经典的线性回归模型主要用来预测一些存在着线性关系的数据集。回归模型可以理解为：存在一个点集，用一条曲线去拟合它分布的过程。如果拟合曲线是一条直线，则称为线性回归。如果是一条二次曲线，则被称为二次回归。线性回归是回归模型中最简单的一种。 本教程使用PaddlePaddle建立起一个房价预测模型。
在线性回归中：
（1）假设函数是指，用数学的方法描述自变量和因变量之间的关系，它们之间可以是一个线性函数或非线性函数。 在本次线性回顾模型中，我们的假设函数为 Y’= wX+b ，其中，Y’表示模型的预测结果（预测房价），用来和真实的Y区分。模型要学习的参数即：w,b。
（2）损失函数是指，用数学的方法衡量假设函数预测结果与真实值之间的误差。这个差距越小预测越准确，而算法的任务就是使这个差距越来越小。 建立模型后，我们需要给模型一个优化目标，使得学到的参数能够让预测值Y’尽可能地接近真实值Y。这个实值通常用来反映模型误差的大小。不同问题场景下采用不同的损失函数。 对于线性模型来讲，最常用的损失函数就是均方误差（Mean Squared Error， MSE）。
（3）优化算法：神经网络的训练就是调整权重（参数）使得损失函数值尽可能得小，在训练过程中，将损失函数值逐渐收敛，得到一组使得神经网络拟合真实模型的权重（参数）。所以，优化算法的最终目标是找到损失函数的最小值。而这个寻找过程就是不断地微调变量w和b的值，一步一步地试出这个最小值。 常见的优化算法有随机梯度下降法（SGD）、Adam算法等等
首先导入必要的包，分别是：
paddle.fluid—>PaddlePaddle深度学习框架
numpy---------->python基本库，用于科学计算
os------------------>python的模块，可使用该模块对操作系统进行操作
matplotlib----->python绘图库，可方便绘制折线图、散点图等图形
import paddle.fluid as fluid
import paddle
import numpy as np
import os
import matplotlib.pyplot as plt
Step1：准备数据。
（1）uci-housing数据集介绍
数据集共506行,每行14列。前13列用来描述房屋的各种信息，最后一列为该类房屋价格中位数。
PaddlePaddle提供了读取uci_housing训练集和测试集的接口，分别为paddle.dataset.uci_housing.train()和paddle.dataset.uci_housing.test()。
(2)train_reader和test_reader
paddle.reader.shuffle()表示每次缓存BUF_SIZE个数据项，并进行打乱
paddle.batch()表示每BATCH_SIZE组成一个batch
BUF_SIZE=500
BATCH_SIZE=20
#用于训练的数据提供器，每次从缓存中随机读取批次大小的数据
train_reader = paddle.batch(
paddle.reader.shuffle(paddle.dataset.uci_housing.train(),
buf_size=BUF_SIZE),
batch_size=BATCH_SIZE)
#用于测试的数据提供器，每次从缓存中随机读取批次大小的数据
test_reader = paddle.batch(
paddle.reader.shuffle(paddle.dataset.uci_housing.test(),
buf_size=BUF_SIZE),
batch_size=BATCH_SIZE)
[==================================================]housing/housing.data not found, downloading http://paddlemodels.bj.bcebos.com/uci_housing/housing.data
/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/paddle/dataset/uci_housing.py:49: UserWarning:
This call to matplotlib.use() has no effect because the backend has already
been chosen; matplotlib.use() must be called before pylab, matplotlib.pyplot,
or matplotlib.backends is imported for the first time.
