Implement GLM Training and Prediction from an Explicit Family and Link

Explain how you would implement training and prediction for a generalized linear model (GLM) from scratch. Define the model, objective, optimization procedure, and prediction behavior for one explicitly chosen illustrative family and link function. ### Constraints The response distribution, link, input schema, regularization, and numerical tolerances are not specified. Clarify them before claiming a unique executable implementation. Use your chosen GLM as an example rather than implying that the original task required logistic regression, linear regression, or another particular family. ### Clarifying Questions - What is the target's domain, and which distribution and link are required? - Is an intercept included, and is regularization part of the objective? - Are predictions expected as conditional means, probabilities, or thresholded labels? - What convergence, initialization, and invalid-input behavior should be supported? ```hint Connect the three GLM components Identify the response family, the linear predictor, and the link between that predictor and the conditional mean before deriving an update. ``` ### What a Strong Answer Covers - A correct GLM formulation and explicit family/link assumptions. - A training loss and optimizer consistent with that model, including numerical stability. - Prediction semantics, validation, convergence checks, and boundaries of the chosen implementation. ### Follow-up Questions - How would changing the response family change the loss and allowable predictions? - What behavior would you expect from unregularized logistic regression on separable data?