一、波士顿房价-线性回归
第一天我们学习了“波士顿房价”案例，编写了第一个线性回归模型。
import numpy as np
import matplotlib.pyplot as plt
def load_data():
# 从文件导入数据
datafile = 'housing.data'
data = np.fromfile(datafile, sep=' ')
# 每条数据包括14项，其中前面13项是影响因素，第14项是相应的房屋价格中位数
feature_names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', \
'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']
feature_num = len(feature_names)
# 将原始数据进行Reshape，变成[N, 14]这样的形状
data = data.reshape([data.shape[0] // feature_num, feature_num])
# 将原数据集拆分成训练集和测试集
# 这里使用80%的数据做训练，20%的数据做测试
# 测试集和训练集必须是没有交集的
ratio = 0.8
offset = int(data.shape[0] * ratio)
training_data = data[:offset]
# 计算训练集的最大值，最小值，平均值
maximums, minimums, avgs = training_data.max(axis=0), training_data.min(axis=0), \
training_data.sum(axis=0) / training_data.shape[0]
# 对数据进行归一化处理
for i in range(feature_num):
# print(maximums[i], minimums[i], avgs[i])
data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
# 训练集和测试集的划分比例
training_data = data[:offset]
test_data = data[offset:]
return training_data, test_data
class Network(object):
def __init__(self, num_of_weights):
# 随机产生w的初始值
# 为了保持程序每次运行结果的一致性，此处设置固定的随机数种子
# np.random.seed(0)
self.w = np.random.randn(num_of_weights, 1)
self.b = 0.
def forward(self, x):
z = np.dot(x, self.w) + self.b
return z
def loss(self, z, y):
error = z - y
num_samples = error.shape[0]
cost = error * error
cost = np.sum(cost) / num_samples
return cost
def gradient(self, x, y):
z = self.forward(x)
N = x.shape[0]
gradient_w = 1. / N * np.sum((z - y) * x, axis=0)
gradient_w = gradient_w[:, np.newaxis]
gradient_b = 1. / N * np.sum(z - y)
return gradient_w, gradient_b
def update(self, gradient_w, gradient_b, eta=0.01):
self.w = self.w - eta * gradient_w
self.b = self.b - eta * gradient_b
def train(self, training_data, num_epoches, batch_size=10, eta=0.01):
n = len(training_data)
losses = []
for epoch_id in range(num_epoches):
# 在每轮迭代开始之前，将训练数据的顺序随机打乱
# 然后再按每次取batch_size条数据的方式取出
np.random.shuffle(training_data)
# 将训练数据进行拆分，每个mini_batch包含batch_size条的数据
mini_batches = [training_data[k:k + batch_size] for k in range(0, n, batch_size)]
for iter_id, mini_batch in enumerate(mini_batches):
# print(self.w.shape)
# print(self.b)
x = mini_batch[:, :-1]
y = mini_batch[:, -1:]
a = self.forward(x)
loss = self.loss(a, y)
gradient_w, gradient_b = self.gradient(x, y)
self.update(gradient_w, gradient_b, eta)
losses.append(loss)
print('Epoch {:3d} / iter {:3d}, loss = {:.4f}'.
format(epoch_id, iter_id, loss))
return losses
# 获取数据
train_data, test_data = load_data()
# 创建网络
net = Network(13)
# 启动训练
losses = net.train(train_data, num_epoches=50, batch_size=100, eta=0.1)
# 画出损失函数的变化趋势
plot_x = np.arange(len(losses))
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()
程序输出打印
Epoch 0 / iter 0, loss = 0.7378
Epoch 0 / iter 1, loss = 1.0192
Epoch 0 / iter 2, loss = 0.8953
Epoch 0 / iter 3, loss = 0.7187
Epoch 0 / iter 4, loss = 0.3238
Epoch 1 / iter 0, loss = 0.7051
Epoch 1 / iter 1, loss = 0.7861
Epoch 1 / iter 2, loss = 0.6244
Epoch 1 / iter 3, loss = 0.5988
Epoch 1 / iter 4, loss = 0.4458
Epoch 2 / iter 0, loss = 0.6392
Epoch 2 / iter 1, loss = 0.6579
Epoch 2 / iter 2, loss = 0.4498
Epoch 2 / iter 3, loss = 0.5088
Epoch 2 / iter 4, loss = 0.0872
Epoch 3 / iter 0, loss = 0.4390
Epoch 3 / iter 1, loss = 0.4419
Epoch 3 / iter 2, loss = 0.5021
Epoch 3 / iter 3, loss = 0.5257
Epoch 3 / iter 4, loss = 0.3474
Epoch 4 / iter 0, loss = 0.3829
Epoch 4 / iter 1, loss = 0.4803
Epoch 4 / iter 2, loss = 0.4093
Epoch 4 / iter 3, loss = 0.3265
Epoch 4 / iter 4, loss = 0.2397
