Start by clearly defining precision and recall with their formulas, then explain the trade-off between them. Use a concrete example to illustrate when to prioritize each, and tie it back to business impact and the specific context of the problem.
Pro tip: Mention that the choice depends on the relative cost of false positives versus false negatives, and that in practice you often tune the threshold to balance them. At Amazon, emphasize customer impact: e.g., for fraud detection, false negatives (missed fraud) are costly, so prioritize recall; for product recommendations, false positives (irrelevant recommendations) can annoy customers, so prioritize precision.
Precision = TP / (TP + FP): of all predicted positives, how many are correct. Recall = TP / (TP + FN): of all actual positives, how many did we find.
Increasing precision typically decreases recall and vice versa. This is controlled by the decision threshold of the model.
When false positives are costly or harmful. Examples: spam detection (marking important email as spam), recommending products (bad recommendations reduce trust), or legal document review.
When false negatives are costly or dangerous. Examples: disease detection (missing a disease is fatal), fraud detection (missing fraud loses money), or security threat detection.
Use F1-score or weighted metrics when both matter. Align with business KPIs: e.g., cost of false positive vs false negative, and customer experience.
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Start by defining each regularization method mathematically and geometrically, then compare their effects on model coefficients and sparsity. Finally, discuss practical scenarios for when to use each, emphasizing trade-offs and Amazon-specific considerations like scalability and feature selection.
Pro tip: Mention that L1 regularization can be solved efficiently with coordinate descent or LARS, which is important for large-scale problems at Amazon. Also, note that elastic net (L1+L2) often outperforms pure L1 or L2 in practice when features are correlated.
Briefly state the penalty term for L0 (count of non-zero coefficients), L1 (sum of absolute values), L2 (sum of squares), and L-infinity (maximum absolute value). Mention that L0 is NP-hard and often approximated.
Explain how L1 induces sparsity (diamond shape), L2 shrinks coefficients smoothly (circle), L0 directly controls sparsity but is non-convex, and L-infinity limits the maximum coefficient, leading to uniform shrinkage.
Highlight that L1 performs feature selection, L2 handles multicollinearity and improves stability, L0 is ideal for sparsity but computationally intractable, and L-infinity is rarely used but can be useful for bounded coefficients.
Give scenarios: L1 for high-dimensional sparse data (e.g., text), L2 for general regularization and when all features are relevant, L0 for strict sparsity (e.g., embedded systems), L-infinity for robust regression or when coefficients need bounding.
Tie to Amazon's scale: L1 for feature selection in large-scale recommendation systems, L2 for stable models in demand forecasting, and mention that elastic net combines benefits.
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Rattled off linearity, independence, homoscedasticity, normality of errors.
Start by defining linear regression and its purpose, then systematically list the core assumptions (linearity, independence, homoscedasticity, normality, no multicollinearity). For each assumption, briefly explain what it means and why it matters, and mention how violations can be detected and addressed. Conclude by tying the assumptions to the reliability of coefficient estimates and predictions, especially in a business context like Amazon.
Pro tip: Emphasize that while normality of errors is often cited, it's less critical for large samples due to the Central Limit Theorem; focus more on linearity, independence, and homoscedasticity for unbiased and efficient estimates. Also, mention that in practice, some assumptions can be relaxed with robust methods, showing you understand real-world trade-offs.
Briefly explain that linear regression models the relationship between a dependent variable and one or more independent variables by fitting a linear equation. Its goal is to estimate the coefficients that minimize the sum of squared errors.
Enumerate the key assumptions: linearity, independence of errors, homoscedasticity, normality of errors, and no multicollinearity (for multiple regression). Provide a one-sentence explanation for each.
For each assumption, describe the consequences of violation: e.g., biased coefficients, inefficient estimates, invalid standard errors, or unreliable hypothesis tests. This shows depth of understanding.
Mention common diagnostic tools (residual plots, VIF, Breusch-Pagan test, etc.) and potential fixes (transformations, robust standard errors, regularization, or alternative models). This demonstrates practical knowledge.
Tie the assumptions back to the role: e.g., in product analytics, violating independence might occur with time-series data, or multicollinearity might arise with highly correlated metrics. Highlight the importance of validating assumptions for reliable insights.
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The link function piece is where I actually felt confident.
Start by writing the mathematical formulas for both models clearly, then explain their conceptual differences in terms of output type, loss function, and interpretation. Emphasize how logistic regression uses a sigmoid to model probabilities for classification, while linear regression predicts continuous values directly.
Pro tip: Connect the models to Amazon's business context—e.g., linear regression for predicting sales, logistic regression for customer churn—to show practical understanding and customer obsession.
Clearly state the linear regression formula: y = β0 + β1x1 + ... + βnxn + ε, and logistic regression formula: p = 1 / (1 + e^-(β0 + β1x1 + ... + βnxn)).
Describe that linear regression predicts a continuous outcome directly, while logistic regression models the probability of a binary outcome using the sigmoid (logistic) function.
Mention that linear regression is typically fit by minimizing mean squared error (MSE), whereas logistic regression uses maximum likelihood estimation (MLE) with cross-entropy loss.
Explain that linear regression coefficients represent the change in the expected value of the outcome per unit change in a predictor, while logistic regression coefficients represent the change in log-odds; then give examples of when to use each.
Concisely contrast the two models: linear regression for regression tasks, logistic regression for classification; linear assumes normality and homoscedasticity, logistic assumes a binomial distribution.
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