feed-forward neural networks thereby update the weight parameters so as to reduce the disagreement and thus improve model performance we will now look into how various loss functions are derived using maximum likelihood specificallywe will see how commonly used loss functions in deep learning--such as binary cross-entropycross-entropy (for non-binary outcomes)and squared error--can be derived using the maximum likelihood principle binary cross-entropy binary cross-entropyor log lossmeasures the performance of classification models where the outcomes are binary and is represented in the forms of probability value between and the log loss value increases as the model performance tarnishes and produces predictions away from the desired value the ideal model would have binary cross-entropy value of let' consider simple example to understand the concept of binary cross entropy and also get fundamental intuition of maximum likelihood we have some data consisting of {( )( )(xnyn)}where rn and { which is the target of interest also known as the criterion variable let' assume that we have generated model that predicts the probability of given we denote this model by (xth)where th represents the parameters of the model the idea behind maximum likelihood is to find th that maximizes (dthassuming bernoulli distributionand given that each of the examples {( )( )(xnyn)is independentwe have the following expressionn xi xi yi