# ============================================================================
# T10 — Cross-validation strategy effects on small-sample model selection
# ----------------------------------------------------------------------------
# Unlike paper_replication's P01-P07, the "synthesis" here frames a research
# QUESTION rather than a known paper's method. The model must design the
# experiment (conditions, metrics, datasets) — we only commit to what a
# competent study of this topic would include and what the rubric expects.
# ============================================================================

id: ML10
title: "Cross-validation strategy reliability for small-sample model selection"
arxiv_id: null
venue: "ARC-Bench 2026"
paper_asset: null

# The "synthesis" plays the role of the upstream briefing: research question,
# background, why the question matters, what "a reasonable experiment" looks
# like. It deliberately does NOT pre-specify a single method to reproduce.
synthesis: |
  With small datasets, model selection can become highly sensitive to the
  validation protocol. Practitioners often choose among k-fold,
  stratified k-fold, repeated k-fold, and leave-one-out cross-validation
  (LOOCV), but these strategies trade off bias, variance, and compute in
  different ways. A method that appears best under one CV scheme may not be
  best under another, especially when class balance is imperfect and sample
  counts are low.

  This topic studies CV strategy as the independent variable while keeping
  candidate models fixed and lightweight. The key quantity is estimation bias:
  the gap between CV-estimated score used for model selection and the realized
  test score of the selected model on a held-out test set. In small-sample
  settings, minimizing this gap is often more important than maximizing raw CV
  score, because over-optimistic selection can produce brittle deployments.

  A credible CPU-scale experiment should evaluate multiple sklearn datasets
  reduced to small training sizes, run several random seeds, and compare at
  least four CV strategies under the same model grid and scoring rule. The
  study should report not only estimation bias but also variance across seeds
  and model-selection stability. Baselines should include standard k-fold and
  stratified k-fold; repeated stratified k-fold and LOOCV serve as contrasting
  alternatives with different variance/compute characteristics.

  The goal is not to prove one universally superior protocol, but to quantify
  when more elaborate CV schemes improve reliability enough to justify their
  cost under strict CPU budgets.

  *Which cross-validation strategy yields the lowest and most stable model-selection estimation bias for small-sample classification tasks under a fixed candidate-model grid?*

hypotheses:
  - id: H1
    statement: "RepeatedStratifiedKFold (5 folds × 3 repeats) achieves lower mean absolute estimation bias than plain KFold (5 folds) on at least 2 of 3 evaluated small-sample datasets, averaged over ≥5 random seeds."
    measurable: true
  - id: H2
    statement: "StratifiedKFold (5 folds) yields lower across-seed standard deviation of selected-model test accuracy than plain KFold (5 folds) on at least 2 of 3 datasets."
    measurable: true
  - id: H3
    statement: "LOOCV does not outperform RepeatedStratifiedKFold in mean absolute estimation bias by more than 0.01 absolute score on any dataset, while requiring greater wall-clock time."
    measurable: true

experiment_design:
  research_question: "For small-sample classification model selection, how do KFold, StratifiedKFold, RepeatedStratifiedKFold, and LOOCV compare in estimation bias, stability, and compute cost?"
  conditions:
    - name: "kfold_5"
      description: "Model selection via 5-fold KFold (shuffle=True) on the training split."
    - name: "stratified_kfold_5"
      description: "Model selection via 5-fold StratifiedKFold (shuffle=True) on the training split."
    - name: "repeated_stratified_5x3"
      description: "Model selection via RepeatedStratifiedKFold with 5 folds and 3 repeats."
    - name: "loocv"
      description: "Model selection via Leave-One-Out cross-validation on the training split."
  baselines:
    - "kfold_5 as the non-stratified baseline"
    - "stratified_kfold_5 as the standard small-sample baseline"
  metrics:
    - name: "estimation_bias"
      direction: "minimize"
      description: "Absolute difference between best CV mean score and held-out test score of the selected model, aggregated over seeds."
    - name: "selected_model_test_accuracy"
      direction: "maximize"
      description: "Held-out test accuracy of the model selected by each CV strategy, mean over seeds."
    - name: "selection_stability"
      direction: "maximize"
      description: "Fraction of seeds selecting the modal hyperparameter configuration (higher = more stable)."
    - name: "wall_clock_sec"
      direction: "minimize"
      description: "Runtime per CV strategy over all seeds and datasets on CPU."
  datasets:
    - name: "breast_cancer_small"
      source: "sklearn.datasets.load_breast_cancer (subsample training set to n<=120)"
    - name: "wine_small"
      source: "sklearn.datasets.load_wine (subsample training set to n<=100)"
    - name: "synthetic_imbalanced_small"
      source: "sklearn.datasets.make_classification (n_samples=160, weights=[0.75,0.25], class_sep tuned for moderate difficulty)"
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 600

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML10.json"