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#!/usr/bin/env python3
"""
数学逻辑测试: 纯偏见减少损失函数
不依赖PyTorch，只验证数学计算逻辑
"""
import math
def test_debiasing_math():
"""测试纯偏见减少的数学逻辑"""
print("🧪 测试纯偏见减少的数学逻辑...")
# 模拟样本熵数据
# 假设批次: [男性1, 女性1, 男性2, 女性2]
sample_entropies = [0.5, 0.8, 0.4, 0.9] # 样本级熵
genders = ['male', 'female', 'male', 'female']
print(f"📊 测试数据:")
for i, (entropy, gender) in enumerate(zip(sample_entropies, genders)):
print(f" 样本{i+1}: {gender}, 熵={entropy}")
# 计算组平均熵
male_entropies = [e for e, g in zip(sample_entropies, genders) if g == 'male']
female_entropies = [e for e, g in zip(sample_entropies, genders) if g == 'female']
H_male = sum(male_entropies) / len(male_entropies)
H_female = sum(female_entropies) / len(female_entropies)
print(f"\n📈 组熵计算:")
print(f" 男性熵: {male_entropies} → 平均={H_male:.4f}")
print(f" 女性熵: {female_entropies} → 平均={H_female:.4f}")
# 计算熵差距
entropy_gap = abs(H_female - H_male)
entropy_gap_signed = H_female - H_male
print(f" 熵差距: |{H_female:.4f} - {H_male:.4f}| = {entropy_gap:.4f}")
print(f" 带符号差距: {entropy_gap_signed:.4f}")
# 纯偏见减少损失
# L2版本: (H_female - H_male)²
loss_l2 = (H_female - H_male) ** 2
# L1版本: |H_female - H_male|
loss_l1 = abs(H_female - H_male)
print(f"\n🎯 纯偏见减少损失:")
print(f" L2损失: ({H_female:.4f} - {H_male:.4f})² = {loss_l2:.6f}")
print(f" L1损失: |{H_female:.4f} - {H_male:.4f}| = {loss_l1:.6f}")
# 对比原GEE损失（模拟）
H_bar = sum(sample_entropies) / len(sample_entropies) # 整体平均熵
lambda_weight = 3.0
loss_em = H_bar # EM项
loss_bias = (H_female - H_male) ** 2 # 偏见项
loss_gee_total = loss_em + lambda_weight * loss_bias # 原GEE总损失
print(f"\n🔄 对比原GEE损失:")
print(f" 整体平均熵(EM项): {H_bar:.6f}")
print(f" 偏见项: {loss_bias:.6f}")
print(f" λ权重: {lambda_weight}")
print(f" 原GEE总损失: {loss_em:.6f} + {lambda_weight} × {loss_bias:.6f} = {loss_gee_total:.6f}")
print(f" 纯Debiasing损失: {loss_l2:.6f}")
print(f"\n📏 关键区别:")
print(f" 原GEE: 同时最小化整体熵({loss_em:.6f}) + 偏见({loss_bias:.6f})")
print(f" 纯Debiasing: 只最小化偏见({loss_l2:.6f})")
print(f" 减少的计算量: {loss_em:.6f} (不再需要优化整体熵)")
return True
def simulate_training_scenarios():
"""模拟不同训练场景下的损失变化"""
print(f"\n📈 模拟训练场景:")
scenarios = [
{
"name": "初始状态 - 严重偏见",
"data": [0.3, 0.9, 0.2, 1.0], # 男性低熵，女性高熵
"genders": ['male', 'female', 'male', 'female']
},
{
"name": "训练中期 - 偏见减少",
"data": [0.4, 0.7, 0.5, 0.6], # 差距缩小
"genders": ['male', 'female', 'male', 'female']
},
{
"name": "训练后期 - 接近平衡",
"data": [0.55, 0.6, 0.58, 0.57], # 几乎相等
"genders": ['male', 'female', 'male', 'female']
},
{
"name": "理想状态 - 完全平衡",
"data": [0.6, 0.6, 0.6, 0.6], # 完全相等
