{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "pml-book1-ex4.5",
    "area": "machine-learning",
    "topic": "theory",
    "origin": "external",
    "title": "BIC for a two-dimensional discrete distribution",
    "skills": [
      "generalization",
      "overfitting",
      "model-complexity"
    ],
    "priority": "core",
    "difficulty": "medium",
    "estimated_minutes": 20,
    "prerequisites": [
      "maximum-likelihood",
      "logarithms",
      "cross-validation"
    ],
    "source_id": "pml-book1-2022",
    "locator": {
      "document": "PML Book 1 online draft (2025-04-18), Chapter 4 exercises",
      "label": "Exercise 4.5",
      "page_label": "book p. 165 (PDF p. 195)",
      "solution_pages": "11–12"
    },
    "links": {
      "problem": "https://github.com/probml/pml-book/releases/download/2025-04-18/book1.pdf#page=195",
      "solution": "https://probml.github.io/pml-book/solns-public.pdf#page=11"
    },
    "selection_note": "Compares nested models using fit, leave-one-out behavior, parameter count, and a complexity penalty.",
    "source_caveat": "The public solution manual predates the dated book draft; the exercise title and task align, but notation may differ.",
    "answer_status": "official-solution"
  }
}