float32``
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and ``order='F'`` for maximum efficiency.
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y : array-like, shape = [n_samples] or [n_samples, n_outputs]
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The target values (integers that correspond to classes in
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classification, real numbers in regression).
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Use ``dtype=np.float64`` and ``order='C'`` for maximum
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efficiency.
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sample_mask : array-like, shape = [n_samples], dtype = bool or None
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A bit mask that encodes the rows of ``X`` that should be
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used to build the decision tree. It can be used for bagging
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without the need to create of copy of ``X``.
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If None a mask will be created that includes all samples.
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X_argsorted : array-like, shape = [n_samples, n_features] or None
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Each column of ``X_argsorted`` holds the row indices of ``X``
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sorted according to the value of the corresponding feature
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in ascending order.
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I.e. ``X[X_argsorted[i, k], k] <= X[X_argsorted[j, k], k]``
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for each j > i.
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If None, ``X_argsorted`` is computed internally.
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The argument is supported to enable multiple decision trees
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to share the data structure and to avoid re-computation in
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tree ensembles. For maximum efficiency use dtype np.int32.
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sample_weight : array-like, shape = [n_samples] or None
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Sample weights. If None, then samples are equally weighted. Splits
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that would create child nodes with net zero or negative weight are
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ignored while searching for a split in each node. In the case of
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classification, splits are also ignored if they would result in any
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single class carrying a negative weight in either child node.
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check_input : boolean, (default=True)
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Allow to bypass several input checking.
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Don't use this parameter unless you know what you do.
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Returns
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-------
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self : object
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Returns self.
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"""
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if check_input:
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X, y = check_arrays(X, y)
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random_state = check_random_state(self.random_state)
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# Convert data
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if (getattr(X, "dtype", None) != DTYPE or
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X.ndim != 2 or
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not X.flags.fortran):
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X = array2d(X, dtype=DTYPE, order="F")
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n_samples, self.n_features_ = X.shape
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is_classification = isinstance(self, ClassifierMixin)
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y = np.atleast_1d(y)
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if y.ndim == 1:
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# reshape is necessary to preserve the data contiguity against vs
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# [:, np.newaxis] that does not.
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y = np.reshape(y, (-1, 1))
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self.n_outputs_ = y.shape[1]
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if is_classification:
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y = np.copy(y)
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self.classes_ = []
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self.n_classes_ = []
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for k in xrange(self.n_outputs_):
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unique = np.unique(y[:, k])
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self.classes_.append(unique)
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self.n_classes_.append(unique.shape[0])
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y[:, k] = np.searchsorted(unique, y[:, k])
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else:
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self.classes_ = [None] * self.n_outputs_
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self.n_classes_ = [1] * self.n_outputs_
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if getattr(y, "dtype", None) != DOUBLE or not y.flags.contiguous:
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y = np.ascontiguousarray(y, dtype=DOUBLE)
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if is_classification:
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criterion = CLASSIFICATION[self.criterion](self.n_outputs_,
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self.n_classes_)
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else:
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criterion = REGRESSION[self.criterion](self.n_outputs_)
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# Check parameters
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max_depth = np.inf if self.max_depth is None else self.max_depth
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if isinstance(self.max_features, six.string_types):
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if self.max_features == "auto":
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if is_classification:
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max_features = max(1, int(np.sqrt(self.n_features_)))
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else:
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max_features = self.n_features_
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elif self.max_features == "sqrt":
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max_features = max(1, int(np.sqrt(self.n_features_)))
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elif self.max_features == "log2":
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max_features = max(1, int(np.log2(self.n_features_)))
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else:
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raise ValueError(
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'Invalid value for max_features. Allowed string '
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'values are "auto", "sqrt" or "log2".')
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elif self.max_features is None:
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max_features = self.n_features_
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elif isinstance(self.max_features, (numbers.Integral, np.integer)):
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max_features = self.max_features
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else: # float
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max_features = int(self.max_features * self.n_features_)
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if len(y) != n_samples:
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raise ValueError("Number of labels=%d does not match "
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"number of samples=%d" % (len(y), n_samples))
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if self.min_samples_split <= 0:
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raise ValueError("min_samples_split must be greater than zero.")
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if self.min_samples_leaf <= 0:
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raise ValueError("min_samples_leaf must be greater than zero.")
