【深度学习】实验09 使用Keras完成线性回归

使用Keras完成线性回归

Keras是一款基于Python的深度学习框架，以Tensorflow、Theano和CNTK作为后端，由François Chollet开发和维护，其目标是使深度学习模型的实现变得快速、简单。它的设计理念是用户友好、可扩展、易于调试和实验。

Keras提供了一系列高级API和便捷的工具，使得用户可以快速构建和训练深度学习模型，而不必关注底层的细节。Keras支持各种类型的网络结构，包括卷积神经网络、循环神经网络、自编码器等，并且可以轻松地在不同的数据集上进行训练和测试。

Keras的主要特点有：

1. 简单易用，快速上手：Keras提供了简单易用的API，用户只需几行代码就能实现复杂的深度学习模型。

2. 支持多种后端：Keras可以用Tensorflow、Theano和CNTK作为后端，用户可以根据自己的需要选择合适的后端。

3. 高度可扩展：Keras提供了模块化的API，用户可以根据需要添加自定义层和函数，以及修改现有的代码。

4. 方便的调试和实验：Keras提供了实时可视化的工具，方便用户查看模型的训练情况和测试结果，并且支持各种回调函数，例如早期停止、学习率调整等。

5. 支持GPU加速：Keras可以利用GPU进行计算，加速深度学习模型的训练和推断过程。

总之，Keras是一款优秀的深度学习框架，它使得深度学习模型的构建和训练变得更加简单和快速，可以帮助用户更加专注于模型的设计和应用。

1. 导入Keras库

import warnings
warnings.filterwarnings("ignore")

import numpy as np
np.random.seed(1337)

from keras.models import Sequential
from keras.layers import Dense
from sklearn.metrics import r2_score
import matplotlib.pyplot as plt
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Using TensorFlow backend.
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2. 创建数据集

