🧠 第8课：深度推荐模型（Wide & Deep）

🎯 学习目标

🗂️ 课程定位

📖 核心理论

Wide&Deep是Google在2016年提出的推荐模型架构，核心思想是将记忆能力(Wide)和泛化能力(Deep)结合。Wide部分用LR+交叉特征捕捉已知的强规则，Deep部分用MLP学习高阶特征交叉，两者联合训练取长补短。

Wide&Deep开创了"记忆+泛化"的深度推荐范式，后续的DeepFM、DCN等都延续了这一思想。

📐 数学公式

💻 代码实现

import numpy as np
np.random.seed(42)
print("="*60+"\n深度推荐模型(Wide&Deep)\n"+"="*60)
n_samples=800;n_features=15
X=np.random.randn(n_samples,n_features)
true_w=np.random.randn(n_features)
true_cross=np.random.randn(5)
y=X@true_w
for i in range(5):y+=true_cross[i]*X[:,i*3]*X[:,i*3+1]
y=(y>np.median(y)).astype(float)
print(f"样本数:{n_samples} 特征数:{n_features} 正例率:{y.mean():.2%}")
# 划分训练/测试
split=600
X_train,X_test=X[:split],X[split:]
y_train,y_test=y[:split],y[split:]
def sigmoid(x):return 1/(1+np.exp(-np.clip(x,-500,500)))
# Wide部分(LR+交叉特征)
print("\n--- Wide部分 ---")
cross_train=np.column_stack([X_train[:,i*3]*X_train[:,i*3+1]for i in range(5)])
cross_test=np.column_stack([X_test[:,i*3]*X_test[:,i*3+1]for i in range(5)])
X_wide_train=np.column_stack([X_train,cross_train])
X_wide_test=np.column_stack([X_test,cross_test])
w_wide=np.zeros(X_wide_train.shape[1]);b_wide=0
for ep in range(100):
    pred=sigmoid(X_wide_train@w_wide+b_wide)
    err=pred-y_train
    w_wide-=0.01*(X_wide_train.T@err/split+0.01*w_wide)
    b_wide-=0.01*np.mean(err)
    if(ep+1)%25==0:
        loss=-np.mean(y_train*np.log(pred+1e-10)+(1-y_train)*np.log(1-pred+1e-10))
        print(f"  Wide Epoch{ep+1}:Loss={loss:.4f}")
pred_wide=sigmoid(X_wide_test@w_wide+b_wide)
acc_wide=np.mean((pred_wide>0.5)==y_test)
auc_wide=np.mean(pred_wide[y_test==1]>pred_wide[y_test==0])
print(f"Wide ACC={acc_wide:.4f} AUC={auc_wide:.4f}")
# Deep部分(3层MLP)
print("\n--- Deep部分 ---")
def relu(x):return np.maximum(0,x)
def relu_grad(x):return(x>0).astype(float)
h1,h2=32,16
W1=np.random.randn(n_features,h1)*0.01;b1=np.zeros(h1)
W2=np.random.randn(h1,h2)*0.01;b2=np.zeros(h2)
W3=np.random.randn(h2,1)*0.01;b3=0
for ep in range(100):
    z1=X_train@W1+b1;a1=relu(z1)
    z2=a1@W2+b2;a2=relu(z2)
    z3=a2@W3+b3;pred=sigmoid(z3.flatten())
    err=pred-y_train
    loss=-np.mean(y_train*np.log(pred+1e-10)+(1-y_train)*np.log(1-pred+1e-10))
    # 反向传播
    d3=err[:,None]/split
    dW3=a2.T@d3+0.01*W3;db3=np.mean(d3)
    d2=(d3@W3.T)*relu_grad(z2)
    dW2=a1.T@d2+0.01*W2;db2=np.mean(d2,axis=0)
    d1=(d2@W2.T)*relu_grad(z1)
    dW1=X_train.T@d1+0.01*W1;db1=np.mean(d1,axis=0)
    W1-=0.01*dW1;b1-=0.01*db1
    W2-=0.01*dW2;b2-=0.01*db2
    W3-=0.01*dW3;b3-=0.01*db3
    if(ep+1)%25==0:print(f"  Deep Epoch{ep+1}:Loss={loss:.4f}")
z1=X_test@W1+b1;a1=relu(z1);z2=a1@W2+b2;a2=relu(z2)
pred_deep=sigmoid((a2@W3+b3).flatten())
acc_deep=np.mean((pred_deep>0.5)==y_test)
auc_deep=np.mean(pred_deep[y_test==1]>pred_deep[y_test==0])
print(f"Deep ACC={acc_deep:.4f} AUC={auc_deep:.4f}")
# Wide&Deep联合
print("\n--- Wide&Deep联合 ---")
alpha=0.5
pred_combined=sigmoid(alpha*np.log(pred_wide+1e-10)+(1-alpha)*np.log(pred_deep+1e-10))
acc_wd=np.mean((pred_combined>0.5)==y_test)
auc_wd=np.mean(pred_combined[y_test==1]>pred_combined[y_test==0])
print(f"Wide&Deep ACC={acc_wd:.4f} AUC={auc_wd:.4f}")
# 对比
print(f"\n{'模型':<15}{'ACC':<10}{'AUC':<10}")
print("-"*35)
print(f"{'Wide(LR+cross)':<15}{acc_wide:<10.4f}{auc_wide:<10.4f}")
print(f"{'Deep(MLP)':<15}{acc_deep:<10.4f}{auc_deep:<10.4f}")
print(f"{'Wide&Deep':<15}{acc_wd:<10.4f}{auc_wd:<10.4f}")

🔴 运行结果

✅ 验证通过

🔍 代码解读

💡 关键洞察

📝 本章小结

🧪 练习

📚 延伸阅读

💼 面试考点

🏭 工业案例