Epoch 5 / iter 0, loss = 0.2519
Epoch 5 / iter 1, loss = 0.3572
Epoch 5 / iter 2, loss = 0.3713
Epoch 5 / iter 3, loss = 0.3993
Epoch 5 / iter 4, loss = 0.1408
Epoch 6 / iter 0, loss = 0.3139
Epoch 6 / iter 1, loss = 0.3148
Epoch 6 / iter 2, loss = 0.3564
Epoch 6 / iter 3, loss = 0.2193
Epoch 6 / iter 4, loss = 0.7519
Epoch 7 / iter 0, loss = 0.3079
Epoch 7 / iter 1, loss = 0.2213
Epoch 7 / iter 2, loss = 0.2008
Epoch 7 / iter 3, loss = 0.2968
Epoch 7 / iter 4, loss = 0.7452
Epoch 8 / iter 0, loss = 0.2508
Epoch 8 / iter 1, loss = 0.2483
Epoch 8 / iter 2, loss = 0.1941
Epoch 8 / iter 3, loss = 0.2225
Epoch 8 / iter 4, loss = 0.3216
Epoch 9 / iter 0, loss = 0.1601
Epoch 9 / iter 1, loss = 0.2106
Epoch 9 / iter 2, loss = 0.1715
Epoch 9 / iter 3, loss = 0.2837
Epoch 9 / iter 4, loss = 0.3635
Epoch 10 / iter 0, loss = 0.1921
Epoch 10 / iter 1, loss = 0.1978
Epoch 10 / iter 2, loss = 0.2064
Epoch 10 / iter 3, loss = 0.1725
Epoch 10 / iter 4, loss = 0.1110
Epoch 11 / iter 0, loss = 0.1593
Epoch 11 / iter 1, loss = 0.2419
Epoch 11 / iter 2, loss = 0.1493
Epoch 11 / iter 3, loss = 0.1792
Epoch 11 / iter 4, loss = 0.1006
Epoch 12 / iter 0, loss = 0.2096
Epoch 12 / iter 1, loss = 0.1531
Epoch 12 / iter 2, loss = 0.1776
Epoch 12 / iter 3, loss = 0.1619
Epoch 12 / iter 4, loss = 0.0634
Epoch 13 / iter 0, loss = 0.2140
Epoch 13 / iter 1, loss = 0.1404
Epoch 13 / iter 2, loss = 0.1582
Epoch 13 / iter 3, loss = 0.1638
Epoch 13 / iter 4, loss = 0.1224
Epoch 14 / iter 0, loss = 0.2183
Epoch 14 / iter 1, loss = 0.1221
Epoch 14 / iter 2, loss = 0.1231
Epoch 14 / iter 3, loss = 0.1846
Epoch 14 / iter 4, loss = 0.0570
Epoch 15 / iter 0, loss = 0.1784
Epoch 15 / iter 1, loss = 0.1674
Epoch 15 / iter 2, loss = 0.1302
Epoch 15 / iter 3, loss = 0.1503
Epoch 15 / iter 4, loss = 0.0683
Epoch 16 / iter 0, loss = 0.1257
Epoch 16 / iter 1, loss = 0.1525
Epoch 16 / iter 2, loss = 0.1778
Epoch 16 / iter 3, loss = 0.1491
Epoch 16 / iter 4, loss = 0.0715
Epoch 17 / iter 0, loss = 0.1233
Epoch 17 / iter 1, loss = 0.1627
Epoch 17 / iter 2, loss = 0.1168
Epoch 17 / iter 3, loss = 0.1766
Epoch 17 / iter 4, loss = 0.1477
Epoch 18 / iter 0, loss = 0.1688
Epoch 18 / iter 1, loss = 0.0969
Epoch 18 / iter 2, loss = 0.1238
Epoch 18 / iter 3, loss = 0.1742
Epoch 18 / iter 4, loss = 0.0897
Epoch 19 / iter 0, loss = 0.1051
Epoch 19 / iter 1, loss = 0.1647
Epoch 19 / iter 2, loss = 0.1124
Epoch 19 / iter 3, loss = 0.1584
Epoch 19 / iter 4, loss = 0.3269
Epoch 20 / iter 0, loss = 0.1371
Epoch 20 / iter 1, loss = 0.1291
Epoch 20 / iter 2, loss = 0.1216
Epoch 20 / iter 3, loss = 0.1345
Epoch 20 / iter 4, loss = 0.2645
Epoch 21 / iter 0, loss = 0.1201
Epoch 21 / iter 1, loss = 0.1283
Epoch 21 / iter 2, loss = 0.1595
Epoch 21 / iter 3, loss = 0.1137
Epoch 21 / iter 4, loss = 0.0603
Epoch 22 / iter 0, loss = 0.1297
Epoch 22 / iter 1, loss = 0.1429
Epoch 22 / iter 2, loss = 0.1249
Epoch 22 / iter 3, loss = 0.1063
Epoch 22 / iter 4, loss = 0.2421
Epoch 23 / iter 0, loss = 0.1291
Epoch 23 / iter 1, loss = 0.1494
Epoch 23 / iter 2, loss = 0.1028
Epoch 23 / iter 3, loss = 0.1186
Epoch 23 / iter 4, loss = 0.1414
Epoch 24 / iter 0, loss = 0.1054
Epoch 24 / iter 1, loss = 0.1349
Epoch 24 / iter 2, loss = 0.1255
Epoch 24 / iter 3, loss = 0.1103
Epoch 24 / iter 4, loss = 0.0228
Epoch 25 / iter 0, loss = 0.1000
Epoch 25 / iter 1, loss = 0.1036
Epoch 25 / iter 2, loss = 0.1254
Epoch 25 / iter 3, loss = 0.1326
Epoch 25 / iter 4, loss = 0.1659
Epoch 26 / iter 0, loss = 0.1149
Epoch 26 / iter 1, loss = 0.0941