# 创建数据集
# 在[-1,1]的区间内等间隔创建200个样本数
X = np.linspace(-1, 1, 200)
X
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   array([-1.        , -0.98994975, -0.9798995 , -0.96984925, -0.95979899,
          -0.94974874, -0.93969849, -0.92964824, -0.91959799, -0.90954774,
          -0.89949749, -0.88944724, -0.87939698, -0.86934673, -0.85929648,
          -0.84924623, -0.83919598, -0.82914573, -0.81909548, -0.80904523,
          -0.79899497, -0.78894472, -0.77889447, -0.76884422, -0.75879397,
          -0.74874372, -0.73869347, -0.72864322, -0.71859296, -0.70854271,
          -0.69849246, -0.68844221, -0.67839196, -0.66834171, -0.65829146,
          -0.64824121, -0.63819095, -0.6281407 , -0.61809045, -0.6080402 ,
          -0.59798995, -0.5879397 , -0.57788945, -0.5678392 , -0.55778894,
          -0.54773869, -0.53768844, -0.52763819, -0.51758794, -0.50753769,
          -0.49748744, -0.48743719, -0.47738693, -0.46733668, -0.45728643,
          -0.44723618, -0.43718593, -0.42713568, -0.41708543, -0.40703518,
          -0.39698492, -0.38693467, -0.37688442, -0.36683417, -0.35678392,
          -0.34673367, -0.33668342, -0.32663317, -0.31658291, -0.30653266,
          -0.29648241, -0.28643216, -0.27638191, -0.26633166, -0.25628141,
          -0.24623116, -0.2361809 , -0.22613065, -0.2160804 , -0.20603015,
          -0.1959799 , -0.18592965, -0.1758794 , -0.16582915, -0.15577889,
          -0.14572864, -0.13567839, -0.12562814, -0.11557789, -0.10552764,
          -0.09547739, -0.08542714, -0.07537688, -0.06532663, -0.05527638,
          -0.04522613, -0.03517588, -0.02512563, -0.01507538, -0.00502513,
           0.00502513,  0.01507538,  0.02512563,  0.03517588,  0.04522613,
           0.05527638,  0.06532663,  0.07537688,  0.08542714,  0.09547739,
           0.10552764,  0.11557789,  0.12562814,  0.13567839,  0.14572864,
           0.15577889,  0.16582915,  0.1758794 ,  0.18592965,  0.1959799 ,
           0.20603015,  0.2160804 ,  0.22613065,  0.2361809 ,  0.24623116,
           0.25628141,  0.26633166,  0.27638191,  0.28643216,  0.29648241,
           0.30653266,  0.31658291,  0.32663317,  0.33668342,  0.34673367,
           0.35678392,  0.36683417,  0.37688442,  0.38693467,  0.39698492,
           0.40703518,  0.41708543,  0.42713568,  0.43718593,  0.44723618,
           0.45728643,  0.46733668,  0.47738693,  0.48743719,  0.49748744,
           0.50753769,  0.51758794,  0.52763819,  0.53768844,  0.54773869,
           0.55778894,  0.5678392 ,  0.57788945,  0.5879397 ,  0.59798995,
           0.6080402 ,  0.61809045,  0.6281407 ,  0.63819095,  0.64824121,
           0.65829146,  0.66834171,  0.67839196,  0.68844221,  0.69849246,
           0.70854271,  0.71859296,  0.72864322,  0.73869347,  0.74874372,
           0.75879397,  0.76884422,  0.77889447,  0.78894472,  0.79899497,
           0.80904523,  0.81909548,  0.82914573,  0.83919598,  0.84924623,
           0.85929648,  0.86934673,  0.87939698,  0.88944724,  0.89949749,
           0.90954774,  0.91959799,  0.92964824,  0.93969849,  0.94974874,
           0.95979899,  0.96984925,  0.9798995 ,  0.98994975,  1.        ])
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# 将数据集随机化
np.random.shuffle(X)
X
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   array([-0.70854271,  0.1758794 , -0.30653266,  0.74874372, -0.02512563,
           0.33668342, -0.85929648,  0.01507538, -0.13567839,  0.72864322,
           0.24623116, -0.74874372, -0.78894472,  0.50753769,  0.03517588,
           0.35678392, -0.55778894,  0.2361809 , -0.25628141, -0.44723618,
           0.2160804 , -0.43718593, -0.64824121,  0.69849246, -0.03517588,
          -0.45728643,  0.86934673,  0.73869347,  0.53768844, -0.67839196,
          -0.75879397,  0.55778894,  0.28643216, -0.05527638, -0.86934673,
           0.1959799 , -0.57788945, -0.9798995 , -0.6080402 , -0.63819095,
           0.84924623,  0.41708543,  0.13567839,  0.79899497, -0.47738693,
           0.46733668,  0.59798995, -0.80904523, -0.98994975, -0.36683417,
          -0.5678392 , -0.00502513, -0.53768844, -0.37688442, -0.65829146,
          -0.1959799 ,  0.06532663,  0.44723618, -0.01507538, -0.6281407 ,
           0.02512563, -0.71859296, -0.14572864, -0.46733668,  0.07537688,
           0.85929648,  0.76884422,  0.40703518, -0.68844221,  0.68844221,
          -0.29648241,  0.66834171, -0.95979899, -0.33668342,  0.26633166,
          -0.82914573,  1.        , -0.5879397 , -0.69849246, -0.20603015,
           0.63819095, -0.88944724, -0.40703518, -0.32663317,  0.15577889,
          -0.41708543,  0.10552764,  0.20603015, -0.04522613,  0.00502513,
          -0.31658291,  0.43718593,  0.42713568,  0.45728643, -0.59798995,
