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This was more involved than I expected for a phone screen.
Start by writing the core functions (sigmoid, loss, gradients) with clear vectorized implementations, then build the training loop with configurable hyperparameters, and finally add predict methods. Optionally implement L2 regularization and explain its effect on the loss and gradients.
Pro tip: Emphasize vectorization for efficiency and numerical stability (e.g., clipping sigmoid inputs) to show production-level awareness. Also, mention that L2 regularization is equivalent to adding a Gaussian prior on weights, which helps prevent overfitting.
Write the sigmoid function and binary cross-entropy loss, ensuring numerical stability by avoiding overflow in exponentials.
Derive and implement the gradients of the loss with respect to weights and bias, using vectorized operations for efficiency.
Create a training loop that iteratively updates weights and bias using gradient descent, with configurable learning rate and number of iterations.
Implement predict_proba to return probabilities and predict to return binary class labels based on a threshold (e.g., 0.5).
Add L2 regularization to the loss and gradients, and explain that it penalizes large weights to reduce overfitting.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.