lectura del código fuente de sklearn GBDT

CSDN

Documentación de ejemplo:

Regresión de aumento de gradiente

Documentación de API:

sklearn.ensemble.GradientBoostingClassifier

sklearn.ensemble.GradientBoostingRegressor

sklearn.ensemble.HistGradientBoostingClassifier

Blog salvaje e implementación:

Derivación matemática + implementación Python pura del algoritmo de aprendizaje automático 15: GBDT

Resumen del principio del árbol de aumento de gradiente (GBDT)

Resumen de los parámetros de ajuste del árbol de aumento de gradiente de scikit-learn (GBDT)

¿Por qué se reemplaza el residuo de gbdt por un gradiente negativo?

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• ls

class LeastSquaresError(RegressionLossFunction):
    def init_estimator(self):
        return DummyRegressor(strategy='mean')

    def __call__(self, y, raw_predictions, sample_weight=None):
        return (1 / sample_weight.sum() * np.sum(
            sample_weight * ((y - raw_predictions.ravel()) ** 2)))

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

• lad

class LeastAbsoluteError(RegressionLossFunction):
    def init_estimator(self):
        return DummyRegressor(strategy='quantile', quantile=.5)

    def __call__(self, y, raw_predictions, sample_weight=None):
        return (1 / sample_weight.sum() * np.sum(
            sample_weight * np.abs(y - raw_predictions.ravel())))

    def negative_gradient(self, y, raw_predictions, **kargs):
        raw_predictions = raw_predictions.ravel()
        return 2 * (y - raw_predictions > 0) - 1

• huber

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

    def init_estimator(self):
        return DummyRegressor(strategy='quantile', quantile=.5)

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

        gamma_mask = np.abs(diff) <= gamma
        sq_loss = np.sum(0.5 * sample_weight[gamma_mask] *
                         diff[gamma_mask] ** 2)
        lin_loss = np.sum(gamma * sample_weight[~gamma_mask] *
                          (np.abs(diff[~gamma_mask]) - gamma / 2))
        loss = (sq_loss + lin_loss) / sample_weight.sum()
        return loss

    def negative_gradient(self, y, raw_predictions, sample_weight=None,
                          **kargs):
        raw_predictions = raw_predictions.ravel()
        diff = y - raw_predictions
        if sample_weight is None:
            gamma = np.percentile(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

• quantile

class QuantileLossFunction(RegressionLossFunction):
    def __init__(self, alpha=0.9):
        super().__init__()
        self.alpha = alpha
        self.percentile = alpha * 100

    def init_estimator(self):
        return DummyRegressor(strategy='quantile', quantile=self.alpha)

    def __call__(self, y, raw_predictions, sample_weight=None):
        raw_predictions = raw_predictions.ravel()
        diff = y - raw_predictions
        alpha = self.alpha

        mask = y > raw_predictions
        if sample_weight is None:
            loss = (alpha * diff[mask].sum() -
                    (1 - alpha) * diff[~mask].sum()) / y.shape[0]
        else:
            loss = ((alpha * np.sum(sample_weight[mask] * diff[mask]) -
                    (1 - alpha) * np.sum(sample_weight[~mask] *
                                         diff[~mask])) / sample_weight.sum())
        return loss

    def negative_gradient(self, y, raw_predictions, **kargs):
        alpha = self.alpha
        raw_predictions = raw_predictions.ravel()
        mask = y > raw_predictions
        return (alpha * mask) - ((1 - alpha) * ~mask)

• deviance

Desviación binomial

from scipy.special import expit, logsumexp

class BinomialDeviance(ClassificationLossFunction):
    def init_estimator(self):
        return DummyClassifier(strategy='prior')

    def __call__(self, y, raw_predictions, sample_weight=None):
        return (-2 / sample_weight.sum() * np.sum(
            sample_weight * ((y * raw_predictions) -
                             np.logaddexp(0, raw_predictions))))

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

Esta fórmula simplificada es $-2[y\cdot \hat{y}-log(1+{mi}^{\hat{y}}\left)\right]$

Esta función de pérdida es diferente de numpy-ml, y este blog es muy completo:

Función de pérdida de desviación binomial de Scikit

Empuje hacia abajo el gradiente negativo de esta fórmula

$=y-\frac{{mi}^{\hat{y}}}{1+e^{\hat{y}}}=y-\frac{1}{1+e^{-\hat{y}}}=y-\sigma \left(\hat{y}\right)$