可以看到，每次 epoch，我们都会更新数据集里每行的系数。系数的更新是基于模型生成的误差。该误差被算作候选系数的预测值和预期输出值之间的差。

error = prediction - expected

有一个系数用于加权每一个输入属性，这些属性将以连续的方式进行更新，比如

b1(t+1) = b1(t) - learning_rate * error(t) * x1(t)

列表开始的特殊系数，也被称为截距（intercept）或偏差（bias），也以类似的方式更新，atv，但因其不与特定输入值相关，所以无输入值。

b0(t+1) = b0(t) - learning_rate * error(t)

现在我们把所有东西组合在一起。coefficients_sgd() 函数正是用随机梯度下降来计算一个训练集的系数值，下面即是该函数：

# Estimate linear regression coefficients using stochastic gradient descent

def coefficients_sgd(train, l_rate, n_epoch):

coef = [0.0 for i in range(len(train[0]))]

for epoch in range(n_epoch):

sum_error = 0

for row in train:

yhat = predict(row, coef)

error = yhat - row[-1]

sum_error += error**2

coef[0] = coef[0] - l_rate * error

for i in range(len(row)-1):

coef[i + 1] = coef[i + 1] - l_rate * error * row[i]

print('>epoch=%d, lrate=%.3f, error=%.3f' % (epoch, l_rate, sum_error))

return coef

此外，我们追踪每个 epoch 的方差（正值）总和从而在循环之后得到一个好的结果。

# Make a prediction with coefficients

def predict(row, coefficients):

yhat = coefficients[0]

for i in range(len(row)-1):

yhat += coefficients[i + 1] * row[i]

return yhat

# Estimate linear regression coefficients using stochastic gradient descent

def coefficients_sgd(train, l_rate, n_epoch):

coef = [0.0 for i in range(len(train[0]))]

for epoch in range(n_epoch):

sum_error = 0

for row in train:

yhat = predict(row, coef)

error = yhat - row[-1]

sum_error += error**2

coef[0] = coef[0] - l_rate * error

for i in range(len(row)-1):

coef[i + 1] = coef[i + 1] - l_rate * error * row[i]

print('>epoch=%d, lrate=%.3f, error=%.3f' % (epoch, l_rate, sum_error))

return coef

# Calculate coefficients

dataset = [[1, 1], [2, 3], [4, 3], [3, 2], [5, 5]]

l_rate = 0.001

n_epoch = 50

coef = coefficients_sgd(dataset, l_rate, n_epoch)

print(coef)