_iforest.py

# Authors: Nicolas Goix <nicolas.goix@telecom-paristech.fr>
#          Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
# License: BSD 3 clause

import numbers
import numpy as np
from scipy.sparse import issparse
from warnings import warn

from ..tree import ExtraTreeRegressor
from ..utils import (
    check_random_state,
    check_array,
    gen_batches,
    get_chunk_n_rows,
)
from ..utils.fixes import _joblib_parallel_args
from ..utils.validation import check_is_fitted, _num_samples
from ..utils.validation import _deprecate_positional_args
from ..base import OutlierMixin

from ._bagging import BaseBagging

__all__ = ["IsolationForest"]


class IsolationForest(OutlierMixin, BaseBagging):
    """
    Isolation Forest Algorithm.

    Return the anomaly score of each sample using the IsolationForest algorithm

    The IsolationForest 'isolates' observations by randomly selecting a feature
    and then randomly selecting a split value between the maximum and minimum
    values of the selected feature.

    Since recursive partitioning can be represented by a tree structure, the
    number of splittings required to isolate a sample is equivalent to the path
    length from the root node to the terminating node.

    This path length, averaged over a forest of such random trees, is a
    measure of normality and our decision function.

    Random partitioning produces noticeably shorter paths for anomalies.
    Hence, when a forest of random trees collectively produce shorter path
    lengths for particular samples, they are highly likely to be anomalies.

    Read more in the :ref:`User Guide <isolation_forest>`.

    .. versionadded:: 0.18

    Parameters
    ----------
    n_estimators : int, default=100
        The number of base estimators in the ensemble.

    max_samples : "auto", int or float, default="auto"
        The number of samples to draw from X to train each base estimator.
            - If int, then draw `max_samples` samples.
            - If float, then draw `max_samples * X.shape[0]` samples.
            - If "auto", then `max_samples=min(256, n_samples)`.

        If max_samples is larger than the number of samples provided,
        all samples will be used for all trees (no sampling).

    contamination : 'auto' or float, default='auto'
        The amount of contamination of the data set, i.e. the proportion
        of outliers in the data set. Used when fitting to define the threshold
        on the scores of the samples.

            - If 'auto', the threshold is determined as in the
              original paper.
            - If float, the contamination should be in the range [0, 0.5].

        .. versionchanged:: 0.22
           The default value of ``contamination`` changed from 0.1
           to ``'auto'``.

    max_features : int or float, default=1.0
        The number of features to draw from X to train each base estimator.

            - If int, then draw `max_features` features.
            - If float, then draw `max_features * X.shape[1]` features.

    bootstrap : bool, default=False
        If True, individual trees are fit on random subsets of the training
        data sampled with replacement. If False, sampling without replacement
        is performed.

    n_jobs : int, default=None
        The number of jobs to run in parallel for both :meth:`fit` and
        :meth:`predict`. ``None`` means 1 unless in a
        :obj:`joblib.parallel_backend` context. ``-1`` means using all
        processors. See :term:`Glossary <n_jobs>` for more details.

    random_state : int or RandomState, default=None
        Controls the pseudo-randomness of the selection of the feature
        and split values for each branching step and each tree in the forest.

        Pass an int for reproducible results across multiple function calls.
        See :term:`Glossary <random_state>`.

    verbose : int, default=0
        Controls the verbosity of the tree building process.

    warm_start : bool, 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 :term:`the Glossary <warm_start>`.

        .. versionadded:: 0.21

    Attributes
    ----------
    estimators_ : list of DecisionTreeClassifier
        The collection of fitted sub-estimators.

    estimators_samples_ : list of arrays
        The subset of drawn samples (i.e., the in-bag samples) for each base
        estimator.

    max_samples_ : int
        The actual number of samples.

    offset_ : float
        Offset used to define the decision function from the raw scores. We
        have the relation: ``decision_function = score_samples - offset_``.
        ``offset_`` is defined as follows. When the contamination parameter is
        set to "auto", the offset is equal to -0.5 as the scores of inliers are
        close to 0 and the scores of outliers are close to -1. When a
        contamination parameter different than "auto" is provided, the offset
        is defined in such a way we obtain the expected number of outliers
        (samples with decision function < 0) in training.

        .. versionadded:: 0.20

    estimators_features_ : list of arrays
        The subset of drawn features for each base estimator.

    Notes
    -----
    The implementation is based on an ensemble of ExtraTreeRegressor. The
    maximum depth of each tree is set to ``ceil(log_2(n))`` where
    :math:`n` is the number of samples used to build the tree
    (see (Liu et al., 2008) for more details).

    References
    ----------
    .. [1] Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. "Isolation forest."
           Data Mining, 2008. ICDM'08. Eighth IEEE International Conference on.
    .. [2] Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. "Isolation-based
           anomaly detection." ACM Transactions on Knowledge Discovery from
           Data (TKDD) 6.1 (2012): 3.

