tensorflow 神经网络基本使用

TF使用ANN(artificial neural network)

简介

• 受到生物神经网络的启发
• 发展历史
  
  • 生物神经网络单元
  • 逻辑运算单元：and、or、xor等运算
  • 感知机(perceptron)： hw(x)=step(wT⋅x)
  • 多层感知机和反向传播(multi-perceptron and backpropagation)

perceptron

• sklearn中也有感知机的库，其参数学习规则是
  
  wnextstepi,j=wi,j+η(y^j−yj)xi
  
  其中 η 是学习率
• 感知机与SGD很类似
• 逻辑斯蒂回归可以给出样本对于每一类的分类概率，而感知机则是直接根据阈值给出分类结果，因此一般在分类时，逻辑斯蒂回归相对感知机来说会常用一点
• 感知机是线性的，难以解决非线性问题；但是如果采用多个感知机，则可以避免这个问题

多层感知机和反向传播

• 感知机的激活函数是step函数，得到的结果非0即1，无法用于反向传播（需要求取微分），因此利用Logistic函数 σ(z)=1/(1+exp(−z)) 替代之前的step函数，这个logistic函数也被称为激活函数
• 常用的激活函数有
  
  • logistic函数
  • 双曲正切函数： tanh(z)=2σ(2z)−1
  • RELU函数： relu(z)=max(z,0) ，RELU函数在 z=0 处不可导，但是由于它计算耗时十分短，在实际应用中应用很广泛，同时它也没有最大值的限制，可以减少GD使用过程中的一些问题
  • softmax函数
• MLP常常用于分类，输出层常常用softmax函数作为激活函数，可以保证所有节点的输出之和为1，相当于每个节点的输出值都是这个节点的概率，softmax函数如下
  
  σ(z)j=ezj∑Kk=1ezk

# 不显示python使用过程中的警告
import warnings
warnings.filterwarnings("ignore")

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
import os

# 这个options只需要在之后第一次使用Session时使用就可以了
gpu_options = tf.GPUOptions(allow_growth=True)

def reset_graph(seed=42):
    tf.reset_default_graph()
    tf.set_random_seed(seed)
    np.random.seed(seed)
    return

with tf.Session( config=tf.ConfigProto(gpu_options=gpu_options) ) as sess:
    print( sess.run( tf.constant(1) ) )

1

# skelarn perceptron
from sklearn.datasets import load_iris
from sklearn.linear_model import Perceptron

iris = load_iris()
X = iris.data[:, (2,3)]
y = (iris.target ==0 ).astype( np.int )
per_clf = Perceptron( random_state=42 )
per_clf.fit(X, y)
y_pred = per_clf.predict( [[2, 0.5]] )
print( y_pred )

[1]

# 定义一些激活函数
def logit(z):
    return 1 / (1 + np.exp(-z))

def relu(z):
    return np.maximum(0, z)

def derivative(f, z, eps=0.000001):
    return (f(z + eps) - f(z - eps))/(2 * eps)

# 可视化激活函数及其导数
z = np.linspace(-5, 5, 200)

plt.figure(figsize=(10,4))

plt.subplot(121)
plt.plot(z, np.sign(z), "r-", linewidth=2, label="Step")
plt.plot(z, logit(z), "g--", linewidth=2, label="Logit")
plt.plot(z, np.tanh(z), "b-", linewidth=2, label="Tanh")
plt.plot(z, relu(z), "m-.", linewidth=2, label="ReLU")
plt.grid(True)
plt.legend(loc="center right", fontsize=14)
plt.title("Activation functions", fontsize=14)
plt.axis([-5, 5, -1.2, 1.2])

plt.subplot(122)
plt.plot(z, derivative(np.sign, z), "r-", linewidth=2, label="Step")
plt.plot(0, 0, "ro", markersize=5)
plt.plot(0, 0, "rx", markersize=10)
plt.plot(z, derivative(logit, z), "g--", linewidth=2, label="Logit")
plt.plot(z, derivative(np.tanh, z), "b-", linewidth=2, label="Tanh")
plt.plot(z, derivative(relu, z), "m-.", linewidth=2, label="ReLU")
plt.grid(True)
#plt.legend(loc="center right", fontsize=14)
plt.title("Derivatives", fontsize=14)
plt.axis([-5, 5, -0.2, 1.2])

plt.show()

使用MLP进行训练

• TF中集成了MLP的库，在tf.learn中
• 下面是一个MLP训练的例子
• 其中infer_real_valued_columns_from_input是根据输入的数据推断出数据的类型以及数据特征的维度等信息，参考链接：http://www.cnblogs.com/wxshi/p/8053973.html

from tensorflow.examples.tutorials.mnist import input_data
from sklearn.metrics import accuracy_score
# 导入数据
mnist = input_data.read_data_sets("dataset/mnist")
X_train = mnist.train.images
X_test = mnist.test.images
y_train = mnist.train.labels.astype("int")
y_test = mnist.test.labels.astype("int")

feature_cols = tf.contrib.learn.infer_real_valued_columns_from_input(X_train)
dnn_clf = tf.contrib.learn.DNNClassifier( hidden_units=[300,100], n_classes=10, feature_columns=feature_cols, model_dir="./models/mnist/" )
dnn_clf.fit( x=X_train, y=y_train, batch_size=2000,steps=1000 )

y_pred = list( dnn_clf.predict(X_test) )
print( "accuracy : ", accuracy_score(y_test, y_pred) )