Epoch 26 / iter 2, loss = 0.1013
Epoch 26 / iter 3, loss = 0.1349
Epoch 26 / iter 4, loss = 0.2580
Epoch 27 / iter 0, loss = 0.0810
Epoch 27 / iter 1, loss = 0.1173
Epoch 27 / iter 2, loss = 0.1268
Epoch 27 / iter 3, loss = 0.1106
Epoch 27 / iter 4, loss = 0.1656
Epoch 28 / iter 0, loss = 0.0983
Epoch 28 / iter 1, loss = 0.1059
Epoch 28 / iter 2, loss = 0.1063
Epoch 28 / iter 3, loss = 0.1162
Epoch 28 / iter 4, loss = 0.0697
Epoch 29 / iter 0, loss = 0.1205
Epoch 29 / iter 1, loss = 0.1385
Epoch 29 / iter 2, loss = 0.0898
Epoch 29 / iter 3, loss = 0.0668
Epoch 29 / iter 4, loss = 0.1555
Epoch 30 / iter 0, loss = 0.0904
Epoch 30 / iter 1, loss = 0.1028
Epoch 30 / iter 2, loss = 0.1114
Epoch 30 / iter 3, loss = 0.1031
Epoch 30 / iter 4, loss = 0.1983
Epoch 31 / iter 0, loss = 0.1194
Epoch 31 / iter 1, loss = 0.0879
Epoch 31 / iter 2, loss = 0.0903
Epoch 31 / iter 3, loss = 0.1049
Epoch 31 / iter 4, loss = 0.1172
Epoch 32 / iter 0, loss = 0.1221
Epoch 32 / iter 1, loss = 0.1013
Epoch 32 / iter 2, loss = 0.1003
Epoch 32 / iter 3, loss = 0.0776
Epoch 32 / iter 4, loss = 0.0643
Epoch 33 / iter 0, loss = 0.0903
Epoch 33 / iter 1, loss = 0.0977
Epoch 33 / iter 2, loss = 0.0780
Epoch 33 / iter 3, loss = 0.1241
Epoch 33 / iter 4, loss = 0.0923
Epoch 34 / iter 0, loss = 0.1095
Epoch 34 / iter 1, loss = 0.0980
Epoch 34 / iter 2, loss = 0.0720
Epoch 34 / iter 3, loss = 0.0987
Epoch 34 / iter 4, loss = 0.1598
Epoch 35 / iter 0, loss = 0.1284
Epoch 35 / iter 1, loss = 0.0898
Epoch 35 / iter 2, loss = 0.0942
Epoch 35 / iter 3, loss = 0.0673
Epoch 35 / iter 4, loss = 0.0563
Epoch 36 / iter 0, loss = 0.0968
Epoch 36 / iter 1, loss = 0.0851
Epoch 36 / iter 2, loss = 0.0861
Epoch 36 / iter 3, loss = 0.0995
Epoch 36 / iter 4, loss = 0.1689
Epoch 37 / iter 0, loss = 0.1013
Epoch 37 / iter 1, loss = 0.0946
Epoch 37 / iter 2, loss = 0.0851
Epoch 37 / iter 3, loss = 0.0825
Epoch 37 / iter 4, loss = 0.0630
Epoch 38 / iter 0, loss = 0.0994
Epoch 38 / iter 1, loss = 0.1142
Epoch 38 / iter 2, loss = 0.0805
Epoch 38 / iter 3, loss = 0.0641
Epoch 38 / iter 4, loss = 0.0974
Epoch 39 / iter 0, loss = 0.0990
Epoch 39 / iter 1, loss = 0.0841
Epoch 39 / iter 2, loss = 0.0884
Epoch 39 / iter 3, loss = 0.0829
Epoch 39 / iter 4, loss = 0.0577
Epoch 40 / iter 0, loss = 0.0895
Epoch 40 / iter 1, loss = 0.0945
Epoch 40 / iter 2, loss = 0.0753
Epoch 40 / iter 3, loss = 0.0919
Epoch 40 / iter 4, loss = 0.0385
Epoch 41 / iter 0, loss = 0.0921
Epoch 41 / iter 1, loss = 0.0930
Epoch 41 / iter 2, loss = 0.0801
Epoch 41 / iter 3, loss = 0.0794
Epoch 41 / iter 4, loss = 0.0722
Epoch 42 / iter 0, loss = 0.0842
Epoch 42 / iter 1, loss = 0.1064
Epoch 42 / iter 2, loss = 0.0851
Epoch 42 / iter 3, loss = 0.0646
Epoch 42 / iter 4, loss = 0.0488
Epoch 43 / iter 0, loss = 0.0758
Epoch 43 / iter 1, loss = 0.0970
Epoch 43 / iter 2, loss = 0.0901
Epoch 43 / iter 3, loss = 0.0722
Epoch 43 / iter 4, loss = 0.0732
Epoch 44 / iter 0, loss = 0.0845
Epoch 44 / iter 1, loss = 0.0646
Epoch 44 / iter 2, loss = 0.0923
Epoch 44 / iter 3, loss = 0.0814
Epoch 44 / iter 4, loss = 0.2753
Epoch 45 / iter 0, loss = 0.0891
Epoch 45 / iter 1, loss = 0.0690
Epoch 45 / iter 2, loss = 0.0776
Epoch 45 / iter 3, loss = 0.0923
Epoch 45 / iter 4, loss = 0.0258
Epoch 46 / iter 0, loss = 0.1082
Epoch 46 / iter 1, loss = 0.0621
Epoch 46 / iter 2, loss = 0.0781
Epoch 46 / iter 3, loss = 0.0718
Epoch 46 / iter 4, loss = 0.0942
Epoch 47 / iter 0, loss = 0.0621
Epoch 47 / iter 1, loss = 0.0870
Epoch 47 / iter 2, loss = 0.0802
