玩具数据集

Question

我创建了以下玩具数据集：

我试图用keras中的神经网络来预测这个类：

model = Sequential()
model.add(Dense(units=2, activation='sigmoid', input_shape= (nr_feats,)))
model.add(Dense(units=nr_classes, activation='softmax'))

model.compile(loss='categorical_crossentropy',
              optimizer='adam',
              metrics=['accuracy'])

将nr_feats和nr_classes设置为2。 神经网络只能以50％的准确度预测返回全部1或全部2。使用Logistic回归可以获得100％的准确度。

我找不到这里出了什么问题。

如果您想快速尝试，我已将notebook上传到github。

编辑1

我大幅增加了纪元的数量，精确度最终从第72纪元的0.5开始提高，并在98纪元收敛到1.0。 对于这样一个简单的数据集，这似乎仍然非常慢。

我知道使用Sigmoid激活的单个输出神经元更好，但我更想知道为什么它不适用于两个输出神经元和softmax激活。

我按如下方式预处理我的数据帧：

from sklearn.preprocessing import LabelEncoder

x_train = df_train.iloc[:,0:-1].values
y_train = df_train.iloc[:, -1]

nr_feats = x_train.shape[1]
nr_classes = y_train.nunique()

label_enc = LabelEncoder()
label_enc.fit(y_train)

y_train = keras.utils.to_categorical(label_enc.transform(y_train), nr_classes)

培训和评估：

model.fit(x_train, y_train, epochs=500, batch_size=32, verbose=True)
accuracy_score(model.predict_classes(x_train),  df_train.iloc[:, -1].values)

编辑2

在将输出层更改为具有S形激活的单个神经元并使用binary_crossentropy损失作为模式建议后，精确度仍然保持在0.5为200个时期并且收敛到1.0 100个时期之后。

Answer 1

问题是您的标签是1和2而不是0和1. Keras在看到2时不会引发错误，但它无法预测{ {1}}。

从所有y值中减去1。作为旁注，在深度学习中常见的是使用1 2 neuron进行二进制分类（0或1），使用sigmoid进行2 softmax。最后，使用binary_crossentropy来解决二进制分类问题。

Answer 2

注意：如果您想要真正的原因，请阅读我的答案末尾的“更新”部分。在这种情况下，我提到的其他两个原因仅在学习率设置为较低值（小于1e-3）时才有效。

我把一些代码放在一起。它与你的非常相似，但我只是稍微清理一下，让自己更简单。如您所见，我使用一个密集图层，其中一个单元的最后一层具有sigmoid激活函数，只需将优化程序从adam更改为rmsprop（这一点并不重要，如果您愿意，可以使用adam：

import numpy as np
import random

# generate random data with two features
n_samples = 200
n_feats = 2

cls0 = np.random.uniform(low=0.2, high=0.4, size=(n_samples,n_feats))
cls1 = np.random.uniform(low=0.5, high=0.7, size=(n_samples,n_feats))
x_train = np.concatenate((cls0, cls1))
y_train = np.concatenate((np.zeros((n_samples,)), np.ones((n_samples,))))

# shuffle data because all negatives (i.e. class "0") are first
# and then all positives (i.e. class "1")
indices = np.arange(x_train.shape[0])
np.random.shuffle(indices)
x_train = x_train[indices]
y_train = y_train[indices]

from keras.models import Sequential
from keras.layers import Dense


model = Sequential()
model.add(Dense(2, activation='sigmoid', input_shape=(n_feats,)))
model.add(Dense(1, activation='sigmoid'))

model.compile(loss='binary_crossentropy',
              optimizer='rmsprop',
              metrics=['accuracy'])

model.summary()

model.fit(x_train, y_train, epochs=5, batch_size=32, verbose=True)

这是输出：

Layer (type)                 Output Shape              Param #   
=================================================================
dense_25 (Dense)             (None, 2)                 6         
_________________________________________________________________
dense_26 (Dense)             (None, 1)                 3         
=================================================================
Total params: 9
Trainable params: 9
Non-trainable params: 0
_________________________________________________________________
Epoch 1/5
400/400 [==============================] - 0s 966us/step - loss: 0.7013 - acc: 0.5000
Epoch 2/5
400/400 [==============================] - 0s 143us/step - loss: 0.6998 - acc: 0.5000
Epoch 3/5
400/400 [==============================] - 0s 137us/step - loss: 0.6986 - acc: 0.5000
Epoch 4/5
400/400 [==============================] - 0s 149us/step - loss: 0.6975 - acc: 0.5000
Epoch 5/5
400/400 [==============================] - 0s 132us/step - loss: 0.6966 - acc: 0.5000

