Tensorflow：结合指标以改善成本函数

Question

I was reading this paper describing the various pros and cons of different metrics for time series forecasting.

I want to combine MAPE (Mean Absolute Percentage Error):

with SMSE (Signed Mean Squared Error):

Where e_t is the difference between the actual value and the forecasting error . So I wanted to know how to implement this in Tensorflow.

The formula should be:

My Try

If we immagine I have already written up the rest of the neural network then:

error = y - prediction
cost = tf.reduce_mean(tf.divide(error, y) * 100) 
       + tf.reduce_mean(tf.divide(error, tf.abs(error)) * tf.square(error)

I am quite unsure about how I have used * instead of tf.multiply. I know they perform different operations, but I can't quite figure out which one should I use here.

Assume that y is a tf.placeholder(tf.float32, [None, #future_predictions]) and that predition is the output of the neural network and should have the same shape as y . Here None is the batch_size .

Answer 1

I think there are a few flaws in your implementation which is otherwise pointing in the right direction.

You forgot the absolute value in the first part. And you did not include the squared error in the second sum. Here is a corrected version.

error = y - prediction
cost = tf.reduce_mean(tf.abs(tf.divide(error, y)) * 100) 
       + tf.reduce_mean(tf.divide(error, tf.abs(error) * tf.square(error))

Using * and tf.multiply is the same. They both do element-wise multiplication between tensors. (For matrix multiplication, you ought to use tf.matmul)