Your cost function in this case will not penalize when either 1 or 7 is predicted, but will penalize when other digits are incorrectly predicted.ConclusionThis all means, that if you doubt some data, you don’t have to drop them, but instead estimate the degree of uncertainty and include that in your algorithm..It is true, that you end up having a custom cost function, but that can be easily addressed by using frameworks like TensorFlow, that compute gradients automatically.You can also use this method to address outliers..We all know that they can affect both regression and classification results rather significantly..Instead, you can assign them lower weight if you believe that there may be a data error.. More details