正如您所看到的，准确度从未从50％增加。如果你将纪元数增加到50，那该怎么办？

Layer (type)                 Output Shape              Param #   
=================================================================
dense_35 (Dense)             (None, 2)                 6         
_________________________________________________________________
dense_36 (Dense)             (None, 1)                 3         
=================================================================
Total params: 9
Trainable params: 9
Non-trainable params: 0
_________________________________________________________________
Epoch 1/50
400/400 [==============================] - 0s 1ms/step - loss: 0.6925 - acc: 0.5000
Epoch 2/50
400/400 [==============================] - 0s 136us/step - loss: 0.6902 - acc: 0.5000
Epoch 3/50
400/400 [==============================] - 0s 133us/step - loss: 0.6884 - acc: 0.5000
Epoch 4/50
400/400 [==============================] - 0s 160us/step - loss: 0.6866 - acc: 0.5000
Epoch 5/50
400/400 [==============================] - 0s 140us/step - loss: 0.6848 - acc: 0.5000
Epoch 6/50
400/400 [==============================] - 0s 168us/step - loss: 0.6832 - acc: 0.5000
Epoch 7/50
400/400 [==============================] - 0s 154us/step - loss: 0.6817 - acc: 0.5000
Epoch 8/50
400/400 [==============================] - 0s 146us/step - loss: 0.6802 - acc: 0.5000
Epoch 9/50
400/400 [==============================] - 0s 161us/step - loss: 0.6789 - acc: 0.5000
Epoch 10/50
400/400 [==============================] - 0s 140us/step - loss: 0.6778 - acc: 0.5000
Epoch 11/50
400/400 [==============================] - 0s 177us/step - loss: 0.6766 - acc: 0.5000
Epoch 12/50
400/400 [==============================] - 0s 180us/step - loss: 0.6755 - acc: 0.5000
Epoch 13/50
400/400 [==============================] - 0s 165us/step - loss: 0.6746 - acc: 0.5000
Epoch 14/50
400/400 [==============================] - 0s 128us/step - loss: 0.6736 - acc: 0.5000
Epoch 15/50
400/400 [==============================] - 0s 125us/step - loss: 0.6728 - acc: 0.5000
Epoch 16/50
400/400 [==============================] - 0s 165us/step - loss: 0.6718 - acc: 0.5000
Epoch 17/50
400/400 [==============================] - 0s 161us/step - loss: 0.6710 - acc: 0.5000
Epoch 18/50
400/400 [==============================] - 0s 170us/step - loss: 0.6702 - acc: 0.5000
Epoch 19/50
400/400 [==============================] - 0s 122us/step - loss: 0.6694 - acc: 0.5000
Epoch 20/50
400/400 [==============================] - 0s 110us/step - loss: 0.6686 - acc: 0.5000
Epoch 21/50
400/400 [==============================] - 0s 142us/step - loss: 0.6676 - acc: 0.5000
Epoch 22/50
400/400 [==============================] - 0s 142us/step - loss: 0.6667 - acc: 0.5000
Epoch 23/50
400/400 [==============================] - 0s 149us/step - loss: 0.6659 - acc: 0.5000
Epoch 24/50
400/400 [==============================] - 0s 125us/step - loss: 0.6651 - acc: 0.5000
Epoch 25/50
400/400 [==============================] - 0s 134us/step - loss: 0.6643 - acc: 0.5000
Epoch 26/50
400/400 [==============================] - 0s 143us/step - loss: 0.6634 - acc: 0.5000
Epoch 27/50
400/400 [==============================] - 0s 137us/step - loss: 0.6625 - acc: 0.5000
Epoch 28/50
400/400 [==============================] - 0s 131us/step - loss: 0.6616 - acc: 0.5025
Epoch 29/50
400/400 [==============================] - 0s 119us/step - loss: 0.6608 - acc: 0.5100
Epoch 30/50
400/400 [==============================] - 0s 143us/step - loss: 0.6601 - acc: 0.5025
Epoch 31/50
400/400 [==============================] - 0s 148us/step - loss: 0.6593 - acc: 0.5350
Epoch 32/50
400/400 [==============================] - 0s 161us/step - loss: 0.6584 - acc: 0.5325
Epoch 33/50
400/400 [==============================] - 0s 152us/step - loss: 0.6576 - acc: 0.5700
Epoch 34/50
400/400 [==============================] - 0s 128us/step - loss: 0.6568 - acc: 0.5850
Epoch 35/50
400/400 [==============================] - 0s 155us/step - loss: 0.6560 - acc: 0.5975
Epoch 36/50
400/400 [==============================] - 0s 136us/step - loss: 0.6552 - acc: 0.6425
Epoch 37/50
400/400 [==============================] - 0s 140us/step - loss: 0.6544 - acc: 0.6150
Epoch 38/50
400/400 [==============================] - 0s 120us/step - loss: 0.6538 - acc: 0.6375
Epoch 39/50
400/400 [==============================] - 0s 140us/step - loss: 0.6531 - acc: 0.6725
Epoch 40/50
400/400 [==============================] - 0s 135us/step - loss: 0.6523 - acc: 0.6750
Epoch 41/50
400/400 [==============================] - 0s 136us/step - loss: 0.6515 - acc: 0.7300
Epoch 42/50
400/400 [==============================] - 0s 126us/step - loss: 0.6505 - acc: 0.7450
Epoch 43/50
400/400 [==============================] - 0s 141us/step - loss: 0.6496 - acc: 0.7425
Epoch 44/50
400/400 [==============================] - 0s 162us/step - loss: 0.6489 - acc: 0.7675
Epoch 45/50
400/400 [==============================] - 0s 161us/step - loss: 0.6480 - acc: 0.7775
Epoch 46/50
400/400 [==============================] - 0s 126us/step - loss: 0.6473 - acc: 0.7575
Epoch 47/50
400/400 [==============================] - 0s 124us/step - loss: 0.6464 - acc: 0.7625
Epoch 48/50
400/400 [==============================] - 0s 130us/step - loss: 0.6455 - acc: 0.7950
Epoch 49/50
400/400 [==============================] - 0s 191us/step - loss: 0.6445 - acc: 0.8100
Epoch 50/50
400/400 [==============================] - 0s 163us/step - loss: 0.6435 - acc: 0.8625

