WEBVTT

NOTE Step through EM by hand: captions match the on-screen steps.

1
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Step 1 of 7. Start from the explainer's worked example: four movie ratings, [2, 3, 7, 8].

2
00:00:05.820 --> 00:00:11.239
Step 2 of 7. The explainer's starting guess: μ = 2.5 and 7.5, σ = 0.5, π = 0.5 for both groups.

3
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Step 3 of 7. E-step 1: each rating's responsibility γ by Bayes' theorem, the explainer's numbers alongside.

4
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Step 4 of 7. The explainer's densities of 0.8 and 0.6 are off: both are 0.4839, one σ from 2.5.

5
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Step 5 of 7. M-step 1: weighted averages give back μ = 2.5 and 7.5, σ = 0.5 and π = 0.5, as written.

6
00:00:32.803 --> 00:00:41.339
Step 6 of 7. Iteration 2 repeats iteration 1: the starting guess was already a fixed point.

7
00:00:41.339 --> 00:00:52.806
Step 7 of 7. The log-likelihood stays at −5.6758, so EM stops; every correction, as written and exact.