I knew the mechanics but fumbled the geometry part.
Start by defining the objective function modifications for L1 and L2, then explain the geometric intuitions (diamond vs. circle constraints) and their effects on parameters (sparsity vs. shrinkage). Conclude with practical implications for model selection and when to use each.
Pro tip: Mention that L1 regularization can be solved efficiently using coordinate descent or LARS, while L2 has closed-form solutions, and relate this to Upstart's use of regularized models for credit risk to show practical awareness.
Explain that L1 adds the sum of absolute weights (λ * Σ|w_i|) and L2 adds the sum of squared weights (λ * Σw_i^2) to the loss function.
Describe the constraint regions: L1 corresponds to a diamond (or polytope) shape, L2 to a circle (or hypersphere). The corners of the diamond lead to sparse solutions.
L1 tends to produce sparse models by driving some weights exactly to zero, while L2 shrinks weights towards zero but rarely makes them exactly zero.
Discuss when to use each: L1 for feature selection and interpretability, L2 for handling multicollinearity and improving generalization. Mention Elastic Net as a combination.
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This felt like a follow-up but was basically its own question.
Start by clearly mapping Ridge to L2 and Lasso to L1 regularization, explaining the penalty terms. Then discuss how L1 induces sparsity and performs feature selection, while L2 shrinks coefficients but keeps all features. Finally, relate this to practical trade-offs in model interpretability and performance.
Pro tip: Mention that Lasso can struggle with correlated features by arbitrarily selecting one, while Ridge distributes weight among them—this shows deeper understanding of real-world data challenges.
State that Ridge regression uses L2 regularization (sum of squared coefficients) and Lasso uses L1 regularization (sum of absolute coefficients).
Describe how L2 shrinks coefficients smoothly toward zero but never exactly zero, while L1 can shrink some coefficients exactly to zero, leading to sparse solutions.
Clarify that Lasso performs automatic feature selection by eliminating irrelevant features, whereas Ridge retains all features but reduces their impact.
Highlight scenarios where each is preferred: Lasso for interpretable models with few important features, Ridge for multicollinearity or when all features contribute.
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The correlated features part tripped me up.
Start by defining the core difference between L1 and L2 regularization, then explain when each is preferred based on feature sparsity and correlation. Discuss elastic net as a compromise that handles correlated features better, and finally address how correlation affects feature selection stability and model interpretation.
Pro tip: Mention that in practice, you often use cross-validation to tune the regularization strength and that elastic net's mix parameter can be optimized, but also note that domain knowledge should guide the choice—especially in regulated industries like fintech where interpretability matters.
Explain that Lasso (L1) performs feature selection by shrinking some coefficients to zero, which is useful when you have many irrelevant features. Ridge (L2) shrinks coefficients but keeps all features, which is better when all features contribute and you want to avoid overfitting.
Describe elastic net as a combination of L1 and L2 penalties, controlled by a mixing parameter. It's particularly useful when there are multiple correlated features because it can select groups of correlated features rather than arbitrarily picking one.
Explain that with correlated features, Lasso tends to randomly select one feature from a group and ignore the others, leading to unstable selection. Ridge distributes the coefficient among correlated features, which can be more stable but doesn't reduce dimensionality.
Summarize when to choose each: Lasso for sparse solutions and feature selection, Ridge for multicollinearity and when all features are relevant, Elastic Net when you have correlated features and want some sparsity. Mention that cross-validation is key for tuning.
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Short answer: regularization penalizes coefficient size, so if features are on different scales the penalty hits them unequally.
Explain that regularization adds a penalty on coefficient magnitudes, and feature scaling ensures that penalty is applied fairly across features. Then discuss the consequences of not scaling, such as biased regularization and poor model performance, and mention practical implications for model selection and interpretation.
Pro tip: Mention that scaling should be done after train-test split to avoid data leakage, and that some regularizers like L1 can be used for feature selection but only if features are on the same scale.
Briefly explain that regularization adds a penalty term to the loss function to prevent overfitting, typically L1 (Lasso) or L2 (Ridge).
Describe how features with larger scales can dominate the penalty term, leading to unfair shrinkage of coefficients.
Highlight that without scaling, regularization may shrink important coefficients too much or too little, resulting in suboptimal models.
Explain that scaling ensures all features contribute equally to the penalty, improving model performance and making coefficients comparable.
Suggest standardizing or normalizing features before regularization, and note that scaling should be fit on training data only.
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Wasn't expecting this one to come up and I think it showed.
Start by clearly defining likelihood as the probability of observed data given model parameters, then explain how maximizing likelihood is equivalent to minimizing negative log-likelihood. Connect this to common loss functions like cross-entropy and mean squared error, and discuss practical implications in model training.
Pro tip: Emphasize that negative log-likelihood is a proper scoring rule and that minimizing it is equivalent to minimizing KL divergence between the model and true distribution, which shows deep understanding. Also, mention that the choice of likelihood depends on the data distribution and affects model calibration.
Explain that likelihood is the probability of the observed data as a function of the model parameters. It measures how well the parameters explain the data.
Describe MLE as the method to find parameters that maximize the likelihood. Mention that it's a fundamental approach in statistical modeling.
Show that maximizing likelihood is equivalent to minimizing negative log-likelihood (NLL) because log is monotonic. NLL is often used as a loss function for optimization.
Give examples: for binary classification, NLL leads to binary cross-entropy; for multiclass, categorical cross-entropy; for regression with Gaussian noise, NLL leads to mean squared error.
Mention that NLL provides a probabilistic framework, handles uncertainty, and connects to information theory (e.g., cross-entropy, KL divergence). Also note that it's used in deep learning for training.
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