Implement a Gaussian Mixture Model with EM from scratch: E-step responsibilities, M-step updates.
A build-it-yourself check on the EM algorithm and soft clustering. What matters is the pair of alternating steps (responsibilities, then weighted re-estimation), log-sum-exp for numerical stability, and seeing how GMM extends k-means. The code follows.
Updated Sep 2026 · Grounded in real GenAI, LLM, and AI/ML engineering interview loops and written to a senior-engineer editorial bar.
A build-it-yourself check on the EM algorithm and soft clustering. What matters is the pair of alternating steps (responsibilities, then weighted re-estimation), log-sum-exp for numerical stability, and seeing how GMM extends k-means. The code follows.
Lead with where the obvious approach breaks, because that is the judgment they are screening for — most candidates jump straight to the happy path and lose the room.
Then walk the failure back through the pipeline in order, naming the one metric the customer's exec sponsor actually cares about before you propose the fix.
