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