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if max_depth <= 0:
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raise ValueError("max_depth must be greater than zero. ")
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if self.min_density < 0.0 or self.min_density > 1.0:
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raise ValueError("min_density must be in [0, 1]")
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if not (0 < max_features <= self.n_features_):
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raise ValueError("max_features must be in (0, n_features]")
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if sample_mask is not None:
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sample_mask = np.asarray(sample_mask, dtype=np.bool)
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if sample_mask.shape[0] != n_samples:
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raise ValueError("Length of sample_mask=%d does not match "
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"number of samples=%d"
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% (sample_mask.shape[0], n_samples))
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if sample_weight is not None:
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if (getattr(sample_weight, "dtype", None) != DOUBLE or
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not sample_weight.flags.contiguous):
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sample_weight = np.ascontiguousarray(
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sample_weight, dtype=DOUBLE)
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if len(sample_weight.shape) > 1:
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raise ValueError("Sample weights array has more "
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"than one dimension: %d" %
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len(sample_weight.shape))
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if len(sample_weight) != n_samples:
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raise ValueError("Number of weights=%d does not match "
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"number of samples=%d" %
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(len(sample_weight), n_samples))
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if X_argsorted is not None:
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X_argsorted = np.asarray(X_argsorted, dtype=np.int32,
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order='F')
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if X_argsorted.shape != X.shape:
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raise ValueError("Shape of X_argsorted does not match "
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"the shape of X")
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# Set min_samples_split sensibly
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min_samples_split = max(self.min_samples_split,
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2 * self.min_samples_leaf)
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# Build tree
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self.tree_ = _tree.Tree(self.n_features_, self.n_classes_,
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self.n_outputs_, criterion, max_depth,
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min_samples_split, self.min_samples_leaf,
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self.min_density, max_features,
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self.find_split_, random_state)
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self.tree_.build(X, y,
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sample_weight=sample_weight,
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sample_mask=sample_mask,
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X_argsorted=X_argsorted)
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if self.n_outputs_ == 1:
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self.n_classes_ = self.n_classes_[0]
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self.classes_ = self.classes_[0]
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return self
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def predict(self, X):
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"""Predict class or regression value for X.
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For a classification model, the predicted class for each sample in X is
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returned. For a regression model, the predicted value based on X is
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returned.
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Parameters
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----------
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X : array-like of shape = [n_samples, n_features]
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The input samples.
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Returns
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-------
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y : array of shape = [n_samples] or [n_samples, n_outputs]
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The predicted classes, or the predict values.
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"""
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if getattr(X, "dtype", None) != DTYPE or X.ndim != 2:
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X = array2d(X, dtype=DTYPE, order="F")
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n_samples, n_features = X.shape
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if self.tree_ is None:
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raise Exception("Tree not initialized. Perform a fit first")
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if self.n_features_ != n_features:
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raise ValueError("Number of features of the model must "
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" match the input. Model n_features is %s and "
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" input n_features is %s "
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% (self.n_features_, n_features))
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proba = self.tree_.predict(X)
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# Classification
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if isinstance(self, ClassifierMixin):
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if self.n_outputs_ == 1:
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return self.classes_.take(np.argmax(proba[:, 0], axis=1),
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axis=0)
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else:
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predictions = np.zeros((n_samples, self.n_outputs_))
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for k in xrange(self.n_outputs_):
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predictions[:, k] = self.classes_[k].take(
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np.argmax(proba[:, k], axis=1),
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axis=0)
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return predictions
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# Regression
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else:
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if self.n_outputs_ == 1:
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return proba[:, 0, 0]
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else:
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return proba[:, :, 0]
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@property
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def feature_importances_(self):
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"""Return the feature importances.
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The importance of a feature is computed as the (normalized) total
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reduction of the criterion brought by that feature.
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It is also known as the Gini importance [4]_.
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Returns
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-------
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feature_importances_ : array, shape = [n_features]
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"""
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if self.tree_ is None:
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raise ValueError("Estimator not fitted, "
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"call `fit` before `feature_importances_`.")
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return self.tree_.compute_feature_importances()
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class DecisionTreeClassifier(BaseDecisionTree, ClassifierMixin):
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"""A decision tree classifier.