Epoch 47 / iter 3, loss = 0.0882
Epoch 47 / iter 4, loss = 0.0273
Epoch 48 / iter 0, loss = 0.0754
Epoch 48 / iter 1, loss = 0.0653
Epoch 48 / iter 2, loss = 0.0695
Epoch 48 / iter 3, loss = 0.1032
Epoch 48 / iter 4, loss = 0.0291
Epoch 49 / iter 0, loss = 0.0999
Epoch 49 / iter 1, loss = 0.0713
Epoch 49 / iter 2, loss = 0.0691
Epoch 49 / iter 3, loss = 0.0691
Epoch 49 / iter 4, loss = 0.0507
损失函数的变化趋势如下图所示：
损失函数的变化趋势1.png
心得
1.numpy的“广播特性”在向量及矩阵运算中十分的方便快捷。
2.数据归一化：对每个特征进行归一化处理，使得每个特征的取值缩放到[-0.5, 0.5]上。这样做有两个好处：一是模型训练更高效；二是特征前的权重大小可以代表该变量对预测结果的贡献度（因为每个特征值本身的范围相同）。
3.随机梯度下降法（Stochastic Gradient Descent，SGD），核心概念如下：
mini-batch：每次迭代时抽取出来的一批数据被称为一个mini-batch。
batch_size：一个mini-batch所包含的样本数目称为batch_size。
epoch：当程序迭代的时候，按mini-batch逐渐抽取出样本，当把整个数据集都遍历到了的时候，则完成了一轮训练，也叫一个epoch。启动训练时，可以将训练的轮数num_epochs和batch_size作为参数传入。
二 利用Paddle飞桨框架重构程序
#加载飞桨、Numpy和相关类库
import paddle
import paddle.fluid as fluid
import paddle.fluid.dygraph as dygraph
from paddle.fluid.dygraph import Linear
import numpy as np
import matplotlib.pyplot as plt
import os
import random
def load_data():
# 从文件导入数据
datafile = 'housing.data'
data = np.fromfile(datafile, sep=' ')
# 每条数据包括14项，其中前面13项是影响因素，第14项是相应的房屋价格中位数
feature_names = [ 'CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', \
'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV' ]
feature_num = len(feature_names)
# 将原始数据进行Reshape，变成[N, 14]这样的形状
data = data.reshape([data.shape[0] // feature_num, feature_num])
# 将原数据集拆分成训练集和测试集
# 这里使用80%的数据做训练，20%的数据做测试
# 测试集和训练集必须是没有交集的
ratio = 0.8
offset = int(data.shape[0] * ratio)
training_data = data[:offset]
# 计算train数据集的最大值，最小值，平均值
maximums, minimums, avgs = training_data.max(axis=0), training_data.min(axis=0), \
training_data.sum(axis=0) / training_data.shape[0]
# 记录数据的归一化参数，在预测时对数据做归一化
global max_values
global min_values
global avg_values
max_values = maximums
min_values = minimums
avg_values = avgs
# 都是1*14的向量
# 对数据进行归一化处理
for i in range(feature_num):
#print(maximums[i], minimums[i], avgs[i])
data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
# 训练集和测试集的划分比例
#ratio = 0.8
#offset = int(data.shape[0] * ratio)
training_data = data[:offset]
test_data = data[offset:]
return training_data, test_data
def load_one_example(data_dir):
f = open(data_dir, 'r')
datas = f.readlines()
# 选择倒数第10条数据用于测试
tmp = datas[-10]
tmp = tmp.strip().split()
one_data = [float(v) for v in tmp]
# 对数据进行归一化处理
for i in range(len(one_data)-1):
one_data[i] = (one_data[i] - avg_values[i]) / (max_values[i] - min_values[i])
data = np.reshape(np.array(one_data[:-1]), [1, -1]).astype(np.float32)
label = one_data[-1]
return data, label
class Regressor(fluid.dygraph.Layer):
def __init__(self):
super(Regressor, self).__init__()
# 定义一层全连接层，输出维度是1，激活函数为None，即不使用激活函数
self.fc = Linear(input_dim=13, output_dim=1, act=None)
# 网络的前向计算函数
def forward(self, inputs):
x = self.fc(inputs)
return x
# 定义飞桨动态图的工作环境
with fluid.dygraph.guard():
# 声明定义好的线性回归模型
model = Regressor()
# 开启模型训练模式
model.train()
# 加载数据
training_data, test_data = load_data()
# 定义优化算法，这里使用随机梯度下降-SGD
# 学习率设置为0.01
opt = fluid.optimizer.SGD(learning_rate=0.01, parameter_list=model.parameters())
with dygraph.guard(fluid.CPUPlace()):
EPOCH_NUM = 10 # 设置外层循环次数
BATCH_SIZE = 10 # 设置batch大小
losses = []
# 定义外层循环
for epoch_id in range(EPOCH_NUM):
# 在每轮迭代开始之前，将训练数据的顺序随机的打乱
np.random.shuffle(training_data)
# 将训练数据进行拆分，每个batch包含10条数据
mini_batches = [training_data[k:k+BATCH_SIZE] for k in range(0, len(training_data), BATCH_SIZE)]
# 定义内层循环
for iter_id, mini_batch in enumerate(mini_batches):
