Tensorflow初探

Hello World

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import tensorflow as tf
hello = tf.constant('Hello, TensorFlow!')
sess = tf.Session()
print(sess.run(hello))
  1. 首先导入tensorflow包
  2. 创建图
  3. 创建一个session
  4. 在session中运行图

基础的机器学习模型

线性回归

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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
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:
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()

需要注意的地方

  1. tf.placeholder(dtype, shape=None, name=None)相当于行参,占位用,参与后面的运算,真正的数值在运算时填充,通过run中的feed_dict

  2. 在TensorFlow的世界里,变量的定义和初始化是分开的,所有关于图变量的赋值和计算都要通过tf.Session的run来进行。想要将所有图变量进行集体初始化时应该使用tf.global_variables_initializer。

  3. 定义一个变量有两个函数,tf.Variable和tf.get_variable

  4. 这里的梯度下降非常简单,一行代码就可以实现!定义一个optimizer即可,tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

  5. 在做图中默认是将点连成线。

MNIST数据集

包括了6万个训练数据和1万个测试数据。手写数字图片都是2828像素固定大小,并且只有0,1两个值构成。这样,每张图可以展开成一个1784的向量,作为特征。

logistic回归

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import tensorflow as tf

# Import MINST data
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=True)
# Parameters
learning_rate = 0.01
training_epochs = 1000
batch_size = 100
display_step = 50

# tf Graph Input
x = tf.placeholder(tf.float32, [None, 784]) # mnist data image of shape 28*28=784
y = tf.placeholder(tf.float32, [None, 10]) # 0-9 digits recognition => 10 classes

# Set model weights
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))

# Construct model
pred = tf.nn.softmax(tf.matmul(x, W) + b) # Softmax

# Minimize error using cross entropy
cost = tf.reduce_mean(-tf.reduce_sum(y*tf.log(pred), reduction_indices=1))
# Gradient Descent
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:
sess.run(init)

# Training cycle
for epoch in range(training_epochs):
avg_cost = 0.
total_batch = int(mnist.train.num_examples/batch_size)
# Loop over all batches
for i in range(total_batch):
batch_xs, batch_ys = mnist.train.next_batch(batch_size)
# Fit training using batch data
_, c = sess.run([optimizer, cost], feed_dict={x: batch_xs,
y: batch_ys})
# Compute average loss
avg_cost += c / total_batch
# Display logs per epoch step
if (epoch+1) % display_step == 0:
print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(avg_cost))

print("Optimization Finished!")

# Test model
correct_prediction = tf.equal(tf.argmax(pred, 1), tf.argmax(y, 1))
# Calculate accuracy for 3000 examples
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
print("Accuracy:", accuracy.eval({x: mnist.test.images[:3000], y: mnist.test.labels[:3000]}))
  1. softmax函数 tf.nn.softmax()
  2. 交叉熵作为损失函数 tf.reduce_mean(-tf.reduce_sum(y*tf.log(pred), reduction_indices=1)) 这里的reduction_indices是维度,1表示每一行的加和。
  3. 这里采用了随机梯度下降,每一个batch为一组
  4. tf.argmax(pred,1)获取每一行的最大值的索引
  5. tf.equal()对应位置相等返回True和False
  6. accuracy.eval()sess.run(accuracy,)是一样的

KNN

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import numpy as np
import tensorflow as tf

# Import MINST data
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=True)
# In this example, we limit mnist data
Xtr, Ytr = mnist.train.next_batch(5000) #5000 for training (nn candidates)
Xte, Yte = mnist.test.next_batch(200) #200 for testing
print(Yte)
# tf Graph Input
xtr = tf.placeholder("float", [None, 784])
xte = tf.placeholder("float", [784])

# Nearest Neighbor calculation using L1 Distance
# Calculate L1 Distance
distance = tf.reduce_sum(tf.abs(tf.add(xtr, tf.negative(xte))), reduction_indices=1)
# Prediction: Get min distance index (Nearest neighbor)
pred = tf.argmin(distance, 0)

accuracy = 0.