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Parameters
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----------
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criterion : string, optional (default="gini")
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The function to measure the quality of a split. Supported criteria are
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"gini" for the Gini impurity and "entropy" for the information gain.
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max_features : int, float, string or None, optional (default=None)
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The number of features to consider when looking for the best split:
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- If int, then consider `max_features` features at each split.
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- If float, then `max_features` is a percentage and
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`int(max_features * n_features)` features are considered at each
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split.
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- If "auto", then `max_features=sqrt(n_features)`.
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- If "sqrt", then `max_features=sqrt(n_features)`.
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- If "log2", then `max_features=log2(n_features)`.
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- If None, then `max_features=n_features`.
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max_depth : integer or None, optional (default=None)
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The maximum depth of the tree. If None, then nodes are expanded until
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all leaves are pure or until all leaves contain less than
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min_samples_split samples.
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min_samples_split : integer, optional (default=2)
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The minimum number of samples required to split an internal node.
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min_samples_leaf : integer, optional (default=1)
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The minimum number of samples required to be at a leaf node.
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min_density : float, optional (default=0.1)
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This parameter controls a trade-off in an optimization heuristic. It
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controls the minimum density of the `sample_mask` (i.e. the
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fraction of samples in the mask). If the density falls below this
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threshold the mask is recomputed and the input data is packed
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which results in data copying. If `min_density` equals to one,
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the partitions are always represented as copies of the original
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data. Otherwise, partitions are represented as bit masks (aka
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sample masks).
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random_state : int, RandomState instance or None, optional (default=None)
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If int, random_state is the seed used by the random number generator;
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If RandomState instance, random_state is the random number generator;
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If None, the random number generator is the RandomState instance used
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by `np.random`.
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Attributes
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----------
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`tree_` : Tree object
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The underlying Tree object.
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`classes_` : array of shape = [n_classes] or a list of such arrays
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The classes labels (single output problem),
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or a list of arrays of class labels (multi-output problem).
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`n_classes_` : int or list
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The number of classes (for single output problems),
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or a list containing the number of classes for each
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output (for multi-output problems).
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`feature_importances_` : array of shape = [n_features]
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The feature importances. The higher, the more important the
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feature. The importance of a feature is computed as the (normalized)
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total reduction of the criterion brought by that feature. It is also
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known as the Gini importance [4]_.
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See also
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--------
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DecisionTreeRegressor
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References
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----------
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.. [1] http://en.wikipedia.org/wiki/Decision_tree_learning
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.. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
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and Regression Trees", Wadsworth, Belmont, CA, 1984.
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.. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
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Learning", Springer, 2009.
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.. [4] L. Breiman, and A. Cutler, "Random Forests",
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http://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm
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Examples
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--------
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>>> from sklearn.datasets import load_iris
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>>> from sklearn.cross_validation import cross_val_score
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>>> from sklearn.tree import DecisionTreeClassifier
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>>> clf = DecisionTreeClassifier(random_state=0)
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>>> iris = load_iris()
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>>> cross_val_score(clf, iris.data, iris.target, cv=10)
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... # doctest: +SKIP
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...
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array([ 1. , 0.93..., 0.86..., 0.93..., 0.93...,
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0.93..., 0.93..., 1. , 0.93..., 1. ])
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"""
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def __init__(self,
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criterion="gini",
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max_depth=None,
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min_samples_split=2,
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min_samples_leaf=1,
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min_density=0.1,
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max_features=None,
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compute_importances=False,
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random_state=None):
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super(DecisionTreeClassifier, self).__init__(criterion,
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max_depth,
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min_samples_split,
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min_samples_leaf,
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min_density,
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max_features,
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compute_importances,
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random_state)
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def predict_proba(self, X):
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"""Predict class probabilities of the input samples X.
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Parameters
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----------
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X : array-like of shape = [n_samples, n_features]
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The input samples.
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Returns
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-------
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p : array of shape = [n_samples, n_classes], or a list of n_outputs
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such arrays if n_outputs > 1.
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The class probabilities of the input samples. Classes are ordered
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by arithmetical order.
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"""
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if getattr(X, "dtype", None) != DTYPE or X.ndim != 2:
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X = array2d(X, dtype=DTYPE, order="F")
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n_samples, n_features = X.shape
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if self.tree_ is None:
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raise Exception("Tree not initialized. Perform a fit first.")
