python之如何教keras神经网络求解sqrt_编程设计

我正在使用 python 和 keras 学习机器学习。我创建了一个神经网络来预测范围为 {1, 4, 9, 16, 25, 36, ..., 100} 的偶数的平方根。我已经编写了代码来做到这一点，但结果远非如此(无论我向网络提供什么数字，它都会预测它是 1.0)。

我已经尝试更改层数、每层中的神经元数量、激活函数，但没有任何帮助。

这是我到目前为止编写的代码:

from numpy import loadtxt 
from keras.models import Sequential 
from keras.layers import Dense 
from keras import optimizers 
 
# laod dataset 
# dataset = loadtxt('pima-indians-diabetes.csv', delimiter=',') 
dataset = loadtxt('sqrt.csv', delimiter=',') 
 
# split into input (X) and output (y) variables 
X = dataset[:,0:1] * 1.0 
y = dataset[:,1] * 1.0 
 
# define the keras model 
model = Sequential() 
model.add(Dense(6, input_dim=1, activation='relu')) 
model.add(Dense(1, activation='linear')) 
 
# compile the keras model 
opt = optimizers.adam(lr=0.01) 
model.compile(loss='mean_squared_error', optimizer=opt, metrics=['accuracy']) 
 
# fit the keras model on the dataset (CPU) 
model.fit(X, y, epochs=150, batch_size=10, verbose=0) 
 
# evaluate the keras model 
_, accuracy = model.evaluate(X, y, verbose=0) 
print('Accuracy: %.2f' % (accuracy*100)) 
 
# make class predictions with the model 
predicitions = model.predict_classes(X) 
 
# summarize the first 10 cases 
for i in range(10): 
    print('%s => %.2f (expected %.2f)' % (X[i].tolist(), predicitions[i], y[i]))

这是数据集:

当我运行这个网络时，我得到以下结果:

[1.0] => 0.00 (expected 1.00) 
[4.0] => 0.00 (expected 2.00) 
[9.0] => 1.00 (expected 3.00) 
[16.0] => 1.00 (expected 4.00) 
[25.0] => 1.00 (expected 5.00) 
[36.0] => 1.00 (expected 6.00) 
[49.0] => 1.00 (expected 7.00) 
[64.0] => 1.00 (expected 8.00) 
[81.0] => 1.00 (expected 9.00) 
[100.0] => 1.00 (expected 10.00)

我做错了什么？

请您参考如下方法:

这是一个回归问题。所以你应该使用 model.predict() 而不是 model.predict_classes()。

数据集也不够大。但是，您可以使用以下代码获得一些合理的预测。

from numpy import loadtxt 
from keras.models import Sequential 
from keras.layers import Dense 
from keras import optimizers 
 
# laod dataset 
# dataset = loadtxt('pima-indians-diabetes.csv', delimiter=',') 
dataset = loadtxt('sqrt.csv', delimiter=',') 
 
# split into input (X) and output (y) variables 
X = dataset[:,0:1] * 1.0 
y = dataset[:,1] * 1.0 
 
# define the keras model 
model = Sequential() 
model.add(Dense(6, input_dim=1, activation='relu')) 
model.add(Dense(10, activation='relu')) 
model.add(Dense(1)) 
 
# compile the keras model 
opt = optimizers.adam(lr=0.001) 
model.compile(loss='mean_squared_error', optimizer=opt) 
 
# fit the keras model on the dataset (CPU) 
model.fit(X, y, epochs=1500, batch_size=10, verbose=0) 
 
# evaluate the keras model 
_, accuracy = model.evaluate(X, y, verbose=0) 
print('Accuracy: %.2f' % (accuracy*100)) 
 
# make class predictions with the model 
predicitions = model.predict(X) 
 
# summarize the first 10 cases 
for i in range(10): 
    print('%s => %.2f (expected %.2f)' % (X[i].tolist(), predicitions[i], y[i]))

输出:

[1.0] => 1.00 (expected 1.00) 
[4.0] => 2.00 (expected 2.00) 
[9.0] => 3.32 (expected 3.00) 
[16.0] => 3.89 (expected 4.00) 
[25.0] => 4.61 (expected 5.00) 
[36.0] => 5.49 (expected 6.00) 
[49.0] => 6.52 (expected 7.00) 
[64.0] => 7.72 (expected 8.00) 
[81.0] => 9.07 (expected 9.00) 
[100.0] => 10.58 (expected 10.00)

编辑:

正如@desertnaut 在评论中指出的那样，accuracy 指标在回归任务中没有任何意义。因此，通常使用自定义 R_squared 值(又名决定系数)作为度量标准。 R_squared 值表示回归模型的拟合优度。以下是计算 R_squared 的代码。

def r_squared(y_true, y_pred): 
    from keras import backend as K 
    SS_res =  K.sum(K.square(y_true - y_pred))  
    SS_tot = K.sum(K.square(y_true - K.mean(y_true)))  
    return ( 1 - SS_res/(SS_tot + K.epsilon()) )

现在，您可以编译模型；

model.compile(loss='mean_squared_error', optimizer=opt, metrics=[r_squared])