The backend was originally set to ‘module://ipykernel.pylab.backend_inline’ by the following code:
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/runpy.py”, line 193, in _run_module_as_main
“main”, mod_spec)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/runpy.py”, line 85, in _run_code
exec(code, run_globals)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel_launcher.py”, line 16, in
app.launch_new_instance()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/traitlets/config/application.py”, line 658, in launch_instance
app.start()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/kernelapp.py”, line 505, in start
self.io_loop.start()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/platform/asyncio.py”, line 132, in start
self.asyncio_loop.run_forever()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/asyncio/base_events.py”, line 421, in run_forever
self._run_once()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/asyncio/base_events.py”, line 1425, in _run_once
handle._run()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/asyncio/events.py”, line 127, in _run
self._callback(*self._args)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/ioloop.py”, line 758, in _run_callback
ret = callback()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/stack_context.py”, line 300, in null_wrapper
return fn(*args, **kwargs)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/gen.py”, line 1233, in inner
self.run()
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/gen.py”, line 1147, in run
yielded = self.gen.send(value)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/kernelbase.py”, line 357, in process_one
yield gen.maybe_future(dispatch(*args))
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/gen.py”, line 326, in wrapper
yielded = next(result)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/kernelbase.py”, line 267, in dispatch_shell
yield gen.maybe_future(handler(stream, idents, msg))
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/gen.py”, line 326, in wrapper
yielded = next(result)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/kernelbase.py”, line 534, in execute_request
user_expressions, allow_stdin,
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/tornado/gen.py”, line 326, in wrapper
yielded = next(result)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/ipkernel.py”, line 294, in do_execute
res = shell.run_cell(code, store_history=store_history, silent=silent)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/zmqshell.py”, line 536, in run_cell
return super(ZMQInteractiveShell, self).run_cell(*args, **kwargs)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/IPython/core/interactiveshell.py”, line 2821, in run_cell
self.events.trigger(‘post_run_cell’, result)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/IPython/core/events.py”, line 88, in trigger
func(*args, **kwargs)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/ipykernel/pylab/backend_inline.py”, line 164, in configure_once
activate_matplotlib(backend)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/IPython/core/pylabtools.py”, line 314, in activate_matplotlib
matplotlib.pyplot.switch_backend(backend)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/matplotlib/pyplot.py”, line 231, in switch_backend
matplotlib.use(newbackend, warn=False, force=True)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/matplotlib/init.py”, line 1422, in use
reload(sys.modules[‘matplotlib.backends’])
