# Expectation-maximization for factor analysis

> ML preparation item.

- Stable ID: `pml-book1-ex20.1`
- Area: Machine Learning
- Topic: Unsupervised Learning
- Origin: external
- Expected time: 30 minutes
- Skills: expectation-maximization
- Item JSON: https://mlprep.iwase.dev/data/items/pml-book1-ex20.1.json

This site does not reproduce the third-party problem.

- Source: Probabilistic Machine Learning: An Introduction — online draft dated 2025-04-18
- Document: PML Book 1 online draft (2025-04-18), Chapter 20 exercises
- Locator: Exercise 20.1, book p. 712 (PDF p. 742)
- Official answer PDF page(s): 39–40
- Original problem: https://github.com/probml/pml-book/releases/download/2025-04-18/book1.pdf#page=742
- Official answer: https://probml.github.io/pml-book/solns-public.pdf#page=39
- Answer status: official-solution
- Source caveat: This is advanced latent-variable practice rather than clustering; the public solution manual predates the dated book draft.


## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `pml-book1-ex20.1`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.