Keras: Calculating loss as *median* across datapoints instead of mean

Question

The Keras losses page says that if we have a custom loss function, then "the actual optimized objective is the mean of the output array across all datapoints." Is there any way we can optimize the median of the output array across all datapoints (instead of the mean)?

Answer 1

In order to do this, you would need to go down to tensorflow level

import keras
import tensorflow


def pick_median(arg_tensor):
    the_upper_tensor = tensorflow.contrib.distributions.percentile(arg_tensor, 50, interpolation='higher')
    the_lower_tensor = tensorflow.contrib.distributions.percentile(arg_tensor, 50, interpolation='lower')

    final_tensor = (the_upper_tensor + the_lower_tensor) / 2
    # print(the_count.eval(session=keras.backend.get_session()))

    return final_tensor

Here is how you would define, let's say, median_squared_error loss function:

def median_squared_error(arg_y_true,
                         arg_y_pred):
    final_tensor = keras.backend.square(arg_y_pred - arg_y_true)
    final_tensor = pick_median(arg_tensor=final_tensor)
    return final_tensor