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/importlib/init.py”, line 166, in reload
_bootstrap._exec(spec, module)
File “/opt/conda/envs/python35-paddle120-env/lib/python3.5/site-packages/matplotlib/backends/init.py”, line 16, in
line for line in traceback.format_stack()
matplotlib.use(‘Agg’)
(3)打印看下数据是什么样的？PaddlePaddle接口提供的数据已经经过归一化等处理
(array([-0.02964322, -0.11363636, 0.39417967, -0.06916996, 0.14260276, -0.10109875, 0.30715859, -0.13176829, -0.24127857, 0.05489093, 0.29196451, -0.2368098 , 0.12850267]), array([15.6])),
#用于打印，查看uci_housing数据
train_data=paddle.dataset.uci_housing.train();
sampledata=next(train_data())
print(sampledata)
(array([-0.0405441 , 0.06636364, -0.32356227, -0.06916996, -0.03435197,
0.05563625, -0.03475696, 0.02682186, -0.37171335, -0.21419304,
-0.33569506, 0.10143217, -0.21172912]), array([24.]))
#定义张量变量x，表示13维的特征值
x = fluid.layers.data(name='x', shape=[13], dtype='float32')
#定义张量y,表示目标值
y = fluid.layers.data(name='y', shape=[1], dtype='float32')
#定义一个简单的线性网络,连接输入和输出的全连接层
#input:输入tensor;
#size:该层输出单元的数目
#act:激活函数
y_predict=fluid.layers.fc(input=x,size=1,act=None)
(2)定义损失函数
此处使用均方差损失函数。
square_error_cost(input,lable):接受输入预测值和目标值，并返回方差估计,即为（y-y_predict）的平方
cost = fluid.layers.square_error_cost(input=y_predict, label=y) #求一个batch的损失值
avg_cost = fluid.layers.mean(cost) #对损失值求平均值
(3)定义优化函数
此处使用的是随机梯度下降。
optimizer = fluid.optimizer.SGDOptimizer(learning_rate=0.001)
opts = optimizer.minimize(avg_cost)
test_program = fluid.default_main_program().clone(for_test=True)
在上述模型配置完毕后，得到两个fluid.Program：fluid.default_startup_program() 与fluid.default_main_program() 配置完毕了。
参数初始化操作会被写入fluid.default_startup_program()
fluid.default_main_program()用于获取默认或全局main program(主程序)。该主程序用于训练和测试模型。fluid.layers 中的所有layer函数可以向 default_main_program 中添加算子和变量。default_main_program 是fluid的许多编程接口（API）的Program参数的缺省值。例如,当用户program没有传入的时候， Executor.run() 会默认执行 default_main_program 。
Step3.模型训练 and Step4.模型评估
（1）创建Executor
首先定义运算场所 fluid.CPUPlace()和 fluid.CUDAPlace(0)分别表示运算场所为CPU和GPU
Executor:接收传入的program，通过run()方法运行program。
use_cuda = False #use_cuda为False,表示运算场所为CPU;use_cuda为True,表示运算场所为GPU
place = fluid.CUDAPlace(0) if use_cuda else fluid.CPUPlace()
exe = fluid.Executor(place) #创建一个Executor实例exe
exe.run(fluid.default_startup_program()) #Executor的run()方法执行startup_program(),进行参数初始化
[]
（2）定义输入数据维度
DataFeeder负责将数据提供器（train_reader,test_reader）返回的数据转成一种特殊的数据结构，使其可以输入到Executor中。
feed_list设置向模型输入的向变量表或者变量表名
# 定义输入数据维度
feeder = fluid.DataFeeder(place=place, feed_list=[x, y])#feed_list:向模型输入的变量表或变量表名
（3）定义绘制训练过程的损失值变化趋势的方法draw_train_process
iter=0;
iters=[]
train_costs=[]
def draw_train_process(iters,train_costs):
title="training cost"
plt.title(title, fontsize=24)
plt.xlabel("iter", fontsize=14)
plt.ylabel("cost", fontsize=14)
plt.plot(iters, train_costs,color='red',label='training cost')
plt.grid()
plt.show()
（4）训练并保存模型
Executor接收传入的program,并根据feed map(输入映射表)和fetch_list(结果获取表) 向program中添加feed operators(数据输入算子)和fetch operators（结果获取算子)。 feed map为该program提供输入数据。fetch_list提供program训练结束后用户预期的变量。
注：enumerate() 函数用于将一个可遍历的数据对象(如列表、元组或字符串)组合为一个索引序列，同时列出数据和数据下标，
EPOCH_NUM=50
model_save_dir = "/home/aistudio/work/fit_a_line.inference.model"
for pass_id in range(EPOCH_NUM): #训练EPOCH_NUM轮
# 开始训练并输出最后一个batch的损失值
train_cost = 0
for batch_id, data in enumerate(train_reader()): #遍历train_reader迭代器
train_cost = exe.run(program=fluid.default_main_program(),#运行主程序
feed=feeder.feed(data), #喂入一个batch的训练数据，根据feed_list和data提供的信息，将输入数据转成一种特殊的数据结构
fetch_list=[avg_cost])
if batch_id % 40 == 0:
