WEBVTT

NOTE Fit the mixture to 200 ratings: captions match the on-screen steps.

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Step 1 of 7. The notebook's 200 synthetic ratings and its own random start, capped at 15 iterations.

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Step 2 of 7. Press play: the log-likelihood climbs from −425.50 and the responsibilities settle.

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Step 3 of 7. Stopped at the cap of 15 with ℓ = −416.51, still rising by 0.0293 per step: not converged.

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Step 4 of 7. Raise the cap: from the same start EM converges after 90 iterations, at ℓ = −415.37.

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Step 5 of 7. Now a bad start: drag μ₁ into the middle of the data and narrow σ₁ to 0.2.

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Step 6 of 7. EM converges again, to a local maximum: ℓ = −423.63, a spike on 2.4% of the ratings at 6.48.

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Step 7 of 7. The log-likelihood never decreased, yet this peak is 8.3 lower: EM cannot see the better one.