Protocol
Latent Variables and Probabilistic Estimation
Build a mixture-model analysis of a synthetic population and one small real dataset. Identify when the fitted components are useful descriptions but weak explanations.
40–65 active hours60–90 min sessionsIntermediate
Mastery contract
Core protocol · Standard 1.0 · Build a mixture-model analysis of a synthetic population and one small real dataset. Identify when the fitted components are useful descriptions but weak explanations.
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Reasoning — not yet passed
Derive both EM steps and explain why likelihood ascent does not imply a global optimum.
Reliable implementation — not yet passed
Responsibilities sum to one and likelihood is nondecreasing within numerical tolerance for the standard unregularized well-conditioned fixture.
Reproducible experiment — not yet passed
Report every restart, distinguish component label switching from failure and record how regularization changes the objective.
Defense and handoff — not yet passed
Defend a probabilistic mixture fit using predictive checks rather than presenting a latent component as a proven real-world category.
All four criteria must pass. Activity completion does not satisfy them.
An independent reviewer reruns your work and varies something you did not rehearse: a fresh input, a different working directory, or a declared edge case.
Pilot decisions are provisional, not external credentials. For an appeal or sensitive artifact, contact your designated pilot operator with the submission ID. Export your assessment history.
What you will do
6 total
Derive Gaussian-mixture responsibilities and EM updates; explain Jensen’s inequality in the lower-bound construction.
Implement Gaussian-mixture EM with log-space responsibilities, covariance regularization and multiple restarts.
Fit 3 component counts across 10 seeds on known synthetic mixtures; compare held-out likelihood, parameter recovery and degenerate fits.
Debug collapsed covariance and responsibilities normalized over the wrong axis; preserve both stress fixtures.
Write a 500–900 word technical report linking the reasoning, code, measurements, and limitations; include the project decision below.
Assess all 4 mastery criteria against saved artifacts, request an independent review, and repeat each failed criterion on a fresh example.
Essentials
A reading session alone never satisfies a mastery criterion.
Store source references, assumptions, and artifact paths beside every result.
Keep an untouched check case that differs from the worked example.
Record all attempts, including failures and results that contradict your prediction.
Use the stated comparison conditions; document every deviation before drawing a conclusion.
Protocol guardrails
Do
- +State the expected result before running the comparison.
- +Keep one minimal reproducible failing case when debugging.
- +Record environment versions and the exact command used.
- +Compare explanations with saved intermediate values.
- +Ask a reviewer to challenge the weakest assumption.
Don't
- ×Do not copy a worked solution and present it as an independent implementation.
- ×Do not tune against held-out evaluation outcomes.
- ×Do not report only the best seed or discard inconvenient runs.
- ×Do not equate elapsed hours or a completed run with a passed assessment.
- ×Do not conceal reduced-scale experiments behind claims about the original full-scale result.
Protocol authorship
Written by NuthinButta as instructional design. The teaching sources are the official references linked in each milestone; the exercises, workload and pass thresholds are ours, not their authors'.