Tensorflow学习笔记4：线性回归

使用TensorFlow的线性回归

本教程是关于通过TensorFlow训练线性模型以适应数据。或者，您可以查看此博客文章。

介绍

在机器学习和统计中，线性回归是对诸如Y的变量和至少一个自变量之间的关系的建模为X.在线性回归中，线性关系将由预测函数建模，其参数将被估计通过数据并称为线性模型。线性回归算法的主要优点是其简单性，使用它可以非常直接地解释新模型并将数据映射到新空间。在本文中，我们将介绍如何使用TensorFLow训练线性模型以及如何展示生成的模型。

整个过程描述

为了训练模型，TensorFlow循环遍历数据，它应该找到适合数据的最佳线（因为我们有一个线性模型）。通过设计适当的优化问题来估计X，Y的两个变量之间的线性关系，其中需求是适当的损失函数。该数据集可从斯坦福大学CS 20SI课程 ：TensorFlow for Deep Learning Research获得。

代码实现

通过加载必要的库和数据集来启动该过程：

＃斯坦福当然CS 20SI提供的数据文件：TensorFlow深学习研究。
＃ https://github.com/chiphuyen/tf-stanford-tutorials 
DATA_FILE = "data/fire_theft.xls"

＃从.xls文件中读取数据。
book = xlrd.open_workbook(DATA_FILE, encoding_override="utf-8")
sheet = book.sheet_by_index(0)
data = np.asarray([sheet.row_values(i) for i in range(1, sheet.nrows)])
num_samples = sheet.nrows - 1

#######################
## Defining flags #####
#######################
tf.app.flags.DEFINE_integer(
    'num_epochs', 50, 'The number of epochs for training the model. Default=50')
# Store all elements in FLAG structure!
FLAGS = tf.app.flags.FLAGS

python操作excel主要用到xlrd和xlwt这两个库，即xlrd是读excel，xlwt是写excel的库。

然后我们继续定义和初始化必要的变量：

# creating the weight and bias.
# The defined variables will be initialized to zero.
W = tf.Variable(0.0, name="weights")
b = tf.Variable(0.0, name="bias")

之后，我们应该定义必要的功能。不同的标签演示了定义的功能：

def inputs():
    """
    Defining the place_holders.
    :return:
            Returning the data and label lace holders.
    """
    X = tf.placeholder(tf.float32, name="X")
    Y = tf.placeholder(tf.float32, name="Y")
    return X,Y

def inference():
    """
    Forward passing the X.
    :param X: Input.
    :return: X*W + b.
    """
    return X * W + b

def loss(X, Y):
    """
    compute the loss by comparing the predicted value to the actual label.
    :param X: The input.
    :param Y: The label.
    :return: The loss over the samples.
    """

    # Making the prediction.
    Y_predicted = inference(X)
    return tf.squared_difference(Y, Y_predicted)

squared_difference( x, y, name=None)
tf.squared_difference返回(x - y)(x - y)元素.
更多函数建议查W3Cschool-tensorflow

# The training function.
def train(loss):
    learning_rate = 0.0001
    return tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)

①tf.train.GradientDescentOptimizer()使用随机梯度下降算法，使参数沿着 梯度的反方向，即总损失减小的方向移动，实现更新参数.
然后使用梯度找到最小train_loss

接下来，我们将循环遍历不同的数据时代并执行优化过程：

with tf.Session() as sess:

    # Initialize the variables[w and b].
    sess.run(tf.global_variables_initializer())

    # Get the input tensors
    X, Y = inputs()

    # Return the train loss and create the train_op.
    train_loss = loss(X, Y)
    train_op = train(train_loss)

    # Step 8: train the model
    for epoch_num in range(FLAGS.num_epochs): # run 100 epochs
        for x, y in data:
          train_op = train(train_loss)

          # Session runs train_op to minimize loss
          loss_value,_ = sess.run([train_loss,train_op], feed_dict={X: x, Y: y})

        # Displaying the loss per epoch.
        print('epoch %d, loss=%f' %(epoch_num+1, loss_value))

        # save the values of weight and bias
        wcoeff, bias = sess.run([W, b])

在上面的代码中，sess.run（tf.global_variables_initializer（））全局初始化所有已定义的变量。train_op建立在train_loss上，并将在每一步中更新。最后，将返回线性模型的参数，例如wcoeff和bias。为了评估，将演示预测线和原始数据以显示模型如何适合数据：

扫描二维码关注公众号，回复： 6469733 查看本文章

###############################
#### Evaluate and plot ########
###############################
Input_values = data[:,0]
Labels = data[:,1]
Prediction_values = data[:,0] * wcoeff + bias
plt.plot(Input_values, Labels, 'ro', label='main')
plt.plot(Input_values, Prediction_values, label='Predicted')

# Saving the result.
plt.legend()
plt.savefig('plot.png')
plt.close()

摘要

在本教程中，我们使用TensorFlow完成了线性模型创建。训练后发现的线不能保证是最好的线。不同的参数会影响收敛精度。使用随机优化找到线性模型，其简单性使我们的世界变得更容易。

修改后的代码：

from __future__ import print_function
import tensorflow as tf
import os
from tensorflow.python.framework import ops
import xlrd
import numpy as np

