Please can you explain the loss function and how its derived in a little more detail

[GSC-30212]

Hi @xiphmont , @pyu1538 , @jmvalin ,

Please can you explain the mathematics present in the below functions (Except binary_crossentropy) and how these were derived (logic behind using these):-

def my_crossentropy(y_true, y_pred):
return K.mean(2*K.abs(y_true-0.5) * K.binary_crossentropy(y_pred, y_true), axis=-1)

def mymask(y_true):
return K.minimum(y_true+1., 1.)

def msse(y_true, y_pred):
return K.mean(mymask(y_true) * K.square(K.sqrt(y_pred) - K.sqrt(y_true)), axis=-1)

def mycost(y_true, y_pred):
return K.mean(mymask(y_true) * (10K.square(K.square(K.sqrt(y_pred) - K.sqrt(y_true))) + K.square(K.sqrt(y_pred) - K.sqrt(y_true)) + 0.01K.binary_crossentropy(y_pred, y_true)), axis=-1)

def my_accuracy(y_true, y_pred):
return K.mean(2*K.abs(y_true-0.5) * K.equal(y_true, K.round(y_pred)), axis=-1)

To be more specific:-
1] Why '2*K.abs(y_true-0.5)' added to binary_crossentropy?
2] What is the purpose of masking?
3] How mycost is derived?
4] Why we are using msse as a performance metric?

[Thanusan19]

For the question : 2] What is the purpose of masking?
The masking set the loss function to "0" when y_true = 0.5. Thus when we are not sure about the ground true, the weights of the models are not tuned.