Explain logistic regression. Why is it still a go-to model in industry despite being decades old?
formulate your answer, then —
You mentioned cross-entropy as the loss. Why not use MSE for classification — it's simpler and works for regression, so what's wrong with it here?
formulate your answer, then —
tldr
Logistic regression applies sigmoid to a linear model, producing calibrated probabilities with an interpretable linear decision boundary. It survives in industry because it's fast, explainable, and often good enough. Cross-entropy beats MSE as a loss because sigmoid saturation kills MSE gradients exactly when the model is most wrong, while cross-entropy gradients scale cleanly with prediction error.
follow-up
- How does L1 vs L2 regularization differ in effect on logistic regression coefficients, and when would you choose one over the other?
- What's the relationship between logistic regression and maximum entropy models?
- How would you extend logistic regression to a multi-class problem, and what changes in the loss function?