Knew binary cross-entropy was the answer but fumbled explaining the 'why' at first.
Start by directly answering that logistic regression typically uses the log loss (binary cross-entropy). Then explain the reasoning: it's derived from maximum likelihood estimation under a Bernoulli distribution, and it provides a convex loss surface that is efficient to optimize. Finally, briefly contrast it with alternatives like MSE to highlight why log loss is preferred.
Pro tip: Mention that log loss heavily penalizes confident misclassifications, which is crucial for probabilistic models, and note that using MSE would lead to a non-convex loss for logistic regression, making optimization harder.
Clearly identify that logistic regression uses the log loss (binary cross-entropy) for binary classification, and categorical cross-entropy for multiclass.
Describe how the loss is derived from maximum likelihood estimation, assuming the target follows a Bernoulli distribution (or categorical for multiclass).
Emphasize that log loss is convex for logistic regression, ensuring that gradient-based methods converge to the global minimum.
Briefly compare with mean squared error (MSE), noting that MSE is non-convex for logistic regression and less suitable for probabilistic outputs.
Mention that log loss penalizes confident wrong predictions heavily, which aligns with the goal of well-calibrated probabilities.
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