# ============================================================================
# T14 — Comparing conformal prediction procedures on heteroscedastic regression
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# 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: ML14
title: "Comparing split-conformal, Mondrian conformal, and CQR-style intervals on heteroscedastic 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: |
  Conformal prediction provides finite-sample coverage guarantees with minimal
  assumptions, making it attractive for uncertainty quantification in practical
  regression. However, standard split-conformal intervals are often globally
  calibrated and can be inefficient when noise is heteroscedastic: they may
  over-cover low-noise regions and under-cover high-noise regions. This
  motivates conditional variants such as Mondrian conformal (group-conditional
  calibration) and CQR-style approaches that adapt interval width through
  quantile modeling before conformal correction.

  In small, CPU-only settings, one can still run a meaningful comparison by
  using sklearn-compatible regressors and synthetic data where heteroscedastic
  structure is controlled. A rigorous setup should evaluate not only marginal
  coverage but also efficiency (mean interval width) and conditional behavior
  (coverage gap across strata of predicted difficulty or input regions). These
  diagnostics reveal when methods achieve nominal coverage by producing overly
  wide intervals versus genuinely adapting to varying noise.

  A credible benchmark should include at least one homoscedastic control and at
  least one heteroscedastic dataset, then compare split-conformal, a Mondrian
  variant (binning by an auxiliary score such as |x| or predicted scale), and a
  CQR-style method based on lower/upper quantile regressors plus conformal
  adjustment. Repeated random splits (multiple seeds) are needed because
  conformal procedures can vary with calibration sample composition.

  The key question is whether adaptive procedures can reduce conditional
  miscoverage while maintaining near-target marginal coverage and reasonable
  interval width under strict runtime constraints.

  *Do Mondrian and CQR-style conformal procedures achieve lower conditional coverage error than vanilla split-conformal at comparable marginal coverage on heteroscedastic regression tasks?*

hypotheses:
  - id: H1
    statement: "On heteroscedastic datasets, at least one adaptive method (Mondrian or CQR-style) attains a lower absolute coverage gap to the 90% target than split-conformal by at least 0.02 on at least 2 of 3 datasets, averaged over \u22655 seeds."
    measurable: true
  - id: H2
    statement: "At matched target 90% coverage, CQR-style conformal yields mean interval width no larger than split-conformal on at least 2 of 3 datasets (difference \u2264 0.00)."
    measurable: true
  - id: H3
    statement: "Mondrian conformal reduces worst-bin conditional miscoverage (max over 4 bins of |bin_coverage-0.90|) by at least 0.03 versus split-conformal on at least 2 of 3 datasets."
    measurable: true

experiment_design:
  research_question: "Do adaptive conformal procedures (Mondrian, CQR-style) improve coverage quality and efficiency over split-conformal for heteroscedastic regression under a fixed 90% target coverage?"
  conditions:
    - name: "split_conformal_rf"
      description: "Vanilla split-conformal regression using RandomForestRegressor point predictor and absolute residual conformity scores on a held-out calibration split."
    - name: "mondrian_conformal_rf_4bins"
      description: "Mondrian split-conformal with the same base predictor, calibration and test points partitioned into 4 bins by an auxiliary score (e.g., fitted value or |x0| proxy), with per-bin quantiles."
    - name: "cqr_gbr"
      description: "CQR-style method using GradientBoostingRegressor quantile models (alpha=0.05, 0.95) and split-conformal correction on calibration residuals of quantile bands."
    - name: "naive_quantile_no_conformal"
      description: "Non-conformal baseline using raw quantile regression interval [q0.05, q0.95] without conformal adjustment."
  baselines:
    - "split_conformal_rf is the primary conformal baseline"
    - "naive_quantile_no_conformal is the non-conformal baseline"
  metrics:
    - name: "coverage_gap"
      direction: "minimize"
      description: "Absolute difference between empirical marginal coverage and target 0.90 on the test split, averaged over seeds."
    - name: "mean_interval_width"
      direction: "minimize"
      description: "Average prediction interval width on test samples, averaged over seeds."
    - name: "worst_bin_miscoverage"
      direction: "minimize"
      description: "Maximum across 4 bins of absolute deviation between bin coverage and 0.90, measuring conditional coverage disparity."
  datasets:
    - name: "hetero_sine"
      source: "synthetic: y = sin(2\u03c0x) + (0.1 + 0.5|x|)\u03b5, x~Uniform(-1,1), n\u22482000"
    - name: "hetero_friedman1"
      source: "synthetic: sklearn.datasets.make_friedman1 with multiplicative noise scale depending on x0"
    - name: "diabetes"
      source: "sklearn.datasets.load_diabetes (tabular regression benchmark)"
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 420

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML14.json"