import numpy as np from sklearn.ensemble import ExtraTreesRegressor as _sk_ExtraTreesRegressor from sklearn.ensemble import RandomForestRegressor as _sk_RandomForestRegressor 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 "squared_error", 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="squared_error") The function to measure the quality of a split. Supported criteria are "squared_error" 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='squared_error', max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features=None, max_leaf_nodes=None, min_impurity_decrease=0.0, 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().__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, min_impurity_decrease=min_impurity_decrease, 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 "squared_error", 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 "squared_error", then `std[i] ~= std(y | X[i])`. """ mean = super().predict(X) if return_std: if self.criterion != "squared_error": raise ValueError( "Expected impurity to be 'squared_error', 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="squared_error") The function to measure the quality of a split. Supported criteria are "squared_error" 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 "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='squared_error', max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features=None, max_leaf_nodes=None, min_impurity_decrease=0.0, 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().__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, min_impurity_decrease=min_impurity_decrease, 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 "squared_error", 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 "squared_error", then `std[i] ~= std(y | X[i])`. """ mean = super().predict(X) if return_std: if self.criterion != "squared_error": raise ValueError( "Expected impurity to be 'squared_error', got %s instead" % self.criterion ) std = _return_std(X, self.estimators_, mean, self.min_variance) return mean, std return mean