python - 如何教keras神经网络解决sqrt
问题描述
我正在使用 python 和 keras 学习机器学习。我创建了一个神经网络,从 {1, 4, 9, 16, 25, 36, ..., 100} 范围内的偶数整数中预测平方根。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,它都预测它是 1.0)。
我试过改变层数、每层神经元的数量、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:
1,1
4,2
9,3
16,4
25,5
36,6
49,7
64,8
81,9
100,10
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)
我究竟做错了什么?
解决方案
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明智的预测。
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,该指标accuracy
在回归任务中没有意义。R_squared
因此,通常使用自定义值(AKA 确定系数)作为度量。R_squared
值表示回归模型中的拟合优度。以下是计算的代码R_squared
。
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,您可以使用以下命令编译模型;
model.compile(loss='mean_squared_error', optimizer=opt, metrics=[r_squared])
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