對(duì)于隨機(jī)梯度下降來說，我們只需

要單次預(yù)測(cè)對(duì)應(yīng)的平方誤差：

def error(x_i, y_i, beta):
return y_i - predict(x_i, beta)
def squared_error(x_i, y_i, beta):
return error(x_i, y_i, beta) ** 2

如果你熟悉微積分，可以通過下面的方式進(jìn)行計(jì)算：

def squared_error_gradient(x_i, y_i, beta):
"""the gradient (with respect to beta)
corresponding to the ith squared error term"""
return [-2 * x_ij * error(x_i, y_i, beta)
for x_ij in x_i]

可以利用隨機(jī)梯度下降法來尋找最優(yōu)的 beta 了：

def estimate_beta(x, y):
beta_initial = [random.random() for x_i in x[0]]
return minimize_stochastic(squared_error,
squared_error_gradient,
x, y,

beta_initial,

0.001)

random.seed(0)

beta = estimate_beta(x, daily_minutes_good) # [30.63, 0.972, -1.868, 0.911]