Explain and quantify bias-variance tradeoff

Q: Explain and quantify bias-variance tradeoff

This question evaluates understanding of the bias–variance tradeoff, the expected test-error decomposition into irreducible noise, bias^2, and variance, and practical model-tuning effects such as regularization and training-set size for models like ridge regression or decision trees.

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Bias–Variance Tradeoff: Intuition, Derivation, and Practical Tuning

Task

Explain the bias–variance tradeoff at two levels and connect it to model tuning.

Requirements

Intuition: In two simple sentences for a non-technical stakeholder, explain the bias–variance tradeoff.
Rigor: Derive the expected test MSE decomposition at a fixed x, showing E[(y − ŷ)^2] = irreducible_noise + bias^2 + variance, and interpret each term.
Using either ridge regression or decision trees: a) Qualitatively explain how training set size and regularization (e.g., lambda or max_depth) affect bias and variance. b) Provide a concrete numeric example where increasing regularization raises bias, lowers variance, and reduces test error—show the numbers. c) Name two diagnostics you would plot to choose the operating point (e.g., learning curves, validation curves) and one method to cut variance with minimal bias increase (e.g., bagging).

Explain and quantify bias-variance tradeoff

Bias–Variance Tradeoff: Intuition, Derivation, and Practical Tuning

Task

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Explain and quantify bias-variance tradeoff

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Bias–Variance Tradeoff: Intuition, Derivation, and Practical Tuning

Task

Requirements

Solution

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