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if self.n_features_ != n_features:
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raise ValueError("Number of features of the model must "
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" match the input. Model n_features is %s and "
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" input n_features is %s "
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% (self.n_features_, n_features))
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proba = self.tree_.predict(X)
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if self.n_outputs_ == 1:
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proba = proba[:, 0, :self.n_classes_]
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normalizer = proba.sum(axis=1)[:, np.newaxis]
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normalizer[normalizer == 0.0] = 1.0
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proba /= normalizer
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return proba
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else:
|
|
all_proba = []
|
|
|
|
for k in xrange(self.n_outputs_):
|
|
proba_k = proba[:, k, :self.n_classes_[k]]
|
|
normalizer = proba_k.sum(axis=1)[:, np.newaxis]
|
|
normalizer[normalizer == 0.0] = 1.0
|
|
proba_k /= normalizer
|
|
all_proba.append(proba_k)
|
|
|
|
return all_proba
|
|
|
|
def predict_log_proba(self, X):
|
|
"""Predict class log-probabilities of the input samples X.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape = [n_samples, n_features]
|
|
The input samples.
|
|
|
|
Returns
|
|
-------
|
|
p : array of shape = [n_samples, n_classes], or a list of n_outputs
|
|
such arrays if n_outputs > 1.
|
|
The class log-probabilities of the input samples. Classes are
|
|
ordered by arithmetical order.
|
|
"""
|
|
proba = self.predict_proba(X)
|
|
|
|
if self.n_outputs_ == 1:
|
|
return np.log(proba)
|
|
|
|
else:
|
|
for k in xrange(self.n_outputs_):
|
|
proba[k] = np.log(proba[k])
|
|
|
|
return proba
|
|
|
|
|
|
class DecisionTreeRegressor(BaseDecisionTree, RegressorMixin):
|
|
"""A tree regressor.
|
|
|
|
Parameters
|
|
----------
|
|
criterion : string, optional (default="mse")
|
|
The function to measure the quality of a split. The only supported
|
|
criterion is "mse" for the mean squared error.
|
|
|
|
max_features : int, float, string or None, optional (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 percentage and
|
|
`int(max_features * n_features)` features are considered at each
|
|
split.
|
|
- If "auto", then `max_features=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`.
|
|
|
|
max_depth : integer or None, optional (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 : integer, optional (default=2)
|
|
The minimum number of samples required to split an internal node.
|
|
|
|
min_samples_leaf : integer, optional (default=1)
|
|
The minimum number of samples required to be at a leaf node.
|
|
|
|
min_density : float, optional (default=0.1)
|
|
This parameter controls a trade-off in an optimization heuristic. It
|
|
controls the minimum density of the `sample_mask` (i.e. the
|
|
fraction of samples in the mask). If the density falls below this
|
|
threshold the mask is recomputed and the input data is packed
|
|
which results in data copying. If `min_density` equals to one,
|
|
the partitions are always represented as copies of the original
|
|
data. Otherwise, partitions are represented as bit masks (aka
|
|
sample masks).
|
|
|
|
random_state : int, RandomState instance or None, optional (default=None)
|
|
If int, random_state is the seed used by the random number generator;
|
|
If RandomState instance, random_state is the random number generator;
|
|
If None, the random number generator is the RandomState instance used
|
|
by `np.random`.
|
|
|
|
Attributes
|
|
----------
|
|
`tree_` : Tree object
|
|
The underlying Tree object.
|
|
|
|
`feature_importances_` : array of shape = [n_features]
|
|
The 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]_.
|
|
|
|
See also
|
|
--------
|
|
DecisionTreeClassifier
|
|
|
|
References
|
|
----------
|
|
|
|
.. [1] http://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",
|
|
http://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm
|
|
|
|
Examples
|
|
--------
|
|
>>> from sklearn.datasets import load_boston
|
|
>>> from sklearn.cross_validation import cross_val_score
|
|
>>> from sklearn.tree import DecisionTreeRegressor
|
|
|
|
>>> boston = load_boston()
|
|
>>> regressor = DecisionTreeRegressor(random_state=0)
|
|
|
|
R2 scores (a.k.a. coefficient of determination) over 10-folds CV:
|
|
|
|
>>> cross_val_score(regressor, boston.data, boston.target, cv=10)
|
|
... # doctest: +SKIP
|
|
...