x = np.array(mini_batch[:, :-1]).astype('float32') # 获得当前批次训练数据
y = np.array(mini_batch[:, -1:]).astype('float32') # 获得当前批次训练标签（真实房价）
# 将numpy数据转为飞桨动态图variable形式
house_features = dygraph.to_variable(x)
prices = dygraph.to_variable(y)
# 前向计算
predicts = model(house_features)
# 计算损失
loss = fluid.layers.square_error_cost(predicts, label=prices)
avg_loss = fluid.layers.mean(loss)
# 记录损失
losses.append(avg_loss.numpy()[0])
if iter_id%20==0:
print("epoch: {}, iter: {}, loss is: {}".format(epoch_id, iter_id, avg_loss.numpy()))
# 反向传播
avg_loss.backward()
# 最小化loss,更新参数
opt.minimize(avg_loss)
# 清除梯度
model.clear_gradients()
# 保存模型
fluid.save_dygraph(model.state_dict(), 'LR_model')
# 画出损失函数的变化趋势
plot_x = np.arange(len(losses))
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()
# 定义飞桨动态图工作环境
with fluid.dygraph.guard():
# 保存模型参数，文件名为LR_model
fluid.save_dygraph(model.state_dict(), 'LR_model')
print("模型保存成功，模型参数保存在LR_model中")
with dygraph.guard():
# 参数为保存模型参数的文件地址
model_dict, _ = fluid.load_dygraph('LR_model')
model.load_dict(model_dict)
model.eval()
# 参数为数据集的文件地址
test_data, label = load_one_example('./work/housing.data')
# 将数据转为动态图的variable格式
test_data = dygraph.to_variable(test_data)
results = model(test_data)
# 对结果做反归一化处理
results = results * (max_values[-1] - min_values[-1]) + avg_values[-1]
print("Inference result is {}, the corresponding label is {}".format(results.numpy(), label))
该程序是利用了倒数第10个样本作为测试，我对程序进行了一些修改。添加了损失函数的变化趋势图，把数据的20%作为测试集对模型进行测试。
#加载飞桨、Numpy和相关类库
import paddle
import paddle.fluid as fluid
import paddle.fluid.dygraph as dygraph
from paddle.fluid.dygraph import Linear
import numpy as np
import matplotlib.pyplot as plt
import os
import random
def load_data():
# 从文件导入数据
datafile = 'housing.data'
data = np.fromfile(datafile, sep=' ')
# 每条数据包括14项，其中前面13项是影响因素，第14项是相应的房屋价格中位数
feature_names = [ 'CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', \
'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV' ]
feature_num = len(feature_names)
# 将原始数据进行Reshape，变成[N, 14]这样的形状
data = data.reshape([data.shape[0] // feature_num, feature_num])
# 将原数据集拆分成训练集和测试集
# 这里使用80%的数据做训练，20%的数据做测试
# 测试集和训练集必须是没有交集的
ratio = 0.8
offset = int(data.shape[0] * ratio)
training_data = data[:offset]
# 计算train数据集的最大值，最小值，平均值
maximums, minimums, avgs = training_data.max(axis=0), training_data.min(axis=0), \
training_data.sum(axis=0) / training_data.shape[0]
# 记录数据的归一化参数，在预测时对数据做归一化
global max_values
global min_values
global avg_values
max_values = maximums
min_values = minimums
avg_values = avgs
# 都是1*14的向量
# 对数据进行归一化处理
for i in range(feature_num):
#print(maximums[i], minimums[i], avgs[i])
data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
# 训练集和测试集的划分比例
#ratio = 0.8
#offset = int(data.shape[0] * ratio)
training_data = data[:offset]
test_data = data[offset:]
return training_data, test_data
class Regressor(fluid.dygraph.Layer):
def __init__(self):
super(Regressor, self).__init__()
# 定义一层全连接层，输出维度是1，激活函数为None，即不使用激活函数
self.fc = Linear(input_dim=13, output_dim=1, act=None)
# 网络的前向计算函数
def forward(self, inputs):
x = self.fc(inputs)
return x
# 定义飞桨动态图的工作环境
with fluid.dygraph.guard():
# 声明定义好的线性回归模型
model = Regressor()
# 开启模型训练模式
model.train()
# 加载数据
training_data, test_data = load_data()
# 定义优化算法，这里使用随机梯度下降-SGD
# 学习率设置为0.01
opt = fluid.optimizer.SGD(learning_rate=0.01, parameter_list=model.parameters())
with dygraph.guard(fluid.CPUPlace()):
EPOCH_NUM = 10 # 设置外层循环次数
BATCH_SIZE = 10 # 设置batch大小
losses = []
# 定义外层循环
for epoch_id in range(EPOCH_NUM):
# 在每轮迭代开始之前，将训练数据的顺序随机的打乱
np.random.shuffle(training_data)
