CBDT 梯度提升树(Gradient Boosting Decison Tree)，是Boosting提升算法的一种。
前一轮迭代生成模型记为，损失函数为
,本轮模型
拟合之前模型损失函数的负梯度。
class sklearn.ensemble.GradientBoostingClassifier(loss=’deviance’, learning_rate=0.1, n_estimators=100, subsample=1.0, criterion=’friedman_mse’, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_depth=3, min_impurity_decrease=0.0, min_impurity_split=None, init=None, random_state=None, max_features=None, verbose=0, max_leaf_nodes=None, warm_start=False, presort=’auto’, validation_fraction=0.1, n_iter_no_change=None, tol=0.0001)
Gradient Boosting for classification.
GB builds an additive model in a forward stage-wise fashion; it allows for the optimization of arbitrary differentiable loss functions. In each stage n_classes_ regression trees are fit on the negative gradient of the binomial or multinomial deviance loss function. Binary classification is a special case where only a single regression tree is induced.
Parameters:
1）loss : {‘deviance’, ‘exponential’}, optional (default=’deviance’)
loss function to be optimized. ‘deviance’ refers to deviance (= logistic regression) for classification with probabilistic outputs. For loss ‘exponential’ gradient boosting recovers the AdaBoost algorithm.
损失函数：对数似然损失函数、指数损失函数
二分类的对数损失函数(Binomial deviance,’deviance’),提供概率估计，模型初值设为对数几率
多分类的对数损失(Multinomial deviance,’deviance’),针对n_classes互斥的多分类，提供概率估计，初始模型值设为各类别的先验概率，每一轮迭代需要构建n类回归树可能会使得模型对于多类别的大数据集不太高效
指数损失函数(Exponential loss),与AdaBoostClassifier的损失函数一致，相对对数损失来说对错误标签的样本不够鲁棒，只能够被用来作二分类
2）learning_rate : float, optional (default=0.1)
learning rate shrinks the contribution of each tree by learning_rate. There is a trade-off between learning_rate and n_estimators.
学习速率
3）n_estimators : int (default=100)
The number of boosting stages to perform. Gradient boosting is fairly robust to over-fitting so a large number usually results in better performance.
基学习器的数量，即学习步长
4）subsample : float, optional (default=1.0)
The fraction of samples to be used for fitting the individual base learners. If smaller than 1.0 this results in Stochastic Gradient Boosting. subsample interacts with the parameter n_estimators. Choosing subsample < 1.0 leads to a reduction of variance and an increase in bias.
针对样本采样率
5）criterion : string, optional (default=”friedman_mse”)
The function to measure the quality of a split. Supported criteria are “friedman_mse” for the mean squared error with improvement score by Friedman, “mse” for mean squared error, and “mae” for the mean absolute error. The default value of “friedman_mse” is generally the best as it can provide a better approximation in some cases.
New in version 0.18.
分裂点评价指标（可参考CART的参数）
'friedman_mse'：'负梯度'（'均方误差'近似值）（？？？）
'mse'：'均方误差'
'mae':：绝对误差
6）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 fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.
Changed in version 0.18: Added float values for fractions.
7）min_samples_leaf : int, float, optional (default=1)
The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.
If int, then consider min_samples_leaf as the minimum number.
If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.
Changed in version 0.18: Added float values for fractions.
8）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.
9）max_depth : integer, optional (default=3)
maximum depth of the individual regression estimators. The maximum depth limits the number of nodes in the tree. Tune this parameter for best performance; the best value depends on the interaction of the input variables.
10）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.
New in version 0.19.
11）min_impurity_split : float, (default=1e-7)
Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.
Deprecated since version 0.19: min_impurity_split has been deprecated in favor ofmin_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.
12）init : estimator or ‘zero’, optional (default=None)
An estimator object that is used to compute the initial predictions. init has to provide fit and predict_proba. If ‘zero’, the initial raw predictions are set to zero. By default, a DummyEstimatorpredicting the classes priors is used.
基学习器的初始化：init,用来计算初始基学习器的预测，需要具备fit和predict方法，若未设置则默认为loss.init_estimator
13）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.
14）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 fraction and int(max_features * n_features) features are considered at each split.
If “auto”, then max_features=sqrt(n_features).
If “sqrt”, then max_features=sqrt(n_features).
If “log2”, then max_features=log2(n_features).
If None, then max_features=n_features.
Choosing max_features < n_features leads to a reduction of variance and an increase in bias.
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.
15）verbose : int, default: 0
Enable verbose output. If 1 then it prints progress and performance once in a while (the more trees the lower the frequency). If greater than 1 then it prints progress and performance for every tree.
生成过程信息
16）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.
17）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 erase the previous solution. See the Glossary.
模型的重复使用(热启动)：warm_start,若设置为True则可以使用已经训练好的学习器，并且在其上添加更多的基学习器
18）presort : bool or ‘auto’, optional (default=’auto’)
Whether to presort the data to speed up the finding of best splits in fitting. Auto mode by default will use presorting on dense data and default to normal sorting on sparse data. Setting presort to true on sparse data will raise an error.
New in version 0.17: presort parameter.
19）validation_fraction : float, optional, default 0.1
The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if n_iter_no_change is set to an integer.
New in version 0.20.
预留一定比例的样本数据，用做验证集
20）n_iter_no_change : int, default None
n_iter_no_change is used to decide if early stopping will be used to terminate training when validation score is not improving. By default it is set to None to disable early stopping. If set to a number, it will set aside validation_fraction size of the training data as validation and terminate training when validation score is not improving in all of the previous n_iter_no_change numbers of iterations. The split is stratified.
New in version 0.20.
如果在 'n_iter_no_change ' 次迭代中，模型效果没有提升，则提前结束。
21）tol : float, optional, default 1e-4
Tolerance for the early stopping. When the loss is not improving by at least tol for n_iter_no_change iterations (if set to a number), the training stops.
New in version 0.20.
如果在 'n_iter_no_change ' 次迭代中，模型效果提升低于 'tol'，则提前结束。
19）、20)、21) 三个参数一起使用
参考：
https://www.cnblogs.com/infaraway/p/7890558.html
https://www.cnblogs.com/ModifyRong/p/7744987.html
https://blog.csdn.net/zpalyq110/article/details/79527653
https://blog.csdn.net/akirameiao/article/details/80009155
注：
以上没有解释的参数可以参考 CART 参数解析 https://www.jianshu.com/p/f0f41ad72e5f