print("Pass:%d, Cost:%0.5f" % (pass_id, train_cost[0][0])) #打印最后一个batch的损失值
iter=iter+BATCH_SIZE
iters.append(iter)
train_costs.append(train_cost[0][0])
# 开始测试并输出最后一个batch的损失值
test_cost = 0
for batch_id, data in enumerate(test_reader()): #遍历test_reader迭代器
test_cost= exe.run(program=test_program, #运行测试cheng
feed=feeder.feed(data), #喂入一个batch的测试数据
fetch_list=[avg_cost]) #fetch均方误差
print('Test:%d, Cost:%0.5f' % (pass_id, test_cost[0][0])) #打印最后一个batch的损失值
#保存模型
# 如果保存路径不存在就创建
if not os.path.exists(model_save_dir):
os.makedirs(model_save_dir)
print ('save models to %s' % (model_save_dir))
#保存训练参数到指定路径中，构建一个专门用预测的program
fluid.io.save_inference_model(model_save_dir, #保存推理model的路径
['x'], #推理（inference）需要 feed 的数据
[y_predict], #保存推理（inference）结果的 Variables
exe) #exe 保存 inference model
draw_train_process(iters,train_costs)
Pass:0, Cost:783.22180
Test:0, Cost:154.32607
Pass:1, Cost:519.22571
Test:1, Cost:92.79891
Pass:2, Cost:606.54010
Test:2, Cost:92.41443
Pass:3, Cost:279.49731
Test:3, Cost:185.88803
Pass:4, Cost:356.30026
Test:4, Cost:129.92186
Pass:5, Cost:419.08685
Test:5, Cost:111.01654
Pass:6, Cost:390.89267
Test:6, Cost:102.50714
Pass:7, Cost:363.88116
Test:7, Cost:103.34782
Pass:8, Cost:256.58975
Test:8, Cost:110.39152
Pass:9, Cost:351.81763
Test:9, Cost:102.23664
Pass:10, Cost:283.22528
Test:10, Cost:28.30433
Pass:11, Cost:168.48587
Test:11, Cost:13.69916
Pass:12, Cost:151.80196
Test:12, Cost:62.51043
Pass:13, Cost:270.92618
Test:13, Cost:86.74022
Pass:14, Cost:277.52686
Test:14, Cost:102.50578
Pass:15, Cost:138.70033
Test:15, Cost:7.86415
Pass:16, Cost:165.45930
Test:16, Cost:64.38410
Pass:17, Cost:152.47154
Test:17, Cost:29.15284
Pass:18, Cost:138.93571
Test:18, Cost:10.48840
Pass:19, Cost:119.68816
Test:19, Cost:29.43134
Pass:20, Cost:197.25444
Test:20, Cost:24.20947
Pass:21, Cost:160.16647
Test:21, Cost:9.46981
Pass:22, Cost:119.94437
Test:22, Cost:44.95092
Pass:23, Cost:123.78200
Test:23, Cost:50.50562
Pass:24, Cost:124.72739
Test:24, Cost:12.59006
Pass:25, Cost:87.68204
Test:25, Cost:1.80894
Pass:26, Cost:120.34269
Test:26, Cost:128.54480
Pass:27, Cost:92.00354
Test:27, Cost:12.28447
Pass:28, Cost:31.87757
Test:28, Cost:97.24959
Pass:29, Cost:53.11855
Test:29, Cost:29.35019
Pass:30, Cost:125.88458
Test:30, Cost:16.12622
Pass:31, Cost:74.63180
Test:31, Cost:13.28822
Pass:32, Cost:31.88729
Test:32, Cost:43.91414
Pass:33, Cost:130.80821
Test:33, Cost:25.24403
Pass:34, Cost:75.27191
Test:34, Cost:12.12042
Pass:35, Cost:93.65819
Test:35, Cost:10.82217
Pass:36, Cost:115.08681
Test:36, Cost:14.19905
Pass:37, Cost:53.95051
Test:37, Cost:13.51565
Pass:38, Cost:63.14687
Test:38, Cost:25.04268
Pass:39, Cost:15.51875
Test:39, Cost:16.89660
Pass:40, Cost:34.37993
Test:40, Cost:7.67218
Pass:41, Cost:105.88936
Test:41, Cost:73.32098
Pass:42, Cost:43.80605
Test:42, Cost:41.20872
Pass:43, Cost:28.96686
Test:43, Cost:0.36368
Pass:44, Cost:113.72699
Test:44, Cost:4.48252
Pass:45, Cost:133.08170
Test:45, Cost:10.91978
Pass:46, Cost:70.03806
Test:46, Cost:48.56998
Pass:47, Cost:68.39425
Test:47, Cost:2.08680
Pass:48, Cost:133.85884
Test:48, Cost:1.99625
Pass:49, Cost:48.71880
Test:49, Cost:19.31082
save models to /home/aistudio/work/fit_a_line.inference.model
Step5.模型预测
（1）创建预测用的Executor
infer_exe = fluid.Executor(place) #创建推测用的executor
inference_scope = fluid.core.Scope() #Scope指定作用域
（2）可视化真实值与预测值方法定义
infer_results=[]
groud_truths=[]
#绘制真实值和预测值对比图
def draw_infer_result(groud_truths,infer_results):
title='Boston'
plt.title(title, fontsize=24)
x = np.arange(1,20)