|
|
array([ 0.61..., 0.57..., -0.34..., 0.41..., 0.75...,
|
|
0.07..., 0.29..., 0.33..., -1.42..., -1.77...])
|
|
"""
|
|
def __init__(self,
|
|
criterion="mse",
|
|
max_depth=None,
|
|
min_samples_split=2,
|
|
min_samples_leaf=1,
|
|
min_density=0.1,
|
|
max_features=None,
|
|
compute_importances=False,
|
|
random_state=None):
|
|
super(DecisionTreeRegressor, self).__init__(criterion,
|
|
max_depth,
|
|
min_samples_split,
|
|
min_samples_leaf,
|
|
min_density,
|
|
max_features,
|
|
compute_importances,
|
|
random_state)
|
|
|
|
|
|
class ExtraTreeClassifier(DecisionTreeClassifier):
|
|
"""An extremely randomized tree classifier.
|
|
|
|
Extra-trees differ from classic decision trees in the way they are built.
|
|
When looking for the best split to separate the samples of a node into two
|
|
groups, random splits are drawn for each of the `max_features` randomly
|
|
selected features and the best split among those is chosen. When
|
|
`max_features` is set 1, this amounts to building a totally random
|
|
decision tree.
|
|
|
|
Warning: Extra-trees should only be used within ensemble methods.
|
|
|
|
See also
|
|
--------
|
|
ExtraTreeRegressor, ExtraTreesClassifier, ExtraTreesRegressor
|
|
|
|
References
|
|
----------
|
|
|
|
.. [1] P. Geurts, D. Ernst., and L. Wehenkel, "Extremely randomized trees",
|
|
Machine Learning, 63(1), 3-42, 2006.
|
|
"""
|
|
def __init__(self,
|
|
criterion="gini",
|
|
max_depth=None,
|
|
min_samples_split=2,
|
|
min_samples_leaf=1,
|
|
min_density=0.1,
|
|
max_features="auto",
|
|
compute_importances=False,
|
|
random_state=None):
|
|
super(ExtraTreeClassifier, self).__init__(criterion,
|
|
max_depth,
|
|
min_samples_split,
|
|
min_samples_leaf,
|
|
min_density,
|
|
max_features,
|
|
compute_importances,
|
|
random_state)
|
|
|
|
self.find_split_ = _tree.TREE_SPLIT_RANDOM
|
|
|
|
|
|
class ExtraTreeRegressor(DecisionTreeRegressor):
|
|
"""An extremely randomized tree regressor.
|
|
|
|
Extra-trees differ from classic decision trees in the way they are built.
|
|
When looking for the best split to separate the samples of a node into two
|
|
groups, random splits are drawn for each of the `max_features` randomly
|
|
selected features and the best split among those is chosen. When
|
|
`max_features` is set 1, this amounts to building a totally random
|
|
decision tree.
|
|
|
|
Warning: Extra-trees should only be used within ensemble methods.
|
|
|
|
See also
|
|
--------
|
|
ExtraTreeClassifier : A classifier base on extremely randomized trees
|
|
sklearn.ensemble.ExtraTreesClassifier : An ensemble of extra-trees for
|
|
classification
|
|
sklearn.ensemble.ExtraTreesRegressor : An ensemble of extra-trees for
|
|
regression
|
|
|
|
References
|
|
----------
|
|
|
|
.. [1] P. Geurts, D. Ernst., and L. Wehenkel, "Extremely randomized trees",
|
|
Machine Learning, 63(1), 3-42, 2006.
|
|
"""
|
|
def __init__(self,
|
|
criterion="mse",
|
|
max_depth=None,
|
|
min_samples_split=2,
|
|
min_samples_leaf=1,
|
|
min_density=0.1,
|
|
max_features="auto",
|
|
compute_importances=False,
|
|
random_state=None):
|
|
super(ExtraTreeRegressor, self).__init__(criterion,
|
|
max_depth,
|
|
min_samples_split,
|
|
min_samples_leaf,
|
|
min_density,
|
|
max_features,
|
|
compute_importances,
|
|
random_state)
|
|
|
|
self.find_split_ = _tree.TREE_SPLIT_RANDOM
|