# 将训练数据进行拆分，每个batch包含10条数据
mini_batches = [training_data[k:k+BATCH_SIZE] for k in range(0, len(training_data), BATCH_SIZE)]
# 定义内层循环
for iter_id, mini_batch in enumerate(mini_batches):
x = np.array(mini_batch[:, :-1]).astype('float32') # 获得当前批次训练数据
y = np.array(mini_batch[:, -1:]).astype('float32') # 获得当前批次训练标签（真实房价）
# 将numpy数据转为飞桨动态图variable形式
house_features = dygraph.to_variable(x)
prices = dygraph.to_variable(y)
# 前向计算
predicts = model(house_features)
# 计算损失
loss = fluid.layers.square_error_cost(predicts, label=prices)
avg_loss = fluid.layers.mean(loss)
# 记录损失
losses.append(avg_loss.numpy()[0])
if iter_id%20==0:
print("epoch: {}, iter: {}, loss is: {}".format(epoch_id, iter_id, avg_loss.numpy()))
# 反向传播
avg_loss.backward()
# 最小化loss,更新参数
opt.minimize(avg_loss)
# 清除梯度
model.clear_gradients()
# 保存模型
fluid.save_dygraph(model.state_dict(), 'LR_model')
# 画出损失函数的变化趋势
plot_x = np.arange(len(losses))
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()
# 定义飞桨动态图工作环境
with fluid.dygraph.guard():
# 保存模型参数，文件名为LR_model
fluid.save_dygraph(model.state_dict(), 'LR_model')
print("模型保存成功，模型参数保存在LR_model中")
with dygraph.guard():
# 参数为保存模型参数的文件地址
model_dict, _ = fluid.load_dygraph('LR_model')
model.load_dict(model_dict)
model.eval()
x = np.array(test_data[:, :-1]).astype('float32') # 获得当前批次测试数据
y = np.array(test_data[:, -1:]).astype('float32') # 获得当前批次测试标签（真实房价）
# 将numpy数据转为飞桨动态图variable形式
house_features = dygraph.to_variable(x)
# prices = dygraph.to_variable(y)
# 前向计算
results = model(house_features)
results = results * (max_values[-1] - min_values[-1]) + avg_values[-1]
label = y * (max_values[-1] - min_values[-1]) + avg_values[-1]
for i in range(len(y)):
print("Inference result is {}, the corresponding label is {}".format(results.numpy()[i], label[i]))
损失函数趋势图2.png
Inference result is [23.46879], the corresponding label is [8.5]
Inference result is [11.9041605], the corresponding label is [5.]
Inference result is [22.795517], the corresponding label is [11.900001]
Inference result is [25.68421], the corresponding label is [27.9]
Inference result is [29.061146], the corresponding label is [17.2]
Inference result is [33.748688], the corresponding label is [27.5]
Inference result is [32.948475], the corresponding label is [15.000001]
Inference result is [41.335762], the corresponding label is [17.2]
Inference result is [41.459164], the corresponding label is [17.9]
Inference result is [28.011595], the corresponding label is [16.3]
Inference result is [33.32433], the corresponding label is [7.]
Inference result is [42.055595], the corresponding label is [7.200001]
Inference result is [45.29074], the corresponding label is [7.5]
Inference result is [36.447838], the corresponding label is [10.400001]
Inference result is [28.811592], the corresponding label is [8.8]
Inference result is [46.1286], the corresponding label is [8.400001]
Inference result is [26.914522], the corresponding label is [16.7]
Inference result is [28.464455], the corresponding label is [14.2]
Inference result is [28.660559], the corresponding label is [20.800001]
Inference result is [46.54187], the corresponding label is [13.400001]
Inference result is [47.16037], the corresponding label is [11.700001]
Inference result is [43.37393], the corresponding label is [8.3]
Inference result is [47.180077], the corresponding label is [10.200001]
Inference result is [39.601448], the corresponding label is [10.900001]
Inference result is [43.32173], the corresponding label is [11.]
