tensorflow--Linear Regression

import tensorflow as tf
import numpy
import matplotlib.pyplot as plt
rng = numpy.random

# Parameters
learning_rate = 0.01
training_epochs = 1000
display_step = 50

# Training Data
train_X = numpy.asarray([3.3,4.4,5.5,6.71,6.93,4.168,9.779,6.182,7.59,2.167,
                         7.042,10.791,5.313,7.997,5.654,9.27,3.1])
train_Y = numpy.asarray([1.7,2.76,2.09,3.19,1.694,1.573,3.366,2.596,2.53,1.221,
                         2.827,3.465,1.65,2.904,2.42,2.94,1.3])
n_samples = train_X.shape[0]

# tf Graph Input
X = tf.placeholder("float")
Y = tf.placeholder("float")

# Set model weights
W = tf.Variable(rng.randn(), name="weight")
b = tf.Variable(rng.randn(), name="bias")

# Construct a linear model
pred = tf.add(tf.multiply(X, W), b)

# Mean squared error
cost = tf.reduce_sum(tf.pow(pred-Y, 2))/(2*n_samples)
# Gradient descent
#  Note, minimize() knows to modify W and b because Variable objects are trainable=True by default
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

# Initialize the variables (i.e. assign their default value)
init = tf.global_variables_initializer()

# Start training
with tf.Session() as sess:

    # Run the initializer
    sess.run(init)

    # Fit all training data
    for epoch in range(training_epochs):
        for (x, y) in zip(train_X, train_Y):
            sess.run(optimizer, feed_dict={X: x, Y: y})

        # Display logs per epoch step
        if (epoch+1) % display_step == 0:
            c = sess.run(cost, feed_dict={X: train_X, Y:train_Y})
            print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(c), \
                "W=", sess.run(W), "b=", sess.run(b))

    print("Optimization Finished!")
    training_cost = sess.run(cost, feed_dict={X: train_X, Y: train_Y})
    print("Training cost=", training_cost, "W=", sess.run(W), "b=", sess.run(b), '\n')

    # Graphic display
    plt.plot(train_X, train_Y, 'ro', label='Original data')
    plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
    plt.legend()
    plt.show()

    # Testing example, as requested (Issue #2)
    test_X = numpy.asarray([6.83, 4.668, 8.9, 7.91, 5.7, 8.7, 3.1, 2.1])
    test_Y = numpy.asarray([1.84, 2.273, 3.2, 2.831, 2.92, 3.24, 1.35, 1.03])

    print("Testing... (Mean square loss Comparison)")
    testing_cost = sess.run(
        tf.reduce_sum(tf.pow(pred - Y, 2)) / (2 * test_X.shape[0]),
        feed_dict={X: test_X, Y: test_Y})  # same function as cost above
    print("Testing cost=", testing_cost)
    print("Absolute mean square loss difference:", abs(
        training_cost - testing_cost))

    plt.plot(test_X, test_Y, 'bo', label='Testing data')
    plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
    plt.legend()
    plt.show()

Variable和Tensor类似，但是有几点不同：

1. Variable可更改，assign函数

2. Variable常用于存储网络权重矩阵等变量，Tensor大多是中间结果

3. Variable会直接分配内存空间，而Tensor则是在运行时才分配

pred = tf.add(tf.multiply(X, W), b) # 线性回归模型，即预测值Y'=WX+b

tf.reduce_sum(
    input_tensor,
    axis=None,
    keepdims=None, # axis没有体现的轴保持原有的维度
    name=None,
    reduction_indices=None, #弃用参数，使用axis
    keep_dims=None #弃用参数，使用keepdims
)# 从维度上对张量进行缩减求和

x = tf.constant([[1, 1, 1], [1, 1, 1]]) # [2,3]
tf.reduce_sum(x)  # 6 默认全部相加得到一个数
tf.reduce_sum(x, 0)  # [2, 2, 2] 沿shape[0]轴缩减 得到shape为[3]
tf.reduce_sum(x, 1)  # [3, 3] 沿shape[1]轴缩减 得到shape[2]
tf.reduce_sum(x, 1, keepdims=True)  # [[3], [3]] 原shape为[2,3] keepdims之后缩减为shape[2,1]
tf.reduce_sum(x, [0, 1])  # 6 对0轴和1轴同时进行缩减

cost = tf.reduce_sum(tf.pow(pred-Y, 2))/(2*n_samples) # 最小二乘法 对所有样本计算 1/2 * (Y'-Y)^2 / n

__init__(
    learning_rate,
    use_locking=False,
    name='GradientDescent'
)

optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

__init__(
    learning_rate, # 学习速率 梯度下降的步长
    use_locking=False,
    name='GradientDescent'
) # tf.train.GradientDescentOptimizer构造函数

minimize(
    loss, # 包含需要求最小值的张量
    global_step=None,
    var_list=None,
    gate_gradients=GATE_OP,
    aggregation_method=None,
    colocate_gradients_with_ops=False,
    name=None,
    grad_loss=None
)

init = tf.global_variables_initializer() # 初始化所有的Variable，在Session.run函数中执行会自动获取所有Variable并进行初始化

# Fit all training data 线性回归模型迭代
for epoch in range(training_epochs):
    for (x, y) in zip(train_X, train_Y): # 逐个样本进行计算
        sess.run(optimizer, feed_dict={X: x, Y: y})
    # Display logs per epoch step
    if (epoch+1) % display_step == 0:
        c = sess.run(cost, feed_dict={X: train_X, Y:train_Y}) # 计算整体损失
        print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(c), \
            "W=", sess.run(W), "b=", sess.run(b)) # 计算W和b

迭代完成后，W和b的值已经确定，测试的时候对使用W和b的计算图都会按照更新后的W和b进行计算