Extracting dataset/mnist/train-images-idx3-ubyte.gz
Extracting dataset/mnist/train-labels-idx1-ubyte.gz
Extracting dataset/mnist/t10k-images-idx3-ubyte.gz
Extracting dataset/mnist/t10k-labels-idx1-ubyte.gz
INFO:tensorflow:Using default config.
INFO:tensorflow:Using config: {'_task_type': None, '_task_id': 0, '_cluster_spec': , '_master': '', '_num_ps_replicas': 0, '_num_worker_replicas': 0, '_environment': 'local', '_is_chief': True, '_evaluation_master': '', '_tf_config': gpu_options {
  per_process_gpu_memory_fraction: 1.0
}
, '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_secs': 600, '_log_step_count_steps': 100, '_session_config': None, '_save_checkpoints_steps': None, '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_model_dir': './models/mnist/'}
INFO:tensorflow:Create CheckpointSaverHook.
INFO:tensorflow:Restoring parameters from ./models/mnist/model.ckpt-1000
INFO:tensorflow:Saving checkpoints for 1001 into ./models/mnist/model.ckpt.
INFO:tensorflow:loss = 0.11683539, step = 1001
INFO:tensorflow:global_step/sec: 110.226
INFO:tensorflow:loss = 0.10939115, step = 1101 (0.908 sec)
INFO:tensorflow:global_step/sec: 111.916
INFO:tensorflow:loss = 0.082077585, step = 1201 (0.894 sec)
INFO:tensorflow:global_step/sec: 108.765
INFO:tensorflow:loss = 0.089471206, step = 1301 (0.920 sec)
INFO:tensorflow:global_step/sec: 121.815
INFO:tensorflow:loss = 0.073814414, step = 1401 (0.820 sec)
INFO:tensorflow:global_step/sec: 106.326
INFO:tensorflow:loss = 0.067025915, step = 1501 (0.940 sec)
INFO:tensorflow:global_step/sec: 125.559
INFO:tensorflow:loss = 0.07670402, step = 1601 (0.796 sec)
INFO:tensorflow:global_step/sec: 118.059
INFO:tensorflow:loss = 0.060902975, step = 1701 (0.848 sec)
INFO:tensorflow:global_step/sec: 107.56
INFO:tensorflow:loss = 0.057678875, step = 1801 (0.929 sec)
INFO:tensorflow:global_step/sec: 109.521
INFO:tensorflow:loss = 0.074146144, step = 1901 (0.913 sec)
INFO:tensorflow:Saving checkpoints for 2000 into ./models/mnist/model.ckpt.
INFO:tensorflow:Loss for final step: 0.057994846.
INFO:tensorflow:Restoring parameters from ./models/mnist/model.ckpt-2000
accuracy :  0.9747

TF构建DNN

• 初始化训练参数时，参数初始值可以设置为符合标准差为 2/ninputs−−−−−√ 的截断正态分布的随机数，这可以加快模型收敛的速度。在TF里，截断的最大值和最小值分别是2和-2。

from tensorflow.contrib.layers import fully_connected

reset_graph()

# MNIST
n_inputs = 28*28
n_hidden1 = 300
n_hidden2 = 100
n_outputs = 10

X = tf.placeholder( tf.float32, shape=(None, n_inputs), name="X" )
y = tf.placeholder( tf.int64, shape=(None), name="y" )

# 自己定义的层，和tf中的fully_connected类似
def neuron_layer(X, n_neurons, name, activation=None):
    with tf.name_scope( name ):
        n_inputs = int(X.shape[1])
        sttdev = 2 / np.sqrt( n_inputs )
        init = tf.truncated_normal( (n_inputs, n_neurons), sttdev=stddev ) # 截断正态分布，可以去除一些特别大的值
        W = tf.Variable( init, name="weights" )
        b = tf.Variable( tf.zeros([n_neurons]), name="bias" ) 
        z = tf.matmul( X, W ) + b
        if activation == "relu":
            return tf.nn.relu( z )
        else:
            return z

