线性回归

张量定义:
TensorFlow operations (also called ops for short) can take any number of inputs and produce any number of outputs. For example, the addition and multiplication ops each take two inputs and produce one output. Constants and variables take no input (they are called source ops). The inputs and outputs are multidimensional arrays, called tensors (hence the name “tensor flow”)

• 下面采用sklearn的加利福尼亚的房屋价格数据做一个回归分析：creates two TensorFlow constant nodes, X and y, to hold this data and the targets,and it uses some of the matrix operations provided by Tensor‐Flow to define theta. These matrix functions—transpose(), matmul(), and matrix_inverse()逆

• 线性回归常数项计算方法：

  
  

# encoding: utf-8
"""
@version: python3.5.2 
@author: kaenlee  @contact: lichaolfm@163.com
@software: PyCharm Community Edition
@time: 2017/8/3 11:33
purpose:
"""
import numpy as np
import pandas as pd
import tensorflow as tf
import sklearn.datasets as dt


housing = dt.fetch_california_housing()
x = housing.data
y = housing.target
m, n = x.shape
print(m, n)

# 给数据添加一个常数项
housing_bias = np.c_[np.ones(shape=(m, 1)), x]
y = np.reshape(y, (-1, 1))
# print(housing_bias[:3])
# print(y[:3])
# 输入张量
X = tf.constant(housing_bias, dtype=tf.float32, name="X")
Y = tf.constant(y, dtype=tf.float32, name="Y")
XT = tf.transpose(X)

theta = tf.matmul(tf.matmul(tf.matrix_inverse(tf.matmul(XT, X)), XT), Y)  # 查看线性回归如何求解delta

with tf.Session() as sess:
    theta_value = sess.run(theta)
    # theta_value = theta.eval()
    print(theta_value)
    sess.close()

# 通过梯度下降法计算
# 随机生成theta 的一组初始值
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
gradients = 2/m * tf.matmul(tf.transpose(X), error)  #此处参考梯度下降算法原理
training_op = tf.assign(theta, theta - 0.01 * gradients) # 更新theta

# op = tf.train.GradientDescentOptimizer(0.01)  # 学习步长
# training_op = op.minimize(mse)
init = tf.global_variables_initializer()
with tf.Session() as sess:
    sess.run(init)
    for epoch in range(1000):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    best_theta = theta.eval()
    print(best_theta)
    sess.close()

ps：梯度下降法返回值会nan，有待解决！