    See Also
    ----------
    sklearn.covariance.EllipticEnvelope : An object for detecting outliers in a
        Gaussian distributed dataset.
    sklearn.svm.OneClassSVM : Unsupervised Outlier Detection.
        Estimate the support of a high-dimensional distribution.
        The implementation is based on libsvm.
    sklearn.neighbors.LocalOutlierFactor : Unsupervised Outlier Detection
        using Local Outlier Factor (LOF).

    Examples
    --------
    >>> from sklearn.ensemble import IsolationForest
    >>> X = [[-1.1], [0.3], [0.5], [100]]
    >>> clf = IsolationForest(random_state=0).fit(X)
    >>> clf.predict([[0.1], [0], [90]])
    array([ 1,  1, -1])
    """
    @_deprecate_positional_args
    def __init__(self, *,
                 n_estimators=100,
                 max_samples="auto",
                 contamination="auto",
                 max_features=1.,
                 bootstrap=False,
                 n_jobs=None,
                 random_state=None,
                 verbose=0,
                 warm_start=False):
        super().__init__(
            base_estimator=ExtraTreeRegressor(
                max_features=1,
                splitter='random',
                random_state=random_state),
            # here above max_features has no links with self.max_features
            bootstrap=bootstrap,
            bootstrap_features=False,
            n_estimators=n_estimators,
            max_samples=max_samples,
            max_features=max_features,
            warm_start=warm_start,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose)

        self.contamination = contamination

    def _set_oob_score(self, X, y):
        raise NotImplementedError("OOB score not supported by iforest")

    def _parallel_args(self):
        # ExtraTreeRegressor releases the GIL, so it's more efficient to use
        # a thread-based backend rather than a process-based backend so as
        # to avoid suffering from communication overhead and extra memory
        # copies.
        return _joblib_parallel_args(prefer='threads')

    def fit(self, X, y=None, sample_weight=None):
        """
        Fit estimator.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples. Use ``dtype=np.float32`` for maximum
            efficiency. Sparse matrices are also supported, use sparse
            ``csc_matrix`` for maximum efficiency.

        y : Ignored
            Not used, present for API consistency by convention.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted.

        Returns
        -------
        self : object
            Fitted estimator.
        """
        X = check_array(X, accept_sparse=['csc'])
        if issparse(X):
            # Pre-sort indices to avoid that each individual tree of the
            # ensemble sorts the indices.
            X.sort_indices()

        rnd = check_random_state(self.random_state)
        y = rnd.uniform(size=X.shape[0])

        # ensure that max_sample is in [1, n_samples]:
        n_samples = X.shape[0]

        if isinstance(self.max_samples, str):
            if self.max_samples == 'auto':
                max_samples = min(256, n_samples)
            else:
                raise ValueError('max_samples (%s) is not supported.'
                                 'Valid choices are: "auto", int or'
                                 'float' % self.max_samples)

        elif isinstance(self.max_samples, numbers.Integral):
            if self.max_samples > n_samples:
                warn("max_samples (%s) is greater than the "
                     "total number of samples (%s). max_samples "
                     "will be set to n_samples for estimation."
                     % (self.max_samples, n_samples))
                max_samples = n_samples
            else:
                max_samples = self.max_samples
        else:  # float
            if not 0. < self.max_samples <= 1.:
                raise ValueError("max_samples must be in (0, 1], got %r"
                                 % self.max_samples)
            max_samples = int(self.max_samples * X.shape[0])

        self.max_samples_ = max_samples
        max_depth = int(np.ceil(np.log2(max(max_samples, 2))))
        super()._fit(X, y, max_samples,
                     max_depth=max_depth,
                     sample_weight=sample_weight)

        if self.contamination == "auto":
            # 0.5 plays a special role as described in the original paper.
            # we take the opposite as we consider the opposite of their score.
            self.offset_ = -0.5
            return self

        # else, define offset_ wrt contamination parameter
        self.offset_ = np.percentile(self.score_samples(X),
                                     100. * self.contamination)

        return self

    def predict(self, X):
        """
        Predict if a particular sample is an outlier or not.

        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
        -------
        is_inlier : ndarray of shape (n_samples,)
            For each observation, tells whether or not (+1 or -1) it should
            be considered as an inlier according to the fitted model.
        """
        check_is_fitted(self)
        X = check_array(X, accept_sparse='csr')
        is_inlier = np.ones(X.shape[0], dtype=int)
        is_inlier[self.decision_function(X) < 0] = -1
        return is_inlier

    def decision_function(self, X):
        """
        Average anomaly score of X of the base classifiers.

        The anomaly score of an input sample is computed as
        the mean anomaly score of the trees in the forest.

        The measure of normality of an observation given a tree is the depth
        of the leaf containing this observation, which is equivalent to
        the number of splittings required to isolate this point. In case of
        several observations n_left in the leaf, the average path length of
        a n_left samples isolation tree is added.