# with tf.name_scope("dnn"):
#     hidden1 = neuron_layer(X, n_hidden1, "hidden1", activation="relu")
#     hidden2 = neuron_layer(hidden1, n_hidden2, "hidden2", activation="relu")
#     logits = neuron_layer( hidden2, n_outputs, "outputs" )

with tf.name_scope("dnn"):
    hidden1 = fully_connected(X, n_hidden1, scope="hidden1")
    hidden2 = fully_connected(hidden1, n_hidden2, scope="hidden2")
    logits = fully_connected( hidden2, n_outputs, scope="outputs", activation_fn=None )

with tf.name_scope("loss"):
    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits( labels=y, logits=logits )
    loss = tf.reduce_mean( xentropy, name="loss" )

lr = 0.01
with tf.name_scope( "train" ):
    optimizer = tf.train.GradientDescentOptimizer( lr )
    training_op = optimizer.minimize( loss )

with tf.name_scope( "eval" ):
    correct = tf.nn.in_top_k( logits, y, 1 )
    accuracy = tf.reduce_mean( tf.cast( correct, tf.float32 ) )

init = tf.global_variables_initializer()
saver = tf.train.Saver()

n_epochs = 30
batch_size = 200

with tf.Session() as sess:
    init.run()
    for epoch in range( n_epochs ):
        for iteration in range( X_train.shape[0] // batch_size ):
            X_batch, y_batch = mnist.train.next_batch( batch_size )
            sess.run( training_op, feed_dict={X:X_batch, y:y_batch} )
        acc_train = accuracy.eval( feed_dict={X:X_batch, y:y_batch} )
        acc_test = accuracy.eval( feed_dict={X:X_test, y:y_test} )
        print( epoch, "train accuracy : ", acc_train, "; Test accuracy : ", acc_test )
    save_path = saver.save( sess, "./models/mnist/my_model_final.ckpt" )

0 train accuracy :  0.82 ; Test accuracy :  0.8298
1 train accuracy :  0.89 ; Test accuracy :  0.8783
2 train accuracy :  0.88 ; Test accuracy :  0.8977
3 train accuracy :  0.885 ; Test accuracy :  0.9043
4 train accuracy :  0.925 ; Test accuracy :  0.9104
5 train accuracy :  0.9 ; Test accuracy :  0.9143
6 train accuracy :  0.915 ; Test accuracy :  0.9204
7 train accuracy :  0.925 ; Test accuracy :  0.9224
8 train accuracy :  0.93 ; Test accuracy :  0.9246
9 train accuracy :  0.925 ; Test accuracy :  0.9283
10 train accuracy :  0.92 ; Test accuracy :  0.9297
11 train accuracy :  0.91 ; Test accuracy :  0.9316
12 train accuracy :  0.95 ; Test accuracy :  0.933
13 train accuracy :  0.93 ; Test accuracy :  0.9356
14 train accuracy :  0.94 ; Test accuracy :  0.9373
15 train accuracy :  0.915 ; Test accuracy :  0.9382
16 train accuracy :  0.94 ; Test accuracy :  0.9398
17 train accuracy :  0.965 ; Test accuracy :  0.9415
18 train accuracy :  0.935 ; Test accuracy :  0.9425
19 train accuracy :  0.95 ; Test accuracy :  0.9433
20 train accuracy :  0.925 ; Test accuracy :  0.9447
21 train accuracy :  0.925 ; Test accuracy :  0.9455
22 train accuracy :  0.93 ; Test accuracy :  0.9461
23 train accuracy :  0.91 ; Test accuracy :  0.9484
24 train accuracy :  0.935 ; Test accuracy :  0.9485
25 train accuracy :  0.95 ; Test accuracy :  0.95
26 train accuracy :  0.94 ; Test accuracy :  0.9511
27 train accuracy :  0.93 ; Test accuracy :  0.9531
28 train accuracy :  0.95 ; Test accuracy :  0.9527
29 train accuracy :  0.965 ; Test accuracy :  0.9541

• 如果要使用之前训练的模型进行分类任务，可以直接读取保存的模型文件

with tf.Session() as sess:
    saver.restore( sess, "./models/mnist/my_model_final.ckpt" )
    X_new_scaled = X_test[:20, :]
    Z = logits.eval( feed_dict={X:X_new_scaled} )
    y_pred = np.argmax( Z, axis=1 )
    print( "real value : ", y_test[0:20] )
    print( "predict value :", y_pred[0:20] )

INFO:tensorflow:Restoring parameters from ./models/mnist/my_model_final.ckpt
real value :  [7 2 1 0 4 1 4 9 5 9 0 6 9 0 1 5 9 7 3 4]
predict value : [7 2 1 0 4 1 4 9 6 9 0 6 9 0 1 5 9 7 3 4]

NN超参数微调

• NN虽然很灵活，但是有许多超参数需要调节，比如隐含层的数量、激活函数等
• 一般情况下，可以首先使用一个隐含层进行训练与测试，得到一个初步结果
• 深层网络比浅层网络在参数调节方面要更加灵活，它们可以使用更少的节点个数，对更加复杂的函数进行建模。
• 训练的过程中，可以逐步增加隐含层的数目，得到更加复杂的网络
• 输入和输出层的神经元节点个数是由输入和输出确定的，对于mnist，输入层有784个节点(特征数目)，输出层有10个节点(类别个数)
• 一般情况下，可以逐步增加隐含层中神经元节点的数量，直到模型发生过拟合；另外一种比较常用的方法是：选择很大的神经元节点个数，然后利用early stopping方法进行训练，得到最优的模型
• 一般情况下，使用RELU作为激活函数就可以达到比较好的结果，因为它的计算速度很快，同时也不会因为输入值过大而饱和；在输出层，只要输出的类别之间相互排斥，则softmax函数一般即可