# Initialize the variables (i.e. assign their default value)
init = tf.global_variables_initializer()
# Start training
with tf.Session() as sess:
sess.run(init)

# loop over test data
for i in range(len(Xte)):
# Get nearest neighbor
nn_index = sess.run(pred, feed_dict={xtr: Xtr, xte: Xte[i, :]})
# Get nearest neighbor class label and compare it to its true label
print("Test", i, "Prediction:", np.argmax(Ytr[nn_index]), \
"True Class:", np.argmax(Yte[i]))
# Calculate accuracy
if np.argmax(Ytr[nn_index]) == np.argmax(Yte[i]):
accuracy += 1./len(Xte)
print("Done!")
print("Accuracy:", accuracy)
  1. 如果需要实现KNN,即比较前K个数,则需要使用tf.nn.top_k()函数
  2. 后续又做了训练集数据大小和准确率的关系

KMeans

Random Forest

神经网络

Raw NN

将通过Tensorflow构建一个2个隐藏层全连接的神经网络

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from __future__ import print_function

# Import MNIST data
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=True)

import tensorflow as tf
# Parameters
learning_rate = 0.1
num_steps = 500
batch_size = 128
display_step = 100

# Network Parameters
n_hidden_1 = 256 # 1st layer number of neurons
n_hidden_2 = 256 # 2nd layer number of neurons
num_input = 784 # MNIST data input (img shape: 28*28)
num_classes = 10 # MNIST total classes (0-9 digits)

# tf Graph input
X = tf.placeholder("float", [None, num_input])
Y = tf.placeholder("float", [None, num_classes])
# Store layers weight & bias
weights = {
'h1': tf.Variable(tf.random_normal([num_input, n_hidden_1])),
'h2': tf.Variable(tf.random_normal([n_hidden_1, n_hidden_2])),
'out': tf.Variable(tf.random_normal([n_hidden_2, num_classes]))
}
biases = {
'b1': tf.Variable(tf.random_normal([n_hidden_1])),
'b2': tf.Variable(tf.random_normal([n_hidden_2])),
'out': tf.Variable(tf.random_normal([num_classes]))
}
# Create model
def neural_net(x):
# Hidden fully connected layer with 256 neurons
layer_1 = tf.add(tf.matmul(x, weights['h1']), biases['b1'])
# Hidden fully connected layer with 256 neurons
layer_2 = tf.add(tf.matmul(layer_1, weights['h2']), biases['b2'])
# Output fully connected layer with a neuron for each class
out_layer = tf.matmul(layer_2, weights['out']) + biases['out']
return out_layer
# Construct model
logits = neural_net(X)

# Define loss and optimizer
loss_op = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(
logits=logits, labels=Y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
train_op = optimizer.minimize(loss_op)

# Evaluate model (with test logits, for dropout to be disabled)
correct_pred = tf.equal(tf.argmax(logits, 1), tf.argmax(Y, 1))
accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32))

# 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)

for step in range(1, num_steps+1):
batch_x, batch_y = mnist.train.next_batch(batch_size)
# Run optimization op (backprop)
sess.run(train_op, feed_dict={X: batch_x, Y: batch_y})
if step % display_step == 0 or step == 1:
# Calculate batch loss and accuracy
loss, acc = sess.run([loss_op, accuracy], feed_dict={X: batch_x,
Y: batch_y})
print("Step " + str(step) + ", Minibatch Loss= " + \
"{:.4f}".format(loss) + ", Training Accuracy= " + \
"{:.3f}".format(acc))

print("Optimization Finished!")

# Calculate accuracy for MNIST test images
print("Testing Accuracy:", \
sess.run(accuracy, feed_dict={X: mnist.test.images,
Y: mnist.test.labels}))
  1. tf.random_normal产生的随机数服从正态分布
  2. tf.nn.softmax_cross_entropy_with_logits

函数主要两个参数,第一个参数logits是神经网络最后一层的输出,如果有batch,大小就是[batchsize,num_classes],第二个参数时实际的标签,大小同上。

具体执行的流程分为两步

第一步是先对网络最后一层的输出做一个softmax,这一步通常是求取输出属于某一类的概率,对于单样本而言,输出就是一个num_classes大小的向量([Y1,Y2,Y3…]其中Y1,Y2,Y3…分别代表了是属于该类的概率)

$$softmax(x_{i}) = \frac{exp(x_{i})}{\sum_{j}{exp(x_{j})}}$$

第二步是softmax的输出向量[Y1,Y2,Y3…]和样本的实际标签做一个交叉熵。

$$H = - \sum{y_{i}log(predict-y_{i})}$$

这个值可以作为loss

  1. tf.train.AdamOptimizer这是采用Adam算法进行优化

NN

这里将采用Tensorflow中的高级封装

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# Import MNIST data
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=False)

import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np
# Parameters
learning_rate = 0.1
num_steps = 1000
batch_size = 128
display_step = 100

