I got the eigenvector/explained variance part fine but then fumbled the normalization distinction harder than I expected.
Start by explaining PCA's core mechanism: it finds orthogonal linear combinations of features that maximize variance, effectively projecting data onto a lower-dimensional subspace. Then address the normalization question by distinguishing between L2 normalization (often used in text/embedding contexts) and standardization (critical for PCA when features have different scales). Finally, clarify the difference between column-wise standardization and row-wise normalization, emphasizing when each is appropriate based on the data type and modeling goal.
Pro tip: Mention that PCA is sensitive to feature scales, so standardization is almost always necessary unless all features are already on the same scale. Also, note that L2 normalization before PCA can be useful for sparse data like text, but it changes the geometry and may not be ideal for all cases.
Describe how PCA computes the covariance matrix, finds eigenvectors (principal components), and projects data onto the top k components that capture the most variance. Emphasize that this reduces dimensionality while preserving as much information as possible.
Clarify that L2 normalization scales each sample to unit norm, which is common in text classification or embedding spaces. Discuss whether it's appropriate: it can help with cosine similarity but may remove magnitude information that PCA could leverage.
Explain that standardizing each column (feature) subtracts mean and divides by standard deviation, making features comparable. Normalizing each row (sample) scales the sample vector to unit norm, often used in text or when sample magnitude is irrelevant.
Highlight scenarios: column-wise standardization is crucial for PCA when features have different units/scales. Row-wise normalization matters when the analysis should be invariant to sample magnitude, e.g., in document clustering or when using cosine similarity.
Conclude that for PCA, standardizing columns is typically recommended. L2 normalization before PCA is context-dependent and should be applied cautiously, often after standardization if at all.
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Start by deriving the gradient for logistic regression using the chain rule, explicitly showing the forward pass (linear combination, sigmoid activation) and backward pass (error term, weight gradients). Then generalize to multi-layer networks by introducing hidden layers, activation functions, and the recursive application of the chain rule through backpropagation, emphasizing the role of the Jacobian and error propagation.
Pro tip: Connect the derivation to practical considerations like numerical stability (e.g., using log-sum-exp trick) and mention how frameworks like TensorFlow/PyTorch automate this, showing awareness of real-world implementation.
State the model: z = w^T x + b, output y_hat = sigmoid(z). Define the loss function (binary cross-entropy) for a single example: L = -[y log(y_hat) + (1-y) log(1-y_hat)].
Derive dL/dz = y_hat - y (a key simplification). Then compute dL/dw = (y_hat - y) x and dL/db = y_hat - y. Show the steps clearly.
Introduce a network with L layers, each with weights W^l, biases b^l, and activation functions a^l. Define forward propagation: z^l = W^l a^{l-1} + b^l, a^l = f^l(z^l).
Define error term δ^l = ∂L/∂z^l. For output layer, δ^L = ∇_a L ⊙ f'(z^L). For hidden layers, δ^l = (W^{l+1}^T δ^{l+1}) ⊙ f'(z^l). Then gradients: ∂L/∂W^l = δ^l (a^{l-1})^T, ∂L/∂b^l = δ^l.
Explain that backprop is a general algorithm for computing gradients in any computational graph, and logistic regression is a special case with no hidden layers. Mention computational efficiency and modularity.
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This was the easiest question of the bunch.
Start by clearly stating the baseline models you compared (e.g., dummy classifier, regularized logistic regression, tree-based models) and the evaluation metrics used. Then explain the trade-offs in performance, interpretability, and operational constraints that led you to choose logistic regression. Emphasize how you validated the decision with business stakeholders and ensured it met regulatory and explainability requirements.
Pro tip: In regulated industries like Experian, interpretability and compliance often outweigh marginal performance gains. Highlight how logistic regression's transparency and ease of explanation to regulators and clients made it the preferred choice, even if a more complex model performed slightly better.
Name the specific baseline models you evaluated, such as a dummy classifier, regularized logistic regression, decision trees, random forests, or gradient boosting. Mention that you used cross-validation and appropriate metrics like AUC-ROC, precision-recall, or F1-score.
Summarize the performance differences: e.g., tree-based models may have higher AUC but lower interpretability. Discuss trade-offs in training time, inference latency, and ease of deployment.
Articulate the key factors that drove the decision: interpretability, regulatory compliance, explainability to stakeholders, robustness to overfitting, and alignment with business goals. Mention any constraints like model risk management policies.
Describe how you involved business partners, compliance, and engineering to ensure the model met their needs. Highlight any A/B tests or shadow deployments that confirmed the choice.
End by stating the outcome: logistic regression delivered sufficient performance with superior explainability, leading to faster adoption and regulatory approval. Mention any monitoring or retraining plans.
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Define knowledge-informed machine learning as the integration of domain knowledge into ML models, then provide a concrete example from your experience or a well-known case. Emphasize how this approach improves model performance, interpretability, and alignment with business constraints, especially in regulated industries like credit scoring.
Pro tip: Relate the example to Experian's business context, such as credit risk modeling, to show you understand their domain and can apply the concept to real-world problems.
Clearly explain that knowledge-informed ML combines data-driven learning with domain expertise, using techniques like constraints, priors, or feature engineering.
Highlight benefits such as improved accuracy with limited data, better interpretability, and compliance with regulations.
Describe a specific case, such as using monotonic constraints in credit scoring to ensure that higher income never decreases creditworthiness.
Tie the example to the Data Scientist role at Experian, emphasizing how knowledge-informed ML can enhance their products and services.
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Short answer to the last part: no, moving a single threshold is a tradeoff.
Start by explaining the trade-off between false positives and true positives when adjusting the classification threshold, and clarify that moving the threshold alone cannot improve both simultaneously. Then, discuss scenarios where you would adjust the threshold based on business costs and benefits, and finally, mention techniques to improve both metrics by enhancing the model itself.
Pro tip: Quantify the business impact of false positives versus false negatives to justify threshold adjustments, and emphasize that model improvement, not threshold tuning, is the key to lifting both metrics simultaneously.
Describe how lowering the threshold increases true positives but also false positives, while raising it reduces false positives but also true positives. This sets the foundation that moving the threshold alone cannot improve both.
Discuss scenarios where business costs dictate the optimal threshold, such as when false positives are very costly (e.g., fraud alerts) or when missing a positive is very costly (e.g., disease detection).
State explicitly that for a fixed model, moving the threshold traces out the ROC curve, so improving one metric necessarily worsens the other. Both cannot be improved simultaneously by threshold adjustment alone.
Explain that improving both requires enhancing the model's discriminative power, e.g., by adding better features, using a more complex model, or collecting more data, which shifts the entire ROC curve upward.
Tie the discussion back to the company's context (e.g., Experian's credit risk models) by emphasizing that threshold selection should align with business objectives and cost matrices.
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