机器学习笔记(5)：多类逻辑回归-手动添加隐藏层

了解神经网络原理的同学们应该都知道，隐藏层越多，最终预测结果的准确度越高，但是计算量也越大，在上一篇的基础上，我们手动添加一个隐藏层，代码如下（主要参考自多层感知机 — 从0开始）：

from mxnet import gluon
from mxnet import ndarray as nd
import matplotlib.pyplot as plt
import mxnet as mx
from mxnet import autograd

def transform(data, label):
return data.astype('float32')/255, label.astype('float32')

mnist_train = gluon.data.vision.FashionMNIST(train=True, transform=transform)
mnist_test = gluon.data.vision.FashionMNIST(train=False, transform=transform)

def show_images(images):
n = images.shape[0]
_, figs = plt.subplots(1, n, figsize=(15, 15))
for i in range(n):
figs[i].imshow(images[i].reshape((28, 28)).asnumpy())
figs[i].axes.get_xaxis().set_visible(False)
figs[i].axes.get_yaxis().set_visible(False)
plt.show()

def get_text_labels(label):
text_labels = [
'T 恤', '长 裤', '套头衫', '裙 子', '外 套',
'凉 鞋', '衬 衣', '运动鞋', '包 包', '短 靴'
]
return [text_labels[int(i)] for i in label]

data, label = mnist_train[0:10]

print('example shape: ', data.shape, 'label:', label)
show_images(data)
print(get_text_labels(label))

batch_size = 256
train_data = gluon.data.DataLoader(mnist_train, batch_size, shuffle=True)
test_data = gluon.data.DataLoader(mnist_test, batch_size, shuffle=False)

num_inputs = 784
num_outputs = 10

#增加一层包含256个节点的隐藏层
num_hidden = 256
weight_scale = .01

#输入层的参数
W1 = nd.random_normal(shape=(num_inputs, num_hidden), scale=weight_scale)
b1 = nd.zeros(num_hidden)

#隐藏层的参数
W2 = nd.random_normal(shape=(num_hidden, num_outputs), scale=weight_scale)
b2 = nd.zeros(num_outputs)

#参数变多了
params = [W1, b1, W2, b2]

for param in params:
param.attach_grad()

#激活函数
def relu(X):
return nd.maximum(X, 0)

#计算模型
def net(X):
X = X.reshape((-1, num_inputs))
#先计算到隐藏层的输出
h1 = relu(nd.dot(X, W1) + b1)
#再利用隐藏层计算最终的输出
output = nd.dot(h1, W2) + b2
return output

#Softmax和交叉熵损失函数
softmax_cross_entropy = gluon.loss.SoftmaxCrossEntropyLoss()

#梯度下降法
def SGD(params, lr):
for param in params:
param[:] = param - lr * param.grad

def accuracy(output, label):
return nd.mean(output.argmax(axis=1) == label).asscalar()

def _get_batch(batch):
if isinstance(batch, mx.io.DataBatch):
data = batch.data[0]
label = batch.label[0]
else:
data, label = batch
return data, label

def evaluate_accuracy(data_iterator, net):
acc = 0.
if isinstance(data_iterator, mx.io.MXDataIter):
data_iterator.reset()
for i, batch in enumerate(data_iterator):
data, label = _get_batch(batch)
output = net(data)
acc += accuracy(output, label)
return acc / (i+1)

learning_rate = .5

for epoch in range(5):
train_loss = 0.
train_acc = 0.
for data, label in train_data:
with autograd.record():
output = net(data)
#使用Softmax和交叉熵损失函数
loss = softmax_cross_entropy(output, label)
loss.backward()
SGD(params, learning_rate / batch_size)
train_loss += nd.mean(loss).asscalar()
train_acc += accuracy(output, label)

test_acc = evaluate_accuracy(test_data, net)
print("Epoch %d. Loss: %f, Train acc %f, Test acc %f" % (
epoch, train_loss / len(train_data), train_acc / len(train_data), test_acc))

data, label = mnist_test[0:10]
show_images(data)
print('true labels')
print(get_text_labels(label))

predicted_labels = net(data).argmax(axis=1)
print('predicted labels')
print(get_text_labels(predicted_labels.asnumpy()))

有变化的地方，都加了注释，主要改动点有5个：

1. 手动添加了1个隐藏层，该层有256个节点

2. 多了一层，所以参数也变多了

3. 计算y=wx+b模型时，就要一层层来算了

4. 将softmax与交叉熵CrossEntropy合并了(这样避免了单独对softmax求导，理论上讲更稳定些）

5. 另外激活函数换成了收敛速度更快的relu（参考：Deep learning系列（七）激活函数 ）

运行效果：



相对原始纯手动版本，准确率提升了不少！

tips：类似的思路，我们可以再手动添加第2层隐藏层，关键代码参考下面

...

#增加一层包含256个节点的隐藏层
num_hidden1 = 256
weight_scale1 = .01

#再增加一层包含512个节点的隐藏层
num_hidden2 = 512
weight_scale2 = .01

#输入层的参数
W1 = nd.random_normal(shape=(num_inputs, num_hidden1), scale=weight_scale1)
b1 = nd.zeros(num_hidden1)

#隐藏层的参数
W2 = nd.random_normal(shape=(num_hidden1, num_hidden2), scale=weight_scale1)
b2 = nd.zeros(num_hidden2)

W3 = nd.random_normal(shape=(num_hidden2, num_outputs), scale=weight_scale2)
b3 = nd.zeros(num_outputs)

#参数变多了
params = [W1, b1, W2, b2, W3, b3]

...

#计算模型
def net(X):
X = X.reshape((-1, num_inputs))
#先计算到隐藏层的输出
h1 = relu(nd.dot(X, W1) + b1)
h2 = relu(nd.dot(h1,W2) + b2)
#再利用隐藏层计算最终的输出
output = nd.dot(h2, W3) + b3
return output