y = x
plt.plot(x, y)
plt.xlabel('ground truth', fontsize=14)
plt.ylabel('infer result', fontsize=14)
plt.scatter(groud_truths, infer_results,color='green',label='training cost')
plt.grid()
plt.show()
(3)开始预测
通过fluid.io.load_inference_model，预测器会从params_dirname中读取已经训练好的模型，来对从未遇见过的数据进行预测。
with fluid.scope_guard(inference_scope):#修改全局/默认作用域（scope）, 运行时中的所有变量都将分配给新的scope。
#从指定目录中加载 推理model(inference model)
[inference_program, #推理的program
feed_target_names, #需要在推理program中提供数据的变量名称
fetch_targets] = fluid.io.load_inference_model(#fetch_targets: 推断结果
model_save_dir, #model_save_dir:模型训练路径
infer_exe) #infer_exe: 预测用executor
#获取预测数据
infer_reader = paddle.batch(paddle.dataset.uci_housing.test(), #获取uci_housing的测试数据
batch_size=200) #从测试数据中读取一个大小为200的batch数据
#从test_reader中分割x
test_data = next(infer_reader())
test_x = np.array([data[0] for data in test_data]).astype("float32")
test_y= np.array([data[1] for data in test_data]).astype("float32")
results = infer_exe.run(inference_program, #预测模型
feed={feed_target_names[0]: np.array(test_x)}, #喂入要预测的x值
fetch_list=fetch_targets) #得到推测结果
print("infer results: (House Price)")
for idx, val in enumerate(results[0]):
print("%d: %.2f" % (idx, val))
infer_results.append(val)
print("ground truth:")
for idx, val in enumerate(test_y):
print("%d: %.2f" % (idx, val))
groud_truths.append(val)
draw_infer_result(groud_truths,infer_results)
infer results: (House Price)
0: 15.05
1: 15.20
2: 15.07
3: 16.41
4: 15.53
5: 16.07
6: 15.84
7: 15.56
8: 13.82
9: 15.49
10: 13.18
11: 14.53
12: 15.07
13: 14.68
14: 14.66
15: 15.43
16: 16.23
17: 16.14
18: 16.56
19: 15.37
20: 16.00
21: 14.77
22: 16.37
23: 15.77
24: 15.60
25: 15.12
26: 16.18
27: 16.04
28: 16.87
29: 15.89
30: 15.74
31: 15.16
32: 15.32
33: 14.41
34: 14.04
35: 15.54
36: 15.59
37: 16.00
38: 16.18
39: 16.03
40: 15.12
41: 14.89
42: 15.99
43: 16.22
44: 16.16
45: 15.94
46: 15.59
47: 16.29
48: 16.37
49: 16.62
50: 15.47
51: 15.68
52: 15.33
53: 15.57
54: 16.32
55: 16.65
56: 16.31
57: 16.69
58: 16.80
59: 17.07
60: 17.30
61: 17.21
62: 15.79
63: 16.29
64: 16.90
65: 17.38
66: 17.09
67: 17.48
68: 17.44
69: 17.73
70: 16.37
71: 15.98
72: 16.69
73: 15.57
74: 16.52
75: 17.01
76: 18.03
77: 18.27
78: 18.41
79: 18.29
80: 17.80
81: 18.08
82: 17.24
83: 17.80
84: 17.32
85: 16.63
86: 16.02
87: 17.39
88: 18.01
89: 21.00
90: 21.09
91: 20.90
92: 19.93
93: 20.66
94: 20.87
95: 20.43
96: 20.56
97: 21.70
98: 21.49
99: 21.83
100: 21.74
101: 21.52
ground truth:
0: 8.50
1: 5.00
2: 11.90
3: 27.90
4: 17.20
5: 27.50
6: 15.00
7: 17.20
8: 17.90
9: 16.30
10: 7.00
11: 7.20
12: 7.50
13: 10.40
14: 8.80
15: 8.40
16: 16.70
17: 14.20
18: 20.80
19: 13.40
20: 11.70
21: 8.30
22: 10.20
23: 10.90
24: 11.00
25: 9.50
26: 14.50
27: 14.10
28: 16.10
29: 14.30
30: 11.70
31: 13.40
32: 9.60
33: 8.70
34: 8.40
35: 12.80
36: 10.50
37: 17.10
38: 18.40
39: 15.40
40: 10.80
41: 11.80
42: 14.90
43: 12.60
44: 14.10
45: 13.00
46: 13.40
47: 15.20
48: 16.10
49: 17.80
50: 14.90
51: 14.10
52: 12.70
53: 13.50
54: 14.90
55: 20.00
56: 16.40
57: 17.70
58: 19.50
59: 20.20
60: 21.40
61: 19.90
62: 19.00
63: 19.10
64: 19.10
65: 20.10
66: 19.90
67: 19.60
68: 23.20
69: 29.80
70: 13.80
71: 13.30
72: 16.70
73: 12.00
74: 14.60
75: 21.40
76: 23.00
77: 23.70
78: 25.00
79: 21.80
80: 20.60
81: 21.20
82: 19.10
83: 20.60
84: 15.20
85: 7.00
86: 8.10
87: 13.60
88: 20.10
89: 21.80
90: 24.50
91: 23.10
92: 19.70
93: 18.30
94: 21.20
95: 17.50
96: 16.80
97: 22.40
98: 20.60
99: 23.90
100: 22.00
101: 11.90
来源：CSDN
作者：PaddlePaddle开发者
链接：https://blog.csdn.net/PaddleLover/article/details/103611241