          -0.66834171,  0.83919598,  0.75879397, -0.24623116,  0.71859296,
          -0.92964824,  0.39698492,  0.61809045, -0.84924623, -0.87939698,
          -0.96984925,  0.87939698,  0.6281407 ,  0.25628141,  0.27638191,
           0.12562814,  0.09547739, -0.89949749,  0.80904523, -0.16582915,
          -0.12562814,  0.30653266,  0.49748744,  0.5879397 , -0.51758794,
          -0.10552764,  0.54773869, -0.94974874,  0.92964824,  0.16582915,
          -0.83919598, -0.35678392, -0.48743719,  0.08542714, -0.61809045,
           0.18592965,  0.57788945,  0.65829146,  0.38693467,  0.91959799,
          -0.26633166, -0.50753769, -1.        , -0.54773869,  0.6080402 ,
          -0.49748744, -0.22613065,  0.9798995 ,  0.98994975,  0.5678392 ,
           0.32663317,  0.64824121, -0.52763819,  0.36683417,  0.81909548,
          -0.11557789,  0.31658291, -0.2160804 ,  0.95979899,  0.77889447,
          -0.73869347, -0.81909548, -0.79899497,  0.78894472,  0.88944724,
          -0.2361809 ,  0.37688442,  0.70854271,  0.22613065, -0.28643216,
          -0.38693467,  0.90954774, -0.91959799,  0.48743719, -0.42713568,
          -0.08542714,  0.11557789, -0.18592965,  0.47738693, -0.39698492,
          -0.34673367,  0.04522613,  0.05527638,  0.93969849, -0.77889447,
          -0.93969849, -0.06532663, -0.72864322,  0.29648241,  0.52763819,
          -0.76884422,  0.94974874,  0.82914573,  0.34673367, -0.90954774,
          -0.27638191, -0.15577889, -0.1758794 ,  0.14572864, -0.09547739,
           0.96984925,  0.67839196, -0.07537688,  0.89949749,  0.51758794])
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# 假设真实模型为：Y=0.5X+2
Y = 0.5 * X + 2 + np.random.normal(0, 0.05, (200,))
Y
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   array([1.66851812, 2.12220988, 1.91611873, 2.38979647, 1.96473269,
          2.11662688, 1.58217043, 2.05326658, 1.95885373, 2.4277956 ,
          2.13544689, 1.68732448, 1.66384243, 2.2702853 , 2.03148986,
          2.14968674, 1.76442495, 2.10802586, 1.93269542, 1.81936289,
          2.15190248, 1.83941395, 1.71399197, 2.21820555, 1.97918099,
          1.79781646, 2.43645587, 2.31211201, 2.21764353, 1.71912829,
          1.64285239, 2.2663785 , 2.11081029, 2.09338152, 1.5614153 ,
          2.19655545, 1.72824772, 1.56444412, 1.72673075, 1.67311017,
          2.39817488, 2.12624087, 2.07791136, 2.40515644, 1.80701389,
          2.16050089, 2.30373845, 1.57656517, 1.52482139, 1.7639545 ,
          1.76787463, 2.01204511, 1.74877623, 1.86751173, 1.67509082,
          1.95941218, 2.0126989 , 2.31574759, 2.04672223, 1.73762178,
          1.97249596, 1.65257838, 1.98435822, 1.74193776, 2.05272917,
          2.41693508, 2.37609913, 2.24686996, 1.61790402, 2.37607665,
          1.82677368, 2.29512653, 1.52756173, 1.79404414, 2.08314   ,
          1.5209276 , 2.48034115, 1.7821867 , 1.60377021, 1.82345627,
          2.23840132, 1.50174227, 1.85127905, 1.92372432, 1.95433662,
          1.8146093 , 1.96513404, 2.0227501 , 1.97564664, 2.09893966,
          1.95392005, 2.2089975 , 2.26074219, 2.24742979, 1.75936195,
          1.69145596, 2.46801952, 2.40938521, 1.98369075, 2.37509171,
          1.53026033, 2.24305926, 2.33309562, 1.49913881, 1.48743005,
          1.54075518, 2.33130062, 2.37463005, 2.19387461, 2.20970603,
          2.04719149, 2.04105128, 1.48410805, 2.34714158, 1.95061571,
          1.89473245, 2.26596278, 2.22430597, 2.29984983, 1.7894671 ,
          1.85995514, 2.31688729, 1.53417344, 2.39777465, 2.12853793,
          1.47736812, 1.90180229, 1.73086567, 2.03772387, 1.67243511,
          2.10115733, 2.26944612, 2.37404859, 2.22042332, 2.4948031 ,
          1.80153666, 1.72069013, 1.44829544, 1.77678155, 2.24291992,
          1.73557503, 1.79249737, 2.52580388, 2.46810975, 2.34211232,
          2.22144569, 2.31945172, 1.72814133, 2.17318812, 2.43560932,
          1.9662451 , 2.14319385, 1.83150682, 2.48805089, 2.28374904,
          1.63645718, 1.57901687, 1.61041853, 2.40884706, 2.37339631,
          1.90728817, 2.09065413, 2.36836694, 2.05400262, 1.87764304,
          1.83547711, 2.45064964, 1.46324772, 2.2429919 , 1.75954149,
          1.97326923, 2.08379661, 2.04616096, 2.3161197 , 1.81470671,
          1.8188581 , 2.11349671, 2.05477704, 2.39622142, 1.61281075,
          1.56914576, 1.96947616, 1.56645219, 2.08002605, 2.2185357 ,
          1.54079134, 2.42384819, 2.41198434, 2.0570266 , 1.55142224,
          1.83396657, 1.92648666, 1.9143498 , 1.9372014 , 1.92794208,
          2.42698754, 2.29871021, 2.03266023, 2.42413239, 2.28286632])
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# 绘制数据集(X, Y)
plt.scatter(X, Y)
plt.show()
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3. 划分数据集

