def estimate_beta_ridge(x, y, alpha):
# use gradient descent to fit a ridge regression with penalty alpha
beta_initial = [random.random() for x_i in x[0]]
return minimize_stochastic(
partial(squared_error_ridge, alpha=alpha),
partial(squared_error_ridge_gradient, alpha=alpha), x, y, beta_initial,
0.001)
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)
return error(alpha, beta, x_i, y_i)**2
def squared_error_gradient(x_i, y_i, theta):
alpha, beta = theta
return [
-2 * error(alpha, beta, x_i, y_i), #alpha partial derivative
-2 * error(alpha, beta, x_i, y_i) * x_i
] #beta partial derivative
# choose random value to start
random.seed(0)
theta = [random.random(), random.random()]
alpha, beta = minimize_stochastic(squared_error, squared_error_gradient,
num_friends_good, daily_minutes_good, theta,
0.0001)
print alpha, beta
if __name__ == "__main__":
num_friends_good = [
49, 41, 40, 25, 21, 21, 19, 19, 18, 18, 16, 15, 15, 15, 15, 14, 14, 13,
13, 13, 13, 12, 12, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1