# 使用线性回归预测波士顿房价¶

## 二、环境配置¶

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import paddle
import numpy as np
import os
import matplotlib
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
import warnings
warnings.filterwarnings("ignore")


2.1.0


## 三、数据集介绍¶

### 3.1 数据处理¶

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#下载数据
!wget https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data -O housing.data

--2021-05-18 16:20:29--  https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data
Resolving archive.ics.uci.edu (archive.ics.uci.edu)... 128.195.10.252
Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 49082 (48K) [application/x-httpd-php]
Saving to: ‘housing.data’

housing.data        100%[===================>]  47.93K  94.2KB/s    in 0.5s

2021-05-18 16:20:31 (94.2 KB/s) - ‘housing.data’ saved [49082/49082]


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# 从文件导入数据
datafile = './housing.data'
housing_data = np.fromfile(datafile, sep=' ')
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
housing_data = housing_data.reshape([housing_data.shape[0] // feature_num, feature_num])

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# 画图看特征间的关系,主要是变量两两之间的关系（线性或非线性，有无明显较为相关关系）
features_np = np.array([x[:13] for x in housing_data], np.float32)
labels_np = np.array([x[-1] for x in housing_data], np.float32)
# data_np = np.c_[features_np, labels_np]
df = pd.DataFrame(housing_data, columns=feature_names)
matplotlib.use('TkAgg')
%matplotlib inline
sns.pairplot(df.dropna(), y_vars=feature_names[-1], x_vars=feature_names[::-1], diag_kind='kde')
plt.show()

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# 相关性分析
fig, ax = plt.subplots(figsize=(15, 1))
corr_data = df.corr().iloc[-1]
corr_data = np.asarray(corr_data).reshape(1, 14)
ax = sns.heatmap(corr_data, cbar=True, annot=True)
plt.show()


### 3.2 数据归一化处理¶

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sns.boxplot(data=df.iloc[:, 0:13])

<matplotlib.axes._subplots.AxesSubplot at 0x7f528b374890>


• 过大或过小的数值范围会导致计算时的浮点上溢或下溢。

• 不同的数值范围会导致不同属性对模型的重要性不同（至少在训练的初始阶段如此），而这个隐含的假设常常是不合理的。这会对优化的过程造成困难，使训练时间大大的加长.

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features_max = housing_data.max(axis=0)
features_min = housing_data.min(axis=0)
features_avg = housing_data.sum(axis=0) / housing_data.shape[0]

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BATCH_SIZE = 20
def feature_norm(input):
f_size = input.shape
output_features = np.zeros(f_size, np.float32)
for batch_id in range(f_size[0]):
for index in range(13):
output_features[batch_id][index] = (input[batch_id][index] - features_avg[index]) / (features_max[index] - features_min[index])
return output_features

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# 只对属性进行归一化
housing_features = feature_norm(housing_data[:, :13])
# print(feature_trian.shape)
housing_data = np.c_[housing_features, housing_data[:, -1]].astype(np.float32)
# print(training_data[0])

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# 归一化后的train_data, 看下各属性的情况
features_np = np.array([x[:13] for x in housing_data],np.float32)
labels_np = np.array([x[-1] for x in housing_data],np.float32)
data_np = np.c_[features_np, labels_np]
df = pd.DataFrame(data_np, columns=feature_names)
sns.boxplot(data=df.iloc[:, 0:13])

<matplotlib.axes._subplots.AxesSubplot at 0x7f528b576e50>

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# 将训练数据集和测试数据集按照8:2的比例分开
ratio = 0.8
offset = int(housing_data.shape[0] * ratio)
train_data = housing_data[:offset]
test_data = housing_data[offset:]


## 四、模型组网¶

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class Regressor(paddle.nn.Layer):
def __init__(self):
super(Regressor, self).__init__()
self.fc = paddle.nn.Linear(13, 1,)

def forward(self, inputs):
pred = self.fc(inputs)
return pred


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train_nums = []
train_costs = []

def draw_train_process(iters, train_costs):
plt.title("training cost", fontsize=24)
plt.xlabel("iter", fontsize=14)
plt.ylabel("cost", fontsize=14)
plt.plot(iters, train_costs, color='red', label='training cost')
plt.show()