Inference result is [42.127296], the corresponding label is [9.5]
Inference result is [40.854256], the corresponding label is [14.500001]
Inference result is [39.635536], the corresponding label is [14.1]
Inference result is [41.5254], the corresponding label is [16.1]
Inference result is [40.946266], the corresponding label is [14.3]
Inference result is [37.743042], the corresponding label is [11.700001]
Inference result is [39.644344], the corresponding label is [13.400001]
Inference result is [42.825386], the corresponding label is [9.600001]
Inference result is [43.60471], the corresponding label is [8.700001]
Inference result is [44.005264], the corresponding label is [8.400001]
Inference result is [25.288311], the corresponding label is [12.800001]
Inference result is [22.868505], the corresponding label is [10.5]
Inference result is [24.687489], the corresponding label is [17.1]
Inference result is [24.240313], the corresponding label is [18.4]
Inference result is [24.199179], the corresponding label is [15.400001]
Inference result is [32.264908], the corresponding label is [10.8]
Inference result is [43.4346], the corresponding label is [11.8]
Inference result is [28.851978], the corresponding label is [14.900001]
Inference result is [23.909576], the corresponding label is [12.600001]
Inference result is [23.095879], the corresponding label is [14.1]
Inference result is [28.766623], the corresponding label is [13.000001]
Inference result is [45.35603], the corresponding label is [13.400001]
Inference result is [26.211393], the corresponding label is [15.2]
Inference result is [25.60134], the corresponding label is [16.1]
Inference result is [24.343767], the corresponding label is [17.800001]
Inference result is [44.01912], the corresponding label is [14.900001]
Inference result is [44.03011], the corresponding label is [14.1]
Inference result is [45.5551], the corresponding label is [12.700001]
Inference result is [45.796387], the corresponding label is [13.500001]
Inference result is [31.424139], the corresponding label is [14.900001]
Inference result is [24.853563], the corresponding label is [20.]
Inference result is [32.392868], the corresponding label is [16.400002]
Inference result is [25.520857], the corresponding label is [17.7]
Inference result is [25.102945], the corresponding label is [19.5]
Inference result is [23.742544], the corresponding label is [20.2]
Inference result is [26.780102], the corresponding label is [21.400002]
Inference result is [33.781395], the corresponding label is [19.900002]
Inference result is [44.426804], the corresponding label is [19.]
Inference result is [27.025349], the corresponding label is [19.1]
Inference result is [25.477282], the corresponding label is [19.1]
Inference result is [26.615618], the corresponding label is [20.1]
Inference result is [23.973948], the corresponding label is [19.900002]
Inference result is [21.988102], the corresponding label is [19.6]
Inference result is [25.950409], the corresponding label is [23.2]
Inference result is [28.721003], the corresponding label is [29.800001]
Inference result is [24.449879], the corresponding label is [13.8]
Inference result is [28.55926], the corresponding label is [13.3]
Inference result is [24.220623], the corresponding label is [16.7]
Inference result is [24.39872], the corresponding label is [12.]
Inference result is [23.342709], the corresponding label is [14.6]
Inference result is [23.42834], the corresponding label is [21.400002]
Inference result is [25.13335], the corresponding label is [23.]
Inference result is [23.576199], the corresponding label is [23.7]
Inference result is [23.001907], the corresponding label is [25.]
Inference result is [28.83557], the corresponding label is [21.800001]
Inference result is [31.343594], the corresponding label is [20.6]
Inference result is [27.788128], the corresponding label is [21.2]
Inference result is [23.594887], the corresponding label is [19.1]
Inference result is [28.645176], the corresponding label is [20.6]
Inference result is [14.703245], the corresponding label is [15.2]
Inference result is [17.27957], the corresponding label is [7.]
Inference result is [19.182281], the corresponding label is [8.1]
Inference result is [14.079249], the corresponding label is [13.6]
Inference result is [15.304695], the corresponding label is [20.1]
Inference result is [25.364271], the corresponding label is [21.800001]
Inference result is [27.597918], the corresponding label is [24.5]
Inference result is [29.918457], the corresponding label is [23.1]
Inference result is [22.525549], the corresponding label is [19.7]
Inference result is [21.98687], the corresponding label is [18.300001]
Inference result is [23.629286], the corresponding label is [21.2]
Inference result is [22.417788], the corresponding label is [17.5]
Inference result is [21.218828], the corresponding label is [16.8]
Inference result is [17.28513], the corresponding label is [22.400002]
Inference result is [15.7654705], the corresponding label is [20.6]
Inference result is [13.413251], the corresponding label is [23.9]
Inference result is [13.544857], the corresponding label is [22.]
Inference result is [14.505701], the corresponding label is [11.900001]
感觉有些样本的损失函数值还是挺大的，损失函数的趋势波动也较大。
修改训练的epoch=30和batchsize=10
损失函数变化趋势图3.png
Inference result is [19.16061], the corresponding label is [8.5]
Inference result is [22.257748], the corresponding label is [5.]
Inference result is [16.415882], the corresponding label is [11.900001]
Inference result is [19.12475], the corresponding label is [27.9]
Inference result is [18.044804], the corresponding label is [17.2]
Inference result is [23.062931], the corresponding label is [27.5]
Inference result is [31.414034], the corresponding label is [15.000001]
Inference result is [24.794533], the corresponding label is [17.2]
Inference result is [21.538464], the corresponding label is [17.9]
Inference result is [23.17853], the corresponding label is [16.3]
Inference result is [20.514303], the corresponding label is [7.]
Inference result is [21.33069], the corresponding label is [7.200001]
Inference result is [21.542526], the corresponding label is [7.5]
Inference result is [20.62424], the corresponding label is [10.400001]
Inference result is [29.712818], the corresponding label is [8.8]
Inference result is [20.930944], the corresponding label is [8.400001]
Inference result is [17.59581], the corresponding label is [16.7]
Inference result is [16.747923], the corresponding label is [14.2]
Inference result is [21.217716], the corresponding label is [20.800001]
Inference result is [23.539066], the corresponding label is [13.400001]
Inference result is [25.752272], the corresponding label is [11.700001]
Inference result is [21.991816], the corresponding label is [8.3]
Inference result is [26.51014], the corresponding label is [10.200001]
Inference result is [26.954044], the corresponding label is [10.900001]
Inference result is [20.668505], the corresponding label is [11.]
