rf_regressor.py

import numpy as np
from sklearn.ensemble import RandomForestRegressor as _sk_RandomForestRegressor
from sklearn.ensemble import ExtraTreesRegressor as _sk_ExtraTreesRegressor


def _return_std(X, trees, predictions, min_variance):
    """
    Returns `std(Y | X)`.

    Can be calculated by E[Var(Y | Tree)] + Var(E[Y | Tree]) where
    P(Tree) is `1 / len(trees)`.

    Parameters
    ----------
    * `X` [array-like, shape=(n_samples, n_features)]:
        Input data.

    * `trees` [list, shape=(n_estimators,)]:
        List of fit sklearn trees as obtained from the ``estimators_``
        attribute of a fit RandomForestRegressor or ExtraTreesRegressor.

    * `predictions` [array-like, shape=(n_samples,)]:
        Prediction of each data point as returned by RandomForestRegressor
        or ExtraTreesRegressor.

    Returns
    -------
    * `std` [array-like, shape=(n_samples,)]:
        Standard deviation of `y` at `X`. If criterion
        is set to "mse", then `std[i] ~= std(y | X[i])`.
    """
    # This derives std(y | x) as described in 4.3.2 of arXiv:1211.0906
    std = np.zeros(len(X))

    for tree in trees:
        var_tree = tree.tree_.impurity[tree.apply(X)]

        # This rounding off is done in accordance with the
        # adjustment done in section 4.3.3
        # of http://arxiv.org/pdf/1211.0906v2.pdf to account
        # for cases such as leaves with 1 sample in which there
        # is zero variance.
        var_tree[var_tree < min_variance] = min_variance
        mean_tree = tree.predict(X)
        std += var_tree + mean_tree ** 2

    std /= len(trees)
    std -= predictions ** 2.0
    std[std < 0.0] = 0.0
    std = std ** 0.5
    return std


class RandomForestRegressor(_sk_RandomForestRegressor):
    """
    RandomForestRegressor that supports conditional std computation.

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        The number of trees in the forest.

    criterion : string, optional (default="mse")
        The function to measure the quality of a split. Supported criteria
        are "mse" for the mean squared error, which is equal to variance
        reduction as feature selection criterion, and "mae" for the mean
        absolute error.

    max_features : int, float, string or None, optional (default="auto")
        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`.
        Note: the search for a split does not stop until at least one
        valid partition of the node samples is found, even if it requires to
        effectively inspect more than ``max_features`` features.

    max_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 : int, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:
        - If int, then consider `min_samples_leaf` as the minimum number.
        - If float, then `min_samples_leaf` is a percentage and
          `ceil(min_samples_leaf * n_samples)` are the minimum
          number of samples for each node.

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees with ``max_leaf_nodes`` in best-first fashion.
        Best nodes are defined as relative reduction in impurity.
        If None then unlimited number of leaf nodes.

    min_impurity_decrease : float, optional (default=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.

    bootstrap : boolean, optional (default=True)
        Whether bootstrap samples are used when building trees.

    oob_score : bool, optional (default=False)
        whether to use out-of-bag samples to estimate
        the R^2 on unseen data.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    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`.

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

    warm_start : bool, optional (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.

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

    feature_importances_ : array of shape = [n_features]
        The feature importances (the higher, the more important the feature).

    n_features_ : int
        The number of features when ``fit`` is performed.

    n_outputs_ : int
        The number of outputs when ``fit`` is performed.

    oob_score_ : float
        Score of the training dataset obtained using an out-of-bag estimate.

    oob_prediction_ : array of shape = [n_samples]
        Prediction computed with out-of-bag estimate on the training set.

    Notes
    -----
    The default values for the parameters controlling the size of the trees
    (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
    unpruned trees which can potentially be very large on some data sets. To
    reduce memory consumption, the complexity and size of the trees should be
    controlled by setting those parameter values.
    The features are always randomly permuted at each split. Therefore,
    the best found split may vary, even with the same training data,
    ``max_features=n_features`` and ``bootstrap=False``, if the improvement
    of the criterion is identical for several splits enumerated during the
    search of the best split. To obtain a deterministic behaviour during
    fitting, ``random_state`` has to be fixed.

    References
    ----------
    .. [1] L. Breiman, "Random Forests", Machine Learning, 45(1), 5-32, 2001.
    """
    def __init__(self, n_estimators=10, criterion='mse', max_depth=None,
                 min_samples_split=2, min_samples_leaf=1,
                 min_weight_fraction_leaf=0.0, max_features='auto',
                 max_leaf_nodes=None, bootstrap=True, oob_score=False,
                 n_jobs=1, random_state=None, verbose=0, warm_start=False,
                 min_variance=0.0):
        self.min_variance = min_variance
        super(RandomForestRegressor, self).__init__(
            n_estimators=n_estimators, criterion=criterion,
            max_depth=max_depth,
            min_samples_split=min_samples_split,
            min_samples_leaf=min_samples_leaf,
            min_weight_fraction_leaf=min_weight_fraction_leaf,
            max_features=max_features, max_leaf_nodes=max_leaf_nodes,
            bootstrap=bootstrap, oob_score=oob_score,
            n_jobs=n_jobs, random_state=random_state,
            verbose=verbose, warm_start=warm_start)

    def predict(self, X, return_std=False):
        """Predict continuous output for X.

