Amazon·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Amazon ML Engineer interview with a statistics-heavy question on comparing multivariate distributions across two user populations. One question, but it had a lot of surface area and I felt like I was scrambling to cover everything.

Questions Asked (1)

You have two groups of users from different regions, each described by a set of continuous behavioral features. How would you test whether the two groups have meaningfully different multivariate distributions?

A/B Testing & ExperimentationProduct Analytics & MetricsTechnical Trade-offs

Author's notes

This one sprawled in a way I didn't expect.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the goal: to detect any distributional difference, not just mean shifts. Then propose a combination of global and local tests, such as energy distance or kernel MMD, and discuss practical considerations like dimensionality, sample size, and multiple testing correction.

Pro tip: Mention that you would first reduce dimensionality with PCA or UMAP for visualization and to mitigate the curse of dimensionality, but run the formal test on the original features or a sufficient summary to avoid losing signal.

1. Clarify the objective and assumptions

Confirm whether the goal is to detect any difference or a specific type (e.g., mean, variance, correlation). Check assumptions like independence, identical distribution within groups, and whether features are on comparable scales.

2. Choose appropriate statistical tests

Select tests that capture multivariate differences: energy distance, kernel MMD, or classifier two-sample test. For high dimensions, consider distance-based tests or random projections.

3. Address practical challenges

Handle high dimensionality via dimensionality reduction or feature selection, ensure sufficient sample size, and correct for multiple comparisons if testing many feature subsets.

4. Validate and interpret results

Use permutation tests to obtain p-values without distributional assumptions. If significant, identify which features or directions drive the difference using feature importance or post-hoc tests.

5. Consider business impact and next steps

Assess whether the detected difference is meaningful for the product or model. If so, propose actions like region-specific models or further investigation.

Key Points to Mention

Energy distance and kernel maximum mean discrepancy (MMD) as omnibus tests for multivariate distributions.
Classifier two-sample test: train a classifier to distinguish groups and evaluate AUC; significant AUC indicates distributional difference.
Permutation testing to obtain p-values without parametric assumptions.
Dimensionality reduction (PCA, UMAP) for visualization and to mitigate curse of dimensionality, but caution about information loss.
Multiple testing correction (e.g., Bonferroni, FDR) when testing many features or subgroups.
Practical significance vs. statistical significance: consider effect size and business impact.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.