## 五、方式1：使用基础API完成模型训练&预测¶

### 5.1 模型训练¶

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import paddle.nn.functional as F
y_preds = []
labels_list = []

def train(model):
print('start training ... ')
# 开启模型训练模式
model.train()
EPOCH_NUM = 500
train_num = 0
optimizer = paddle.optimizer.SGD(learning_rate=0.001, parameters=model.parameters())
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(train_data)
# 将训练数据进行拆分，每个batch包含20条数据
mini_batches = [train_data[k: k+BATCH_SIZE] for k in range(0, len(train_data), BATCH_SIZE)]
for batch_id, data in enumerate(mini_batches):
features_np = np.array(data[:, :13], np.float32)
labels_np = np.array(data[:, -1:], np.float32)
# 前向计算
y_pred = model(features)
cost = F.mse_loss(y_pred, label=labels)
train_cost = cost.numpy()[0]
# 反向传播
cost.backward()
# 最小化loss，更新参数
optimizer.step()
# 清除梯度

if batch_id%30 == 0 and epoch_id%50 == 0:
print("Pass:%d,Cost:%0.5f"%(epoch_id, train_cost))

train_num = train_num + BATCH_SIZE
train_nums.append(train_num)
train_costs.append(train_cost)

model = Regressor()
train(model)

start training ...
Pass:0,Cost:731.48828
Pass:50,Cost:77.37501
Pass:100,Cost:21.86424
Pass:150,Cost:23.56446
Pass:200,Cost:68.49669
Pass:250,Cost:13.10599
Pass:300,Cost:20.35128
Pass:350,Cost:34.87028
Pass:400,Cost:24.54537
Pass:450,Cost:20.29261

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matplotlib.use('TkAgg')
%matplotlib inline
draw_train_process(train_nums, train_costs)


### 5.2 模型预测¶

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# 获取预测数据
INFER_BATCH_SIZE = 100

infer_features_np = np.array([data[:13] for data in test_data]).astype("float32")
infer_labels_np = np.array([data[-1] for data in test_data]).astype("float32")

fetch_list = model(infer_features)

sum_cost = 0
for i in range(INFER_BATCH_SIZE):
infer_result = fetch_list[i][0]
ground_truth = infer_labels[i]
if i % 10 == 0:
print("No.%d: infer result is %.2f,ground truth is %.2f" % (i, infer_result, ground_truth))
cost = paddle.pow(infer_result - ground_truth, 2)
sum_cost += cost
mean_loss = sum_cost / INFER_BATCH_SIZE
print("Mean loss is:", mean_loss.numpy())

No.0: infer result is 12.17,ground truth is 8.50
No.10: infer result is 5.70,ground truth is 7.00
No.20: infer result is 14.81,ground truth is 11.70
No.30: infer result is 16.45,ground truth is 11.70
No.40: infer result is 13.50,ground truth is 10.80
No.50: infer result is 15.98,ground truth is 14.90
No.60: infer result is 18.55,ground truth is 21.40
No.70: infer result is 15.36,ground truth is 13.80
No.80: infer result is 17.89,ground truth is 20.60
No.90: infer result is 21.31,ground truth is 24.50
Mean loss is: [12.873257]

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def plot_pred_ground(pred, ground):
plt.figure()
plt.title("Predication v.s. Ground truth", fontsize=24)
plt.xlabel("ground truth price(unit:\$1000)", fontsize=14)
plt.ylabel("predict price", fontsize=14)
plt.scatter(ground, pred, alpha=0.5)  #  scatter:散点图,alpha:"透明度"
plt.plot(ground, ground, c='red')
plt.show()

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plot_pred_ground(fetch_list, infer_labels_np)


## 六、方式2：使用高层API完成模型训练&预测¶

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import paddle

# step1:用高层API定义数据集，无需进行数据处理等，高层API为你一条龙搞定

# step2:定义模型
def __init__(self):
super(UCIHousing, self).__init__()
self.fc = paddle.nn.Linear(13, 1, None)

def forward(self, input):
pred = self.fc(input)
return pred

# step3:训练模型
model.fit(train_dataset, eval_dataset, epochs=5, batch_size=8, verbose=1)

The loss value printed in the log is the current step, and the metric is the average value of previous steps.
Epoch 1/5
step 51/51 [==============================] - loss: 624.0728 - 2ms/step
Eval begin...
step 13/13 [==============================] - loss: 397.2567 - 878us/step
Eval samples: 102
Epoch 2/5
step 51/51 [==============================] - loss: 422.2296 - 1ms/step
Eval begin...
step 13/13 [==============================] - loss: 394.6901 - 750us/step
Eval samples: 102
Epoch 3/5
step 51/51 [==============================] - loss: 417.4614 - 1ms/step
Eval begin...
step 13/13 [==============================] - loss: 392.1667 - 810us/step
Eval samples: 102
Epoch 4/5
step 51/51 [==============================] - loss: 423.6764 - 1ms/step
Eval begin...
step 13/13 [==============================] - loss: 389.6587 - 772us/step
Eval samples: 102
Epoch 5/5
step 51/51 [==============================] - loss: 461.0751 - 1ms/step
Eval begin...
step 13/13 [==============================] - loss: 387.1344 - 828us/step
Eval samples: 102