"genders": ['male', 'female', 'male', 'female']
}
]
for i, scenario in enumerate(scenarios):
print(f"\n🔄 场景 {i+1}: {scenario['name']}")
entropies = scenario['data']
genders = scenario['genders']
# 计算组熵
male_entropies = [e for e, g in zip(entropies, genders) if g == 'male']
female_entropies = [e for e, g in zip(entropies, genders) if g == 'female']
H_male = sum(male_entropies) / len(male_entropies)
H_female = sum(female_entropies) / len(female_entropies)
# 纯偏见减少损失
debiasing_loss = (H_female - H_male) ** 2
entropy_gap = abs(H_female - H_male)
# 评估偏见程度
if entropy_gap <= 0.01:
bias_level = "无偏见 ✅"
elif entropy_gap <= 0.05:
bias_level = "轻微偏见 ⚠️"
elif entropy_gap <= 0.1:
bias_level = "中等偏见 ❌"
else:
bias_level = "严重偏见 💥"
print(f" H_male={H_male:.4f}, H_female={H_female:.4f}")
print(f" 熵差距: {entropy_gap:.4f}")
print(f" Debiasing损失: {debiasing_loss:.6f}")
print(f" 偏见程度: {bias_level}")
print(f"\n✅ 预期训练效果: 损失和熵差距逐步下降，偏见程度改善")
def test_edge_cases():
"""测试边界情况"""
print(f"\n⚠️ 测试边界情况:")
edge_cases = [
{
"name": "完全平衡",
"data": [0.5, 0.5, 0.5, 0.5],
"genders": ['male', 'female', 'male', 'female']
},
{
"name": "极端偏见",
"data": [0.0, 1.0, 0.0, 1.0],
"genders": ['male', 'female', 'male', 'female']
},
{
"name": "反向偏见",
"data": [0.8, 0.2, 0.9, 0.1], # 男性高熵，女性低熵
"genders": ['male', 'female', 'male', 'female']
}
]
for case in edge_cases:
print(f"\n🔍 {case['name']}:")
entropies = case['data']
genders = case['genders']
male_entropies = [e for e, g in zip(entropies, genders) if g == 'male']
female_entropies = [e for e, g in zip(entropies, genders) if g == 'female']
H_male = sum(male_entropies) / len(male_entropies)
H_female = sum(female_entropies) / len(female_entropies)
debiasing_loss = (H_female - H_male) ** 2
entropy_gap = abs(H_female - H_male)
print(f" H_male={H_male:.4f}, H_female={H_female:.4f}")
print(f" 熵差距: {entropy_gap:.4f}")
print(f" Debiasing损失: {debiasing_loss:.6f}")
# 验证数学正确性
expected_loss = (H_female - H_male) ** 2
assert abs(debiasing_loss - expected_loss) < 1e-10, "数学计算错误!"
print(f" ✅ 数学验证通过")
if __name__ == "__main__":
print("🚀 开始纯偏见减少数学逻辑测试")
# 基础数学测试
success = test_debiasing_math()
if success:
print("\n✅ 基础数学测试通过！")
# 训练场景模拟
simulate_training_scenarios()
# 边界情况测试
test_edge_cases()
print(f"\n🎉 所有数学测试完成！")
print(f"📋 关键发现:")
print(f" ✅ 纯偏见减少只关注 |H_female - H_male|")
print(f" ✅ 不再需要优化整体熵最小化")
print(f" ✅ 计算更简单，目标更明确")
print(f" ✅ L2损失: (H_female - H_male)²")
print(f" ✅ L1损失: |H_female - H_male|")
print(f" 🎯 准备就绪，可以开始纯debiasing训练！")
else:
print("\n❌ 数学测试失败！")
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