使用Tensorflow处理多元回归问题

处理回归问题是人工智能的一项能力，这篇文章将使用tensorflow处理一个简单的多元线性回归问题：波士顿房价预测项目。

1.导入库

import tensorflow as tf
from tensorflow import keras
import numpy as np
from sklearn import preprocessing
import pandas as pd
import matplotlib.pyplot as plt

import tensorflow as tf

from tensorflow import keras

import numpy as np

from sklearn import preprocessing

import pandas as pd

import matplotlib.pyplot as plt

其中pandas与matplotlib用于绘图

2.导入与处理数据

def deal_file(file):
    data_list_text = file.readlines()
    data_list = []
    for i in data_list_text:
    data_list.append(list(map(float, i.split(','))))
    data_list = np.asarray(data_list, float)
    return data_list

def deal_file(file):

data_list_text = file.readlines()

data_list = []

for i in data_list_text:

data_list.append(list(map(float, i.split(','))))

data_list = np.asarray(data_list, float)

return data_list

data=deal_file(open('in.txt'))
label=deal_file(open('out.txt'))
test=deal_file(open('test.txt'))
testsplit=np.split(test,[0,13],axis=1) testx=testsplit[1] testy=testsplit[2] print('prompt: data load finished')

data=deal_file(open('in.txt'))

label=deal_file(open('out.txt'))

test=deal_file(open('test.txt'))

testsplit=np.split(test,[0,13],axis=1) testx=testsplit[1] testy=testsplit[2] print('prompt: data load finished')

这里我使用的数据：仓库链接

3.对数据进行预处理

def scale(x):
    return preprocessing.StandardScaler().fit_transform(x)
data=scale(data)
label=scale(label)
testx=scale(testx)
testy=scale(testy)

def scale(x):

return preprocessing.StandardScaler().fit_transform(x)

data=scale(data)

label=scale(label)

testx=scale(testx)

testy=scale(testy)

4.建立神经网络模型

model=tf.keras.Sequential([
    keras.layers.Dense(16,input_shape=([13]),activation='relu'),
    keras.layers.Dense(32,activation='relu'),
    keras.layers.Dense(1)
])

model=tf.keras.Sequential([

keras.layers.Dense(16,input_shape=([13]),activation='relu'),

keras.layers.Dense(32,activation='relu'),

keras.layers.Dense(1)

])

relu为回归模型常用的激活函数

model.summary()

1	model.summary()

Model: "sequential"<br><strong><em><strong><em>_____________________________________________________</em></strong></em></strong><br>Layer (type) Output Shape Param #<br>=================================================================<br>dense (Dense) (None, 16) 224<br><strong><em><strong><em>_____________________________________________________</em></strong></em></strong><br>dense_1 (Dense) (None, 32) 544<br><strong>_____________________________________________________</strong><br>dense_2 (Dense) (None, 1) 33<br>=================================================================<br>Total params: 801<br>Trainable params: 801<br>Non-trainable params: 0<br><strong><em><strong><em>_____________________________________________________</em></strong></em></strong>

Model: "sequential" _____________________________________________________ Layer (type) Output Shape Param # ================================================================= dense (Dense) (None, 16) 224 _____________________________________________________ dense_1 (Dense) (None, 32) 544 _____________________________________________________ dense_2 (Dense) (None, 1) 33 ================================================================= Total params: 801 Trainable params: 801 Non-trainable params: 0 _____________________________________________________

由于样本数量比较小，所以我们使用神经元数量相对较少的三层神经网络

5.设置回调

class PrintDot(keras.callbacks.Callback):
    def on_epoch_end(self, epoch, logs):
        if epoch % 100 == 0: print('')
        print('.', end='')
early_stop = keras.callbacks.EarlyStopping(monitor='val_loss', patience=10)

class PrintDot(keras.callbacks.Callback):

def on_epoch_end(self, epoch, logs):

if epoch % 100 == 0: print('')

print('.', end='')

early_stop = keras.callbacks.EarlyStopping(monitor='val_loss', patience=10)

适当设置回调可以防止过拟合，PrintDot可以简化神经网络在训练时的输出

6.训练模型

model.compile(optimizer=tf.keras.optimizers.RMSprop(0.001),loss='mse',metrics=['mae','mse'])

history=model.fit(
    data,label,epochs=200,
    validation_split = 0.2,
    verbose=0,
    callbacks=[early_stop,PrintDot()]
)

model.compile(optimizer=tf.keras.optimizers.RMSprop(0.001),loss='mse',metrics=['mae','mse'])

history=model.fit(

data,label,epochs=200,

validation_split = 0.2,

verbose=0,

callbacks=[early_stop,PrintDot()]

)

RMSProp算法是AdaGrad算法的一种改进，常用于回归模型，将训练结果存储在history中便于后续查看训练情况

7.训练过程分析

def plot_history(history):
    hist = pd.DataFrame(history.history)
    hist['epoch'] = history.epoch
    plt.figure()
    plt.xlabel('Epoch')
    plt.ylabel('Mean Abs Error')
    plt.plot(hist['epoch'], hist['mae'],label='Train Error')
    plt.plot(hist['epoch'], hist['val_mae'],label = 'Val Error')
    plt.ylim([0,1])
    plt.legend()
    plt.show()

def plot_history(history):

hist = pd.DataFrame(history.history)

hist['epoch'] = history.epoch

plt.figure()

plt.xlabel('Epoch')

plt.ylabel('Mean Abs Error')

plt.plot(hist['epoch'], hist['mae'],label='Train Error')

plt.plot(hist['epoch'], hist['val_mae'],label = 'Val Error')

plt.ylim([0,1])

plt.legend()

plt.show()

plot_history(history)

1	plot_history(history)

8.训练结果分析

predict=model.predict(testx).flatten()

1	predict=model.predict(testx).flatten()

plt.scatter(testy, predict)
plt.xlabel('True Values')
plt.ylabel('Predictions')
plt.axis('equal')
plt.axis('square')
plt.xlim([0,plt.xlim()[1]])
plt.ylim([0,plt.ylim()[1]])
_ = plt.plot([-100, 100], [-100, 100])

plt.scatter(testy, predict)

plt.xlabel('True Values')

plt.ylabel('Predictions')

plt.axis('equal')

plt.axis('square')

plt.xlim([0,plt.xlim()[1]])

plt.ylim([0,plt.ylim()[1]])

_ = plt.plot([-100, 100], [-100, 100])

error = predict - testy
plt.hist(error)
plt.xlabel("Prediction Error")
_ = plt.ylabel("Count")

error = predict - testy

plt.hist(error)

plt.xlabel("Prediction Error")

_ = plt.ylabel("Count")

从图中可以看出，虽然有异常数据，但误差基本符合高斯分布

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