# creating the weight and bias.
# The defined variables will be initialized to zero.
W = tf.Variable(0.0, name="weights")
b = tf.Variable(0.0, name="bias")

def inputs():
    """
    Defining the place_holders.
    :return:
            Returning the data and label lace holders.
    """
    X = tf.placeholder(tf.float32, name="X")
    Y = tf.placeholder(tf.float32, name="Y")
    return X,Y

def inference(X):
    """
    Forward passing the X.
    :param X: Input.
    :return: X*W + b.
    """
    return X * W + b

def loss(X, Y):
    """
    compute the loss by comparing the predicted value to the actual label.
    :param X: The input.
    :param Y: The label.
    :return: The loss over the samples.
    """

    # Making the prediction.
    Y_predicted = inference(X)
    return tf.squared_difference(Y, Y_predicted)

# The training function.
def train(loss):
    learning_rate = 0.0001
    return tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)

FLAGS = tf.app.flags.FLAGS# Now, the variable must be initialized.
tf.app.flags.DEFINE_string('log_dir', os.path.dirname(os.path.abspath(__file__)) + '/logs',
'Directory where event logs are written to.')

DATA_FILE = "data/fire_theft.xls"
book = xlrd.open_workbook(DATA_FILE, encoding_override="utf-8")
sheet = book.sheet_by_index(0)
data = np.asarray([sheet.row_values(i) for i in range(1, sheet.nrows)])
num_samples = sheet.nrows - 1

tf.app.flags.DEFINE_integer('num_epochs', 50, 'The number of epochs for training the model. Default=50')

with tf.Session() as sess:
    writer = tf.summary.FileWriter(os.path.expanduser(FLAGS.log_dir), sess.graph)
    # Initialize the variables[w and b].
    sess.run(tf.global_variables_initializer())
    # Get the input tensors
    X, Y = inputs()
    # Return the train loss and create the train_op.
    train_loss = loss(X, Y)
    train_op = train(train_loss)
    # Step 8: train the model
    for epoch_num in range(FLAGS.num_epochs): # run 100 epochs
        for x, y in data:
          train_op = train(train_loss)

          # Session runs train_op to minimize loss
          loss_value,_ = sess.run([train_loss,train_op], feed_dict={X: x, Y: y})

        # Displaying the loss per epoch.
        print('epoch %d, loss=%f' %(epoch_num+1, loss_value))

        # save the values of weight and bias
        wcoeff, bias = sess.run([W, b])
    
writer.close()

另外一个例子：

import numpy as np
import tensorflow as tf
import xlrd
import matplotlib.pyplot as plt
import os
from sklearn.utils import check_random_state

# Generating artificial data.
n = 50
XX = np.arange(n)
rs = check_random_state(0)
YY = rs.randint(-20, 20, size=(n,)) + 2.0 * XX
data = np.stack([XX,YY], axis=1)

#######################
## Defining flags #####
#######################
tf.app.flags.DEFINE_integer('num_epochs', 50, 'The number of epochs for training the model. Default=50')
# Store all elemnts in FLAG structure!
FLAGS = tf.app.flags.FLAGS


# creating the weight and bias.
# The defined variables will be initialized to zero.
W = tf.Variable(0.0, name="weights")
b = tf.Variable(0.0, name="bias")


#  Creating placeholders for input X and label Y.
def inputs():
    """
    Defining the place_holders.
    :return:
            Returning the data and label place holders.
    """
    X = tf.placeholder(tf.float32, name="X")
    Y = tf.placeholder(tf.float32, name="Y")
    return X,Y

# Create the prediction.
def inference(X):
    """
    Forward passing the X.
    :param X: Input.
    :return: X*W + b.
    """
    return X * W + b

def loss(X, Y):
    '''
    compute the loss by comparing the predicted value to the actual label.
    :param X: The input.
    :param Y: The label.
    :return: The loss over the samples.
    '''

    # Making the prediction.
    Y_predicted = inference(X)
    return tf.reduce_sum(tf.squared_difference(Y, Y_predicted))/(2*data.shape[0])


# The training function.
def train(loss):
    learning_rate = 0.0001
    return tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)


with tf.Session() as sess:

    # Initialize the variables[w and b].
    sess.run(tf.global_variables_initializer())

    # Get the input tensors
    X, Y = inputs()

    # Return the train loss and create the train_op.
    train_loss = loss(X, Y)
    train_op = train(train_loss)

    # Step 8: train the model
    for epoch_num in range(FLAGS.num_epochs): # run 100 epochs
        loss_value, _ = sess.run([train_loss,train_op],
                                 feed_dict={X: data[:,0], Y: data[:,1]})

        # Displaying the loss per epoch.
        print('epoch %d, loss=%f' %(epoch_num+1, loss_value))

        # save the values of weight and bias
        wcoeff, bias = sess.run([W, b])


###############################
#### Evaluate and plot ########
###############################
Input_values = data[:,0]
Labels = data[:,1]
Prediction_values = data[:,0] * wcoeff + bias

# # uncomment if plotting is desired!
plt.plot(Input_values, Labels, 'ro', label='main')
plt.plot(Input_values, Prediction_values, label='Predicted')

# # Saving the result.
plt.legend()
plt.savefig('plot.png')
plt.close()

结果如下图所示：

图1：原始数据以及估计的线性模型。

上面的动画GIF显示模型带有一些微小的动作，展示了更新过程。可以观察到，线性模型肯定不是最好的！但是，正如我们所提到的，它的简单性是它的优势！