# 划分训练集和测试集
X_train, Y_train = X[:160], Y[:160]
X_test, Y_test = X[160:], Y[160:]
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4. 构造神经网络模型

# 定义一个model
# Keras有两种类型的模型，序列模型和函数式模型
# 比较常用的是Sequential，它是单输入单输出的
model = Sequential()

# 通过add()方法一层层添加模型
# Dense是全连接层，第一层需要定义输入
model.add(Dense(output_dim=1,input_dim=1))

# 定义完成模型就要训练了，不过训练之前我们需要指定一些训练参数
# 通过compile()方法选择损失函数和优化器
# 这里我们用均方差作为损失函数，随机梯度下降作为优化方法
model.compile(loss='mse', optimizer='sgd')
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5. 训练模型

# 开始训练
print('Training ----------')

# Keras有很多开始训练的函数，这里用train_on_batch（）
for step in range(301):
    cost = model.train_on_batch(X_train,Y_train)
    if step%100 == 0:
        print('train cost: ', cost)
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Training ----------
WARNING:tensorflow:From /home/nlp/anaconda3/lib/python3.7/site-packages/keras/backend/tensorflow_backend.py:422: The name tf.global_variables is deprecated. Please use tf.compat.v1.global_variables instead.

train cost:  4.0225005
train cost:  0.073238626
train cost:  0.00386274
train cost:  0.002643449
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6. 测试模型

# 测试训练好的模型
print('Testing ----------')
cost = model.evaluate(X_test, Y_test, batch_size = 40)
print('test cost: ',cost)
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Testing ----------
40/40 [==============================] - 0s 508us/step
test cost:  0.0031367032788693905
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7. 分析模型

# 查看训练出的网络参数
# 由于我们网络只有一层，且每次训练的输入只有一个，输出只有一个
# 因此第一层训练出Y=WX+B这个模型，其中W,b为训练出的参数
W, b = model.layers[0].get_weights()
print('Weights = ', W, '\nbiases = ', b)
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Weights =  [[0.4922711]] 
biases =  [1.9995022]
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# 画出预测图
Y_pred = model.predict(X_test)
plt.scatter(X_test, Y_test)
plt.plot(X_test, Y_pred)
plt.show()
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#使用r2 score评估准确度
pred_acc = r2_score(Y_test, Y_pred)
print('pred_acc',pred_acc)
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pred_acc 0.9591211310535933
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#保存模型
model.save('keras_linear.h5')
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