Inference result is [20.789043], the corresponding label is [9.5]
Inference result is [24.6804], the corresponding label is [14.500001]
Inference result is [24.709906], the corresponding label is [14.1]
Inference result is [25.601355], the corresponding label is [16.1]
Inference result is [20.507002], the corresponding label is [14.3]
Inference result is [21.430033], the corresponding label is [11.700001]
Inference result is [18.807175], the corresponding label is [13.400001]
Inference result is [21.33551], the corresponding label is [9.600001]
Inference result is [19.707918], the corresponding label is [8.700001]
Inference result is [17.18261], the corresponding label is [8.400001]
Inference result is [13.55842], the corresponding label is [12.800001]
Inference result is [15.544412], the corresponding label is [10.5]
Inference result is [14.980553], the corresponding label is [17.1]
Inference result is [14.699271], the corresponding label is [18.4]
Inference result is [15.10469], the corresponding label is [15.400001]
Inference result is [16.296833], the corresponding label is [10.8]
Inference result is [19.446524], the corresponding label is [11.8]
Inference result is [15.883473], the corresponding label is [14.900001]
Inference result is [15.515961], the corresponding label is [12.600001]
Inference result is [15.753342], the corresponding label is [14.1]
Inference result is [16.83473], the corresponding label is [13.000001]
Inference result is [22.049944], the corresponding label is [13.400001]
Inference result is [16.336561], the corresponding label is [15.2]
Inference result is [15.805071], the corresponding label is [16.1]
Inference result is [17.090681], the corresponding label is [17.800001]
Inference result is [22.074022], the corresponding label is [14.900001]
Inference result is [20.900843], the corresponding label is [14.1]
Inference result is [20.975655], the corresponding label is [12.700001]
Inference result is [22.099005], the corresponding label is [13.500001]
Inference result is [18.327238], the corresponding label is [14.900001]
Inference result is [16.442745], the corresponding label is [20.]
Inference result is [18.279144], the corresponding label is [16.400002]
Inference result is [16.227621], the corresponding label is [17.7]
Inference result is [16.755377], the corresponding label is [19.5]
Inference result is [17.453497], the corresponding label is [20.2]
Inference result is [19.145613], the corresponding label is [21.400002]
Inference result is [19.356253], the corresponding label is [19.900002]
Inference result is [22.969572], the corresponding label is [19.]
Inference result is [19.506191], the corresponding label is [19.1]
Inference result is [21.565527], the corresponding label is [19.1]
Inference result is [21.56257], the corresponding label is [20.1]
Inference result is [20.077593], the corresponding label is [19.900002]
Inference result is [22.145761], the corresponding label is [19.6]
Inference result is [20.706675], the corresponding label is [23.2]
Inference result is [20.985466], the corresponding label is [29.800001]
Inference result is [19.808105], the corresponding label is [13.8]
Inference result is [19.584246], the corresponding label is [13.3]
Inference result is [18.44503], the corresponding label is [16.7]
Inference result is [18.256538], the corresponding label is [12.]
Inference result is [19.182587], the corresponding label is [14.6]
Inference result is [20.70591], the corresponding label is [21.400002]
Inference result is [23.339006], the corresponding label is [23.]
Inference result is [24.103197], the corresponding label is [23.7]
Inference result is [24.418491], the corresponding label is [25.]
Inference result is [23.418371], the corresponding label is [21.800001]
Inference result is [21.484959], the corresponding label is [20.6]
Inference result is [22.13229], the corresponding label is [21.2]
Inference result is [20.684986], the corresponding label is [19.1]
Inference result is [21.5238], the corresponding label is [20.6]
Inference result is [27.038603], the corresponding label is [15.2]
Inference result is [26.51231], the corresponding label is [7.]
Inference result is [25.597708], the corresponding label is [8.1]
Inference result is [27.377956], the corresponding label is [13.6]
Inference result is [28.548033], the corresponding label is [20.1]
Inference result is [19.40799], the corresponding label is [21.800001]
Inference result is [19.465754], the corresponding label is [24.5]
Inference result is [18.937977], the corresponding label is [23.1]
Inference result is [17.23689], the corresponding label is [19.7]
Inference result is [18.954657], the corresponding label is [18.300001]
Inference result is [19.263266], the corresponding label is [21.2]
Inference result is [18.391119], the corresponding label is [17.5]
Inference result is [18.768625], the corresponding label is [16.8]
Inference result is [19.263432], the corresponding label is [22.400002]
Inference result is [18.777313], the corresponding label is [20.6]
Inference result is [19.743137], the corresponding label is [23.9]
Inference result is [19.618513], the corresponding label is [22.]
Inference result is [18.951277], the corresponding label is [11.900001]
随着训练次数的增加，损失函数趋向于越来越小。
模型在eval模式时只有前向计算方法，感觉应该还要有评价函数来量化模型的好坏。
程序有个小缺陷：label的值是归一化之后又经过了一次反归一化，个别样本是有一些误差的。
