1. 比较一般的自定义函数：

需要注意的是，不能像sklearn那样直接定义，因为这里的y_true和y_pred是张量，不是numpy数组。示例如下：

from keras import backend

def rmse(y_true, y_pred):
    return backend.sqrt(backend.mean(backend.square(y_pred - y_true), axis=-1))

用的时候直接：

model.compile(optimizer='adam', loss='binary_crossentropy', metrics=[rmse])

2. 比较复杂的如AUC函数：

AUC的计算需要整体数据，如果直接在batch里算，误差就比较大，不能合理反映整体情况。这里采用回调函数写法，每个epoch计算一次：

from sklearn.metrics import roc_auc_score

class roc_callback(keras.callbacks.Callback):
    def __init__(self,training_data, validation_data):
        
        self.x = training_data[0]
        self.y = training_data[1]
        self.x_val = validation_data[0]
        self.y_val = validation_data[1]
        
    
    def on_train_begin(self, logs={}):
        return
 
    def on_train_end(self, logs={}):
        return
 
    def on_epoch_begin(self, epoch, logs={}):
        return
 
    def on_epoch_end(self, epoch, logs={}):        
        y_pred = self.model.predict(self.x)
        roc = roc_auc_score(self.y, y_pred)      
        
        y_pred_val = self.model.predict(self.x_val)
        roc_val = roc_auc_score(self.y_val, y_pred_val)      
        
        print('\rroc-auc: %s - roc-auc_val: %s' % (str(round(roc,4)),str(round(roc_val,4))),end=100*' '+'\n')
        return
 
    def on_batch_begin(self, batch, logs={}):
        return
 
    def on_batch_end(self, batch, logs={}):
        return   

调用回调函数示例：

model.fit(X_train, y_train, epochs=10, batch_size=4, 
          callbacks = [roc_callback(training_data=[X_train, y_train], validation_data=[X_test, y_test])] )

整体示例：

from tensorflow import keras
from sklearn import datasets
from sklearn import model_selection
from sklearn.metrics import roc_auc_score

def rmse(y_true, y_pred):
    return keras.backend.sqrt(keras.backend.mean(keras.backend.square(y_pred - y_true), axis=-1))

class roc_callback(keras.callbacks.Callback):
    def __init__(self,training_data, validation_data):
        
        self.x = training_data[0]
        self.y = training_data[1]
        self.x_val = validation_data[0]
        self.y_val = validation_data[1]
        
    
    def on_train_begin(self, logs={}):
        return
 
    def on_train_end(self, logs={}):
        return
 
    def on_epoch_begin(self, epoch, logs={}):
        return
 
    def on_epoch_end(self, epoch, logs={}):        
        y_pred = self.model.predict(self.x)
        roc = roc_auc_score(self.y, y_pred)      
        
        y_pred_val = self.model.predict(self.x_val)
        roc_val = roc_auc_score(self.y_val, y_pred_val)      
        
        print('\rroc-auc: %s - roc-auc_val: %s' % (str(round(roc,4)),str(round(roc_val,4))),end=100*' '+'\n')
        return
 
    def on_batch_begin(self, batch, logs={}):
        return
 
    def on_batch_end(self, batch, logs={}):
        return   
    
    
X, y = datasets.make_classification(n_samples=100, n_features=4, n_classes=2, random_state=2018)
X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=0.2, random_state=2018)
print("TrainSet", X_train.shape, "TestSet", X_test.shape)

model = keras.models.Sequential()
model.add(keras.layers.Dense(20, input_shape=(4,), activation='relu'))
model.add(keras.layers.Dense(1, activation='sigmoid'))
model.compile(optimizer='adam', loss='binary_crossentropy', metrics=[rmse])

model.fit(X_train, y_train, epochs=10, batch_size=4, 
          callbacks = [roc_callback(training_data=[X_train, y_train], validation_data=[X_test, y_test])] )

运行结果：

TrainSet (80, 4) TestSet (20, 4)
Epoch 1/10
roc-auc: 0.1604 - roc-auc_val: 0.2738                                                                                                    
80/80 [==============================] - 0s - loss: 0.8132 - rmse: 0.5298     
Epoch 2/10
roc-auc: 0.4874 - roc-auc_val: 0.619                                                                                                    
80/80 [==============================] - 0s - loss: 0.7432 - rmse: 0.5049     
Epoch 3/10
roc-auc: 0.7715 - roc-auc_val: 0.9643                                                                                                    
80/80 [==============================] - 0s - loss: 0.6821 - rmse: 0.4807     
Epoch 4/10
roc-auc: 0.9602 - roc-auc_val: 1.0                                                                                                    
80/80 [==============================] - 0s - loss: 0.6268 - rmse: 0.4560     
Epoch 5/10
roc-auc: 0.9842 - roc-auc_val: 1.0                                                                                                    
80/80 [==============================] - 0s - loss: 0.5747 - rmse: 0.4301     
Epoch 6/10
roc-auc: 0.9956 - roc-auc_val: 1.0                                                                                                    
80/80 [==============================] - 0s - loss: 0.5230 - rmse: 0.4025     
Epoch 7/10
roc-auc: 0.9975 - roc-auc_val: 1.0                                                                                                    
80/80 [==============================] - 0s - loss: 0.4743 - rmse: 0.3739     
Epoch 8/10
roc-auc: 0.9987 - roc-auc_val: 1.0                                                                                                    
80/80 [==============================] - 0s - loss: 0.4289 - rmse: 0.3454     
Epoch 9/10
roc-auc: 0.9987 - roc-auc_val: 1.0...] - ETA: 0s - loss: 0.4019 - rmse: 0.3301                                                                                                    
80/80 [==============================] - 0s - loss: 0.3830 - rmse: 0.3149     
Epoch 10/10
roc-auc: 0.9987 - roc-auc_val: 1.0                                                                                                    
80/80 [==============================] - 0s - loss: 0.3424 - rmse: 0.2865