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Explain the EM algorithm and walk through it for a Gaussian Mixture Model.

EM is the classic latent-variable algorithm, and a GMM is how it appears in practice. What interviewers reward is the E-step/M-step alternation, why it is soft clustering where k-means is hard, and the honest caveat that it only reaches a local optimum. Here is the answer.

Updated Sep 2026 · Grounded in real GenAI, LLM, and AI/ML engineering interview loops and written to a senior-engineer editorial bar.

EM is the classic latent-variable algorithm, and a GMM is how it appears in practice. What interviewers reward is the E-step/M-step alternation, why it is soft clustering where k-means is hard, and the honest caveat that it only reaches a local optimum. Here is the answer.

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