# ============================================================================
# T02 — Ensemble-method comparison for non-linear regression under noise
# ----------------------------------------------------------------------------
# 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: ML02
title: "Bagging vs boosting vs stacking for noisy non-linear regression"
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: |
  Ensemble learning is often presented as a broadly reliable way to improve
  predictive performance, but different ensemble families can react very
  differently to observation noise in regression. Bagging primarily reduces
  variance by averaging many weakly correlated models. Boosting is sequential
  and can aggressively fit residuals, which can help on structured non-linear
  signals but may overfit high-noise targets if regularization is not tuned.
  Stacking combines heterogeneous base learners through a meta-model and may
  benefit from diversity, but it also introduces extra fitting stages that can
  be sensitive to data size and leakage handling.

  A focused CPU-scale benchmark can probe these tradeoffs using synthetic and
  lightweight sklearn regression datasets where non-linearity and noise are
  controllable. By varying noise level explicitly in generated data, the study
  can test whether relative ranking among bagging, boosting, and stacking is
  stable or changes materially as signal-to-noise degrades. This design also
  encourages careful evaluation with repeated random seeds and test-set metrics
  that capture both average error and fit quality.

  A credible implementation should compare at least one representative for each
  family (e.g., RandomForestRegressor for bagging, GradientBoostingRegressor
  for boosting, StackingRegressor with diverse base estimators for stacking),
  include a single-model baseline, and report RMSE-centered conclusions. Since
  this benchmark is intended for fast autonomous execution, datasets and models
  must remain small enough to run in minutes on one CPU core while still
  producing clear numeric contrasts across noise regimes.

  The key outcome is not reproducing a known paper result but determining when
  each ensemble strategy is most robust for noisy non-linear regression in a
  constrained practical setting.

  *How does predictive robustness (RMSE) of bagging, boosting, and stacking change as regression noise increases on small non-linear benchmarks?*

hypotheses:
  - id: H1
    statement: "On the high-noise synthetic dataset (noise >= 25), bagging (RandomForestRegressor) achieves lower mean RMSE than boosting (GradientBoostingRegressor), averaged over at least 5 seeds."
    measurable: true
  - id: H2
    statement: "On at least 2 of 3 evaluated datasets, at least one ensemble method (bagging, boosting, or stacking) improves RMSE by >= 10% relative to the single DecisionTreeRegressor baseline."
    measurable: true
  - id: H3
    statement: "StackingRegressor attains the best (lowest) mean RMSE on at least 1 of 3 datasets while not being worst on more than 1 dataset, averaged over at least 5 seeds."
    measurable: true

experiment_design:
  research_question: "How does RMSE performance of bagging, boosting, and stacking vary with increasing noise in non-linear regression tasks under CPU-only constraints?"
  conditions:
    - name: "decision_tree_baseline"
      description: "Single DecisionTreeRegressor (max_depth tuned over a small grid) as non-ensemble baseline."
    - name: "bagging_random_forest"
      description: "RandomForestRegressor representing bagging-style averaging across trees."
    - name: "boosting_gbrt"
      description: "GradientBoostingRegressor representing sequential boosting on residuals."
    - name: "stacking_heterogeneous"
      description: "StackingRegressor with base learners {kNN regressor, ridge regression, shallow random forest} and a linear meta-regressor."
  baselines:
    - "decision_tree_baseline is the single-model baseline"
    - "bagging_random_forest serves as a strong classical ensemble reference"
  metrics:
    - name: "rmse"
      direction: "minimize"
      description: "Root Mean Squared Error on held-out test split, averaged over seeds."
    - name: "mae"
      direction: "minimize"
      description: "Mean Absolute Error on held-out test split, averaged over seeds."
    - name: "r2"
      direction: "maximize"
      description: "Coefficient of determination on held-out test split, averaged over seeds."
  datasets:
    - name: "friedman1_low_noise"
      source: "sklearn.datasets.make_friedman1 (n_samples=1200, n_features=10, noise=1.0)"
    - name: "friedman1_high_noise"
      source: "sklearn.datasets.make_friedman1 (n_samples=1200, n_features=10, noise=30.0)"
    - name: "diabetes"
      source: "sklearn.datasets.load_diabetes"
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 420

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML02.json"