最近面试有要求手撕SGD，这里顺便就把梯度下降、随机梯度下降、批次梯度下降给写出来了
有几个注意点：
1.求梯度时注意label[i]和pred[i]不要搞反，否则会导致模型发散
2.如果跑了几千个epoch，还是没有收敛，可能是学习率太小了
# X：n*k
# Y: n*1import random
import numpyclass GD:def __init__(self,w_dim,r):# 随机初始化self.w = [random.random() for _ in range(w_dim)]self.bias = random.random()self.learningRate = rprint(f"original w is {self.w}, original bias is {self.bias}")def forward(self,x):# 前馈网络ans = []for i in range(len(x)):y=0for j in range(len(x[0])):y+=self.w[j]*x[i][j]ans.append(y+self.bias)return ansdef bp(self,X,pred,label,op="GD"):# 计算均方差loss = 0for i in range(len(pred)):loss+=(label[i]-pred[i])**2loss = loss/len(X)# 计算梯度# 梯度下降if op=="GD":grad_w = [0 for _ in range(len(self.w))]grad_bias=0for i in range(len(X)):grad_bias+=-2*(label[i]-pred[i])for j in range(len(self.w)):grad_w[j]+=-2*(label[i]-pred[i])*X[i][j] # 反向传播，更新梯度self.bias=self.bias-self.learningRate*grad_bias/len(X)for i in range(len(self.w)):self.w[i]-=self.learningRate*grad_w[i]/len(X)# 随机梯度下降if op=="SGD":grad_w = [0 for _ in range(len(self.w))]grad_bias=0randInd = random.randint(0,len(X)-1)grad_bias+=-2*(label[randInd]-pred[randInd])for j in range(len(self.w)):grad_w[j]+=-2*(label[randInd]-pred[randInd])*X[randInd][j] # 反向传播，更新梯度self.bias=self.bias-self.learningRate*grad_biasfor i in range(len(self.w)):self.w[i]-=self.learningRate*grad_w[i]# 批次梯度下降if op=="BGD": grad_w = [0 for _ in range(len(self.w))]grad_bias=0BS=8randInd = random.randint(0,len(X)/BS-1)X = X[BS*randInd:BS*(randInd+1)]label = label[BS*randInd:BS*(randInd+1)]pred = pred[BS*randInd:BS*(randInd+1)]for i in range(len(X)):grad_bias+=-2*(label[i]-pred[i])for j in range(len(self.w)):grad_w[j]+=-2*(label[i]-pred[i])*X[i][j] # 反向传播，更新梯度self.bias=self.bias-self.learningRate*grad_bias/len(X)for i in range(len(self.w)):self.w[i]-=self.learningRate*grad_w[i]/len(X)return lossdef testY(X,w):Y = []for x in X:y=0for i in range(len(x)):y+=w[i]*x[i]Y.append(y)return Y# 构建数据
n = 1000
X=[[random.random() for _ in range(2)] for _ in range(n)]
w=[0.2,0.3]
B=0.4
Y = testY(X,w)# 设置样本维度为2
k = 2
lr = GD(k,0.01)
Loss=0
epochs=2000for e in range(epochs):Loss = 0pred = lr.forward(X)loss=lr.bp(X,pred,Y,"BGD")Loss+=loss if (e%100)==0: print(f"step:{e},Loss:{Loss}") X_test=[[random.random() for _ in range(2)] for _ in range(2)]
Y_test=testY(X_test,w)print("X_test=",X_test)
print("Y_test=",Y_test)
print("Y_pred=",lr.forward(X_test))测试效果如下：
也还行
