"""
Focal Loss - 处理类别不平衡的损失函数
Focal Loss通过降低易分类样本的权重，专注于难分类样本，特别适合金融风控场景中的
不平衡数据问题（如坏账率通常很低）。
"""
import numpy as np
from typing import Optional
from .base import BaseLoss
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class FocalLoss(BaseLoss):
"""Focal Loss，通过调整样本权重来解决类别不平衡问题。
数学公式:
FL(p_t) = -α_t * (1 - p_t)^γ * log(p_t)
其中:
p_t = p if y=1 else 1-p
α_t = α if y=1 else 1-α
:param alpha: 正样本权重，默认为0.25，用于平衡正负样本的总体权重
:param gamma: 聚焦参数，默认为2.0，控制易分类样本的权重衰减程度
- gamma=0: 等价于标准交叉熵
- gamma越大，易分类样本权重越小
:param name: 损失函数名称，默认为"focal_loss"
**参考样例**
>>> import numpy as np
>>> from hscredit.core.models.losses import FocalLoss
>>>
>>> # 创建损失函数
>>> loss = FocalLoss(alpha=0.75, gamma=2.0)
>>>
>>> # 计算损失
>>> y_true = np.array([0, 0, 1, 1])
>>> y_pred = np.array([0.1, 0.4, 0.6, 0.9])
>>> loss_value = loss(y_true, y_pred)
>>>
>>> # 在XGBoost中使用
>>> import xgboost as xgb
>>> dtrain = xgb.DMatrix(X_train, label=y_train)
>>> params = {'objective': 'binary:logistic'}
>>> bst = xgb.train(params, dtrain, obj=loss.to_xgboost(), num_boost_round=100)
**引用**
Lin, T.-Y., Goyal, P., Girshick, R., He, K., & Dollár, P. (2017). *Focal Loss for
Dense Object Detection.* ICCV 2017. https://arxiv.org/abs/1708.02002
"""
def __init__(
self,
alpha: float = 0.25,
gamma: float = 2.0,
name: str = "focal_loss"
):
super().__init__(name)
self.alpha = alpha
self.gamma = gamma
def __call__(
self,
y_true: np.ndarray,
y_pred: np.ndarray
) -> float:
"""计算Focal Loss。
:param y_true: 真实标签, shape (n_samples,)
:param y_pred: 预测概率, shape (n_samples,)
:return: 平均损失值
"""
# 确保概率在[0, 1]范围内
y_pred = np.clip(y_pred, 1e-7, 1 - 1e-7)
# 计算p_t
p_t = np.where(y_true == 1, y_pred, 1 - y_pred)
# 计算alpha_t
alpha_t = np.where(y_true == 1, self.alpha, 1 - self.alpha)
# 计算focal weight
focal_weight = (1 - p_t) ** self.gamma
# 计算交叉熵
ce_loss = -np.log(p_t)
# 计算focal loss
focal_loss = alpha_t * focal_weight * ce_loss
return np.mean(focal_loss)
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def gradient(
self,
y_true: np.ndarray,
y_pred: np.ndarray
) -> np.ndarray:
"""计算Focal Loss的梯度（一阶导数）。
推导过程: d(FL)/d(p) = d/dp [ -α_t * (1-p_t)^γ * log(p_t) ]
:param y_true: 真实标签
:param y_pred: 预测概率
:return: 梯度数组
"""
# 确保概率在合理范围内
y_pred = np.clip(y_pred, 1e-7, 1 - 1e-7)
# 计算alpha_t
alpha_t = np.where(y_true == 1, self.alpha, 1 - self.alpha)
# 计算梯度
grad = np.zeros_like(y_pred)
# 正样本梯度
pos_mask = y_true == 1
if np.any(pos_mask):
p = y_pred[pos_mask]
grad[pos_mask] = (
alpha_t[pos_mask] * (
self.gamma * (1 - p) ** (self.gamma - 1) * np.log(p) -
(1 - p) ** self.gamma / p
)
)
# 负样本梯度
neg_mask = y_true == 0
if np.any(neg_mask):
p = y_pred[neg_mask]
grad[neg_mask] = (
alpha_t[neg_mask] * (
-self.gamma * p ** (self.gamma - 1) * np.log(1 - p) +
p ** self.gamma / (1 - p)
)
)
return grad
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def hessian(
self,
y_true: np.ndarray,
y_pred: np.ndarray
) -> np.ndarray:
"""计算Focal Loss的二阶导数。
:param y_true: 真实标签
:param y_pred: 预测概率
:return: 二阶导数数组
"""
# 确保概率在合理范围内
y_pred = np.clip(y_pred, 1e-7, 1 - 1e-7)
# 计算alpha_t
alpha_t = np.where(y_true == 1, self.alpha, 1 - self.alpha)
# 计算二阶导数（简化版本）
hess = np.zeros_like(y_pred)
# 正样本二阶导
pos_mask = y_true == 1
if np.any(pos_mask):
p = y_pred[pos_mask]
hess[pos_mask] = alpha_t[pos_mask] * (
self.gamma * (self.gamma - 1) * (1 - p) ** (self.gamma - 2) * np.log(p) +
2 * self.gamma * (1 - p) ** (self.gamma - 1) / p +
(1 - p) ** self.gamma / (p ** 2)
)
# 负样本二阶导
neg_mask = y_true == 0
if np.any(neg_mask):
p = y_pred[neg_mask]
hess[neg_mask] = alpha_t[neg_mask] * (
self.gamma * (self.gamma - 1) * p ** (self.gamma - 2) * np.log(1 - p) +
2 * self.gamma * p ** (self.gamma - 1) / (1 - p) +
p ** self.gamma / ((1 - p) ** 2)
)
# 确保二阶导为正
hess = np.abs(hess) + 1e-6
return hess