# Network Parameters
n_hidden_1 = 256 # 1st layer number of neurons
n_hidden_2 = 256 # 2nd layer number of neurons
num_input = 784 # MNIST data input (img shape: 28*28)
num_classes = 10 # MNIST total classes (0-9 digits)
# Define the input function for training
input_fn = tf.estimator.inputs.numpy_input_fn(
x={'images': mnist.train.images}, y=mnist.train.labels,
batch_size=batch_size, num_epochs=None, shuffle=True)

# Define the neural network
def neural_net(x_dict):
# TF Estimator input is a dict, in case of multiple inputs
x = x_dict['images']
# Hidden fully connected layer with 256 neurons
layer_1 = tf.layers.dense(x, n_hidden_1)
# Hidden fully connected layer with 256 neurons
layer_2 = tf.layers.dense(layer_1, n_hidden_2)
# Output fully connected layer with a neuron for each class
out_layer = tf.layers.dense(layer_2, num_classes)
return out_layer

# Define the model function (following TF Estimator Template)
def model_fn(features, labels, mode):

# Build the neural network
logits = neural_net(features)

# Predictions
pred_classes = tf.argmax(logits, axis=1)
pred_probas = tf.nn.softmax(logits)

# If prediction mode, early return
if mode == tf.estimator.ModeKeys.PREDICT:
return tf.estimator.EstimatorSpec(mode, predictions=pred_classes)

# Define loss and optimizer
loss_op = tf.reduce_mean(tf.nn.sparse_softmax_cross_entropy_with_logits(
logits=logits, labels=tf.cast(labels, dtype=tf.int32)))
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
train_op = optimizer.minimize(loss_op, global_step=tf.train.get_global_step())

# Evaluate the accuracy of the model
acc_op = tf.metrics.accuracy(labels=labels, predictions=pred_classes)

# TF Estimators requires to return a EstimatorSpec, that specify
# the different ops for training, evaluating, ...
estim_specs = tf.estimator.EstimatorSpec(
mode=mode,
predictions=pred_classes,
loss=loss_op,
train_op=train_op,
eval_metric_ops={'accuracy': acc_op})

return estim_specs
# Build the Estimator
model = tf.estimator.Estimator(model_fn)
# Train the Model
model.train(input_fn, steps=num_steps)
# Evaluate the Model
# Define the input function for evaluating
input_fn = tf.estimator.inputs.numpy_input_fn(
x={'images': mnist.test.images}, y=mnist.test.labels,
batch_size=batch_size, shuffle=False)
# Use the Estimator 'evaluate' method
model.evaluate(input_fn)
# Predict single images
n_images = 4
# Get images from test set
test_images = mnist.test.images[:n_images]
# Prepare the input data
input_fn = tf.estimator.inputs.numpy_input_fn(
x={'images': test_images}, shuffle=False)
# Use the model to predict the images class
preds = list(model.predict(input_fn))

# Display
for i in range(n_images):
plt.imshow(np.reshape(test_images[i], [28, 28]), cmap='gray')
plt.show()
print("Model prediction:", preds[i])

  1. tf.nn.sparse_softmax_cross_entropy_with_logits是非稀疏的表示

RNN


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def RNN(x, weights, biases):

# Prepare data shape to match `rnn` function requirements
# Current data input shape: (batch_size, timesteps, n_input)
# Required shape: 'timesteps' tensors list of shape (batch_size, n_input)

# Unstack to get a list of 'timesteps' tensors of shape (batch_size, n_input)
x = tf.unstack(x, timesteps, 1)

# Define a lstm cell with tensorflow
lstm_cell = rnn.BasicLSTMCell(num_hidden, forget_bias=1.0)

# Get lstm cell output
outputs, states = rnn.static_rnn(lstm_cell, x, dtype=tf.float32)

# Linear activation, using rnn inner loop last output
return tf.matmul(outputs[-1], weights['out']) + biases['out']
`