准确性开始增加（请注意，如果您多次训练此模型，每次可能需要不同数量的时期才能达到可接受的准确度，从10到100个时期的任何时间）。

此外，在我的实验中，我注意到增加第一个密集层中的单位数量，例如增加5或10个单位，可以使模型更快地训练（即快速收敛）。

为什么需要这么多时代？

我认为这是因为这两个原因（合并）：

1）尽管这两个类很容易分离，但您的数据由随机样本组成，并且

2）数据点的数量与神经网络的大小相比（即可训练参数的数量，在上面的示例代码中为9）相对较大。

因此，模型学习权重需要更多的时代。就好像模型非常有限，需要越来越多的经验来正确找到合适的权重。作为证据，只是尝试增加第一个密集层中的单位数。每次尝试训练此模型时，几乎可以保证精度达到+ 90％且不到10个时期。在这里你增加了容量，因此模型收敛（即列车）的速度要快得多（应该注意的是，如果容量太高或者你为太多时期训练模型，它会开始过度拟合。你应该有一个验证方案来监控这个问题）。

旁注：

不要将high参数设置为小于low中numpy.random.uniform参数的数字，因为根据documentation，结果将是“正式未定义” “在这种情况下。

更新

这里的一个更重要的事情（也许是这个场景中最重要的事情）是优化器的学习率。如果学习率太低，则模型收敛缓慢。尝试提高学习率，您可以看到在不到5个时期内达到100％的准确度：

from keras import optimizers

model.compile(loss='binary_crossentropy',
              optimizer=optimizers.RMSprop(lr=1e-1),
              metrics=['accuracy'])

# or you may use adam
model.compile(loss='binary_crossentropy',
              optimizer=optimizers.Adam(lr=1e-1),
              metrics=['accuracy'])