import numpy as np
import tensorflow as tf
from sklearn.datasets import fetch_california_housing
from show import show_graph # 辅助函数，显示计算图
# 趟数
n_epochs = 1000
# 学习率
learning_rate = 0.01
# 载入数据
housing = fetch_california_housing()
m, n = housing.data.shape
m, n
# 数据归一化（使用梯度下降时，一定要注意数据归一化处理）
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaled_housing_data = scaler.fit_transform(housing.data)
# 创建自变量、因变量结点（同Normal Equation）
scaled_housing_data_plus_bias = np.c_[np.ones((m, 1)), scaled_housing_data]
X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
# 创建theta系数，用均匀分布、范围-1~1的随机数（以42为种子）进行初始化
theta = tf.Variable( tf.random_uniform( [n+1, 1], -1., 1., seed=42 ), name='theta' )
$ \widehat{y} = X \cdot \theta $
# 预测的y
y_pred = tf.matmul(X, theta, name='predictions')
计算均方误差（损失函数） $$ MSE = \frac{1}{m} \sum^{m} error_i^2 $$
error = y_pred - y
mse = tf.reduce_mean( tf.square(error), name='mse' )
$ \theta $更新公式——
$ \theta = \theta - \alpha \bigtriangledown_\theta MSE(\theta) $
1. 手动求导
$$ \frac{d\ MSE}{d\ error_i} = \frac{1}{2} error_i $$
# # 手动求导，直接给出求导公式
# gradients = 2/m * tf.matmul(tf.transpose(X), error)
# training_op = tf.assign( theta, theta - learning_rate * gradients )
2. 利用tf提供的自动微分（autodiff）
tf使用的是擅长多输入少输出（如神经网络）的Reverse-mode autodiff，具有较高的准确性和泛用性；
# # 自动微分
# gradients = tf.gradients(mse, [theta])[0]
# training_op = tf.assign( theta, theta - learning_rate * gradients )
3. 使用优化器
# 使用梯度下降优化器
optimizer = tf.train.GradientDescentOptimizer( learning_rate=learning_rate )
# # 还可以使用其他优化器，如：
# optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate, momentum=0.9)
# 指定优化目标——最小化mse
training_op = optimizer.minimize(mse)
init = tf.global_variables_initializer()
with tf.Session() as sess:
sess.run(init)
for epoch in range(n_epochs):
if epoch % 100 == 0:
print("Epoch", epoch, "MSE =", mse.eval())
sess.run(training_op)
best_theta = theta.eval()
best_theta