scikit-learn(GBDT GradientBoostingClassifier)源码解析

 

 

损失函数（目标函数）

【概述】共支持五个类别六个种类的的损失函数，分别是：

       'ls': LeastSquaresError
       'lad': LeastAbsoluteError
       'huber': HuberLossFunction
       'quantile': QuantileLossFunction
       'deviance': None,如果二分类：BinomialDeviance，多分类：MultinomialDeviance
       'exponential': ExponentialLoss,

'''判断损失函数手否支持'''
if (self.loss not in self._SUPPORTED_LOSS
        or self.loss not in LOSS_FUNCTIONS):
    raise ValueError("Loss '{0:s}' not supported. ".format(self.loss))

'''所支持的loss函数实现'''
LOSS_FUNCTIONS = {'ls': LeastSquaresError,
                  'lad': LeastAbsoluteError,
                  'huber': HuberLossFunction,
                  'quantile': QuantileLossFunction,
                  'deviance': None,    # for both, multinomial and binomial
                  'exponential': ExponentialLoss,
                  }
''''''
if self.loss == 'deviance':
    loss_class = (MultinomialDeviance
                  if len(self.classes_) > 2
                  else BinomialDeviance)

【LeastSquaresError】

    pythons实现版本支持传入样本权重，默认情况下按照权重全为1的方式计算。有权重和无权重loss计算方式如下：

       【无权重loss计算方式】

                  

       【有权重计算方式】：带权最小二乘

                 

 负梯度公式：y-f(x)

class LeastSquaresError(RegressionLossFunction):
    """Loss function for least squares (LS) estimation.
    Terminal regions need not to be updated for least squares. """
    def init_estimator(self):
        return MeanEstimator()

    def __call__(self, y, pred, sample_weight=None):
        if sample_weight is None:
            return np.mean((y - pred.ravel()) ** 2.0)
        else:
            return (1.0 / sample_weight.sum() *
                    np.sum(sample_weight * ((y - pred.ravel()) ** 2.0)))

    def negative_gradient(self, y, pred, **kargs):
        return y - pred.ravel()

    def update_terminal_regions(self, tree, X, y, residual, y_pred,
                                sample_weight, sample_mask,
                                learning_rate=1.0, k=0):
        """Least squares does not need to update terminal regions.

        But it has to update the predictions.
        """
        # update predictions
        y_pred[:, k] += learning_rate * tree.predict(X).ravel()

    def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                residual, pred, sample_weight):
        pass

 

LeastAbsoluteError(最小绝对值误差)

【loss计算方式】同样支持权重和非权重

       【不带权最小绝对值】

         

         【带权最小绝对值】

         

    【负梯度】

       如果误差大于0 取值1 ，如果误差小于0 取值-1

class LeastAbsoluteError(RegressionLossFunction):
    """Loss function for least absolute deviation (LAD) regression. """
    def init_estimator(self):
        return QuantileEstimator(alpha=0.5)

    def __call__(self, y, pred, sample_weight=None):
        if sample_weight is None:
            return np.abs(y - pred.ravel()).mean()
        else:
            return (1.0 / sample_weight.sum() *
                    np.sum(sample_weight * np.abs(y - pred.ravel())))

    def negative_gradient(self, y, pred, **kargs):
        """1.0 if y - pred > 0.0 else -1.0"""
        pred = pred.ravel()
        return 2.0 * (y - pred > 0.0) - 1.0

    def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                residual, pred, sample_weight):
        """LAD updates terminal regions to median estimates. """
        terminal_region = np.where(terminal_regions == leaf)[0]
        sample_weight = sample_weight.take(terminal_region, axis=0)
        diff = y.take(terminal_region, axis=0) - pred.take(terminal_region, axis=0)
        tree.value[leaf, 0, 0] = _weighted_percentile(diff, sample_weight, percentile=50)

【HuberLossFunction】

   

class HuberLossFunction(RegressionLossFunction):
    def __init__(self, n_classes, alpha=0.9):
        super(HuberLossFunction, self).__init__(n_classes)
        self.alpha = alpha
        self.gamma = None

    def init_estimator(self):
        return QuantileEstimator(alpha=0.5)

    def __call__(self, y, pred, sample_weight=None):
        pred = pred.ravel()
        diff = y - pred
        gamma = self.gamma
        if gamma is None:
            if sample_weight is None:
                gamma = stats.scoreatpercentile(np.abs(diff), self.alpha * 100)
            else:
                gamma = _weighted_percentile(np.abs(diff), sample_weight, self.alpha * 100)

        gamma_mask = np.abs(diff) <= gamma
        if sample_weight is None:
            sq_loss = np.sum(0.5 * diff[gamma_mask] ** 2.0)
            lin_loss = np.sum(gamma * (np.abs(diff[~gamma_mask]) - gamma / 2.0))
            loss = (sq_loss + lin_loss) / y.shape[0]
        else:
            sq_loss = np.sum(0.5 * sample_weight[gamma_mask] * diff[gamma_mask] ** 2.0)
            lin_loss = np.sum(gamma * sample_weight[~gamma_mask] *
                              (np.abs(diff[~gamma_mask]) - gamma / 2.0))
            loss = (sq_loss + lin_loss) / sample_weight.sum()
        return loss

    def negative_gradient(self, y, pred, sample_weight=None, **kargs):
        pred = pred.ravel()
        diff = y - pred
        if sample_weight is None:
            gamma = stats.scoreatpercentile(np.abs(diff), self.alpha * 100)
        else:
            gamma = _weighted_percentile(np.abs(diff), sample_weight, self.alpha * 100)
        gamma_mask = np.abs(diff) <= gamma
        residual = np.zeros((y.shape[0],), dtype=np.float64)
        residual[gamma_mask] = diff[gamma_mask]
        residual[~gamma_mask] = gamma * np.sign(diff[~gamma_mask])
        self.gamma = gamma
        return residual

    def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                residual, pred, sample_weight):
        terminal_region = np.where(terminal_regions == leaf)[0]
        sample_weight = sample_weight.take(terminal_region, axis=0)
        gamma = self.gamma
        diff = (y.take(terminal_region, axis=0)
                - pred.take(terminal_region, axis=0))
        median = _weighted_percentile(diff, sample_weight, percentile=50)
        diff_minus_median = diff - median
        tree.value[leaf, 0] = median + np.mean(
            np.sign(diff_minus_median) *
            np.minimum(np.abs(diff_minus_median), gamma))