        Parameters
        ----------
        X : array of shape = (n_samples, n_features)
            Input data.

        return_std : boolean
            Whether or not to return the standard deviation.

        Returns
        -------
        predictions : array-like of shape = (n_samples,)
            Predicted values for X. If criterion is set to "mse",
            then `predictions[i] ~= mean(y | X[i])`.

        std : array-like of shape=(n_samples,)
            Standard deviation of `y` at `X`. If criterion
            is set to "mse", then `std[i] ~= std(y | X[i])`.
        """
        mean = super(RandomForestRegressor, self).predict(X)

        if return_std:
            if self.criterion != "mse":
                raise ValueError(
                    "Expected impurity to be 'mse', got %s instead"
                    % self.criterion)
            std = _return_std(X, self.estimators_, mean, self.min_variance)
            return mean, std
        return mean


class ExtraTreesRegressor(_sk_ExtraTreesRegressor):
    """
    ExtraTreesRegressor that supports conditional standard deviation.

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        The number of trees in the forest.

    criterion : string, optional (default="mse")
        The function to measure the quality of a split. Supported criteria
        are "mse" for the mean squared error, which is equal to variance
        reduction as feature selection criterion, and "mae" for the mean
        absolute error.

    max_features : int, float, string or None, optional (default="auto")
        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`.
        Note: the search for a split does not stop until at least one
        valid partition of the node samples is found, even if it requires to
        effectively inspect more than ``max_features`` features.

    max_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 : int, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:
        - If int, then consider `min_samples_leaf` as the minimum number.
        - If float, then `min_samples_leaf` is a percentage and
          `ceil(min_samples_leaf * n_samples)` are the minimum
          number of samples for each node.

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees with ``max_leaf_nodes`` in best-first fashion.
        Best nodes are defined as relative reduction in impurity.
        If None then unlimited number of leaf nodes.

    min_impurity_decrease : float, optional (default=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.

    bootstrap : boolean, optional (default=True)
        Whether bootstrap samples are used when building trees.

    oob_score : bool, optional (default=False)
        whether to use out-of-bag samples to estimate
        the R^2 on unseen data.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    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`.

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

    warm_start : bool, optional (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.

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

    feature_importances_ : array of shape = [n_features]
        The feature importances (the higher, the more important the feature).

    n_features_ : int
        The number of features when ``fit`` is performed.

    n_outputs_ : int
        The number of outputs when ``fit`` is performed.

    oob_score_ : float
        Score of the training dataset obtained using an out-of-bag estimate.

    oob_prediction_ : array of shape = [n_samples]
        Prediction computed with out-of-bag estimate on the training set.

    Notes
    -----
    The default values for the parameters controlling the size of the trees
    (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
    unpruned trees which can potentially be very large on some data sets. To
    reduce memory consumption, the complexity and size of the trees should be
    controlled by setting those parameter values.
    The features are always randomly permuted at each split. Therefore,
    the best found split may vary, even with the same training data,
    ``max_features=n_features`` and ``bootstrap=False``, if the improvement
    of the criterion is identical for several splits enumerated during the
    search of the best split. To obtain a deterministic behaviour during
    fitting, ``random_state`` has to be fixed.

    References
    ----------
    .. [1] L. Breiman, "Random Forests", Machine Learning, 45(1), 5-32, 2001.
    """
    def __init__(self, n_estimators=10, criterion='mse', max_depth=None,
                 min_samples_split=2, min_samples_leaf=1,
                 min_weight_fraction_leaf=0.0, max_features='auto',
                 max_leaf_nodes=None, bootstrap=False, oob_score=False,
                 n_jobs=1, random_state=None, verbose=0, warm_start=False,
                 min_variance=0.0):
        self.min_variance = min_variance
        super(ExtraTreesRegressor, self).__init__(
            n_estimators=n_estimators, criterion=criterion,
            max_depth=max_depth,
            min_samples_split=min_samples_split,
            min_samples_leaf=min_samples_leaf,
            min_weight_fraction_leaf=min_weight_fraction_leaf,
            max_features=max_features, max_leaf_nodes=max_leaf_nodes,
            bootstrap=bootstrap, oob_score=oob_score,
            n_jobs=n_jobs, random_state=random_state,
            verbose=verbose, warm_start=warm_start)

    def predict(self, X, return_std=False):
        """
        Predict continuous output for X.

        Parameters
        ----------
        X : array-like of shape=(n_samples, n_features)
            Input data.

        return_std : boolean
            Whether or not to return the standard deviation.

        Returns
        -------
        predictions : array-like of shape=(n_samples,)
            Predicted values for X. If criterion is set to "mse",
            then `predictions[i] ~= mean(y | X[i])`.

        std : array-like of shape=(n_samples,)
            Standard deviation of `y` at `X`. If criterion
            is set to "mse", then `std[i] ~= std(y | X[i])`.
        """
        mean = super(ExtraTreesRegressor, self).predict(X)

        if return_std:
            if self.criterion != "mse":
                raise ValueError(
                    "Expected impurity to be 'mse', got %s instead"
                    % self.criterion)
            std = _return_std(X, self.estimators_, mean, self.min_variance)
            return mean, std

        return mean