Experimental binary cross entropy with ranking loss function

binary_crossentropy_with_ranking.py

def binary_crossentropy_with_ranking(y_true, y_pred):
    """ Trying to combine ranking loss with numeric precision"""
    # first get the log loss like normal
    logloss = K.mean(K.binary_crossentropy(y_pred, y_true), axis=-1)
    
    # next, build a rank loss
    
    # clip the probabilities to keep stability
    y_pred_clipped = K.clip(y_pred, K.epsilon(), 1-K.epsilon())

    # translate into the raw scores before the logit
    y_pred_score = K.log(y_pred_clipped / (1 - y_pred_clipped))

    # determine what the maximum score for a zero outcome is
    y_pred_score_zerooutcome_max = K.max(y_pred_score * (y_true <1))

    # determine how much each score is above or below it
    rankloss = y_pred_score - y_pred_score_zerooutcome_max

    # only keep losses for positive outcomes
    rankloss = rankloss * y_true

    # only keep losses where the score is below the max
    rankloss = K.square(K.clip(rankloss, -100, 0))

    # average the loss for just the positive outcomes
    rankloss = K.sum(rankloss, axis=-1) / (K.sum(y_true > 0) + 1)

    # return (rankloss + 1) * logloss - an alternative to try
    return rankloss + logloss

K is Keras, It's a Neural Network framework which gives very fast prototyping, and sits on top of Keras or Theano.

K is the backend (could be tensorflow, theano, or cntk at the time of writing).
It is common when writing functions for keras to import the backend as K:
from keras import backend as K

import keras.backend as K

^ That's where K comes from.

This is based on which paper? I am going to cite the original paper.

I can't remember for sure, but I don't think I based this on a paper.

FYI: Found a link to this from https://www.reddit.com/r/MachineLearning/comments/3zksod/has_anyone_successfully_implemented_auroc_as_a/