I listed the usual ones: linearity, independence of errors, homoscedasticity, normality of residuals.
Start by defining linear regression and its goal, then systematically list the key assumptions (linearity, independence, homoscedasticity, normality, no multicollinearity, no autocorrelation). For each assumption, briefly explain why it matters and how to check it, and mention potential consequences if violated.
Pro tip: Emphasize that in practice, some assumptions (like normality) are less critical for prediction but crucial for inference, and that violations can be addressed with transformations or robust methods. This shows you understand the trade-offs between model interpretability and predictive performance.
Briefly state that linear regression models the relationship between a dependent variable and one or more independent variables by fitting a linear equation. Mention that assumptions ensure valid inference and reliable predictions.
Enumerate the main assumptions: linearity, independence of errors, homoscedasticity, normality of errors, no multicollinearity, and no autocorrelation. Group them logically (e.g., about errors vs. about predictors).
For each assumption, describe its impact: e.g., linearity ensures the model form is correct; independence and homoscedasticity affect standard errors; normality enables valid hypothesis tests; no multicollinearity ensures stable coefficient estimates.
Mention diagnostic tools (residual plots, Q-Q plots, VIF, Durbin-Watson) and remedies (transformations, robust standard errors, regularization, removing correlated features).
Highlight that in large-scale ML systems, some assumptions may be relaxed for prediction, but understanding them is key for model debugging, feature engineering, and ensuring business impact.
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This tripped me up more than it should have.
Start by explaining the statistical and optimization properties of squared loss, such as its connection to Gaussian noise and convexity. Then compare with absolute error, highlighting robustness to outliers and differentiability. Finally, discuss practical trade-offs and when each is appropriate, tying back to the role at Amazon.
Pro tip: Mention that squared loss is not always the best choice; showing awareness of when to use alternatives like Huber loss demonstrates deeper understanding and practical maturity.
Briefly define squared loss (L2) and absolute error (L1) to set the stage. Mention their mathematical forms and basic properties.
Explain that squared loss corresponds to maximum likelihood estimation under Gaussian noise, while absolute error corresponds to Laplacian noise. This connects the choice to assumptions about data distribution.
Discuss that squared loss is differentiable everywhere and convex, leading to closed-form solutions in linear regression and efficient gradient-based optimization. Absolute error is non-differentiable at zero, requiring subgradient methods or linear programming.
Highlight that squared loss is sensitive to outliers because errors are squared, while absolute error is more robust. This is a key trade-off: squared loss penalizes large errors more heavily.
Conclude with when to use each: squared loss for well-behaved data with Gaussian noise, absolute error for data with outliers. Mention alternatives like Huber loss that combine benefits.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.