        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
        -------
        scores : ndarray of shape (n_samples,)
            The anomaly score of the input samples.
            The lower, the more abnormal. Negative scores represent outliers,
            positive scores represent inliers.
        """
        # We subtract self.offset_ to make 0 be the threshold value for being
        # an outlier:

        return self.score_samples(X) - self.offset_

    def score_samples(self, X):
        """
        Opposite of the anomaly score defined in the original paper.

        The anomaly score of an input sample is computed as
        the mean anomaly score of the trees in the forest.

        The measure of normality of an observation given a tree is the depth
        of the leaf containing this observation, which is equivalent to
        the number of splittings required to isolate this point. In case of
        several observations n_left in the leaf, the average path length of
        a n_left samples isolation tree is added.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples.

        Returns
        -------
        scores : ndarray of shape (n_samples,)
            The anomaly score of the input samples.
            The lower, the more abnormal.
        """
        # code structure from ForestClassifier/predict_proba

        check_is_fitted(self)

        # Check data
        X = check_array(X, accept_sparse='csr')
        if self.n_features_ != X.shape[1]:
            raise ValueError("Number of features of the model must "
                             "match the input. Model n_features is {0} and "
                             "input n_features is {1}."
                             "".format(self.n_features_, X.shape[1]))

        # Take the opposite of the scores as bigger is better (here less
        # abnormal)
        return -self._compute_chunked_score_samples(X)

    def _compute_chunked_score_samples(self, X):

        n_samples = _num_samples(X)

        if self._max_features == X.shape[1]:
            subsample_features = False
        else:
            subsample_features = True

        # We get as many rows as possible within our working_memory budget
        # (defined by sklearn.get_config()['working_memory']) to store
        # self._max_features in each row during computation.
        #
        # Note:
        #  - this will get at least 1 row, even if 1 row of score will
        #    exceed working_memory.
        #  - this does only account for temporary memory usage while loading
        #    the data needed to compute the scores -- the returned scores
        #    themselves are 1D.

        chunk_n_rows = get_chunk_n_rows(row_bytes=16 * self._max_features,
                                        max_n_rows=n_samples)
        slices = gen_batches(n_samples, chunk_n_rows)

        scores = np.zeros(n_samples, order="f")

        for sl in slices:
            # compute score on the slices of test samples:
            scores[sl] = self._compute_score_samples(X[sl], subsample_features)

        return scores

    def _compute_score_samples(self, X, subsample_features):
        """
        Compute the score of each samples in X going through the extra trees.

        Parameters
        ----------
        X : array-like or sparse matrix
            Data matrix.

        subsample_features : bool
            Whether features should be subsampled.
        """
        n_samples = X.shape[0]

        depths = np.zeros(n_samples, order="f")

        for tree, features in zip(self.estimators_, self.estimators_features_):
            X_subset = X[:, features] if subsample_features else X

            leaves_index = tree.apply(X_subset)
            node_indicator = tree.decision_path(X_subset)
            n_samples_leaf = tree.tree_.n_node_samples[leaves_index]

            depths += (
                np.ravel(node_indicator.sum(axis=1))
                + _average_path_length(n_samples_leaf)
                - 1.0
            )

        scores = 2 ** (
            -depths
            / (len(self.estimators_)
               * _average_path_length([self.max_samples_]))
        )
        return scores

    def _more_tags(self):
        return {
            '_xfail_checks': {
                'check_sample_weights_invariance(kind=zeros)':
                'zero sample_weight is not equivalent to removing samples',
            }
        }


def _average_path_length(n_samples_leaf):
    """
    The average path length in a n_samples iTree, which is equal to
    the average path length of an unsuccessful BST search since the
    latter has the same structure as an isolation tree.
    Parameters
    ----------
    n_samples_leaf : array-like of shape (n_samples,)
        The number of training samples in each test sample leaf, for
        each estimators.

    Returns
    -------
    average_path_length : ndarray of shape (n_samples,)
    """

    n_samples_leaf = check_array(n_samples_leaf, ensure_2d=False)

    n_samples_leaf_shape = n_samples_leaf.shape
    n_samples_leaf = n_samples_leaf.reshape((1, -1))
    average_path_length = np.zeros(n_samples_leaf.shape)

    mask_1 = n_samples_leaf <= 1
    mask_2 = n_samples_leaf == 2
    not_mask = ~np.logical_or(mask_1, mask_2)

    average_path_length[mask_1] = 0.
    average_path_length[mask_2] = 1.
    average_path_length[not_mask] = (
        2.0 * (np.log(n_samples_leaf[not_mask] - 1.0) + np.euler_gamma)
        - 2.0 * (n_samples_leaf[not_mask] - 1.0) / n_samples_leaf[not_mask]
    )

    return average_path_length.reshape(n_samples_leaf_shape)