CE Regression Intervals

You are configuring or interpreting regression intervals in CE. This skill covers the three distinct regression modes defined in ADR-021. A fully fit + calibrated WrapCalibratedExplainer (regression model) is required.

Load references/difficulty_estimator_guide.md for per-instance adaptive intervals using DifficultyEstimator.

Three Modes — Decision Tree

Is threshold= provided?
├── NO  -> Mode 2: Percentile conformal intervals (CPS)
│         Use low_high_percentiles=(low%, high%)
│         Result: interval is a percentile band (e.g., 5th-95th percentile)
│
└── YES -> Mode 3: Thresholded probabilistic regression (CPS + Venn-Abers)
          Result: calibrated P(y <= threshold) with probability interval
          Interval semantics = probability mass (NOT a percentile band)

Mode 1 (classification) is handled by ce-pipeline-builder and ce-factual-explain.

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Mode 2: Percentile Conformal Intervals

Use when: you want a confidence band around the regression prediction.

explanations = explainer.explain_factual(X_query)                              # default 5th-95th, 90% condfidence
explanations = explainer.explain_factual(X_query, low_high_percentiles=(10, 90))  # tighter, 80% confidence
explanations = explainer.explain_factual(X_query, low_high_percentiles=(-np.Inf, 90))  # upper bounded, 90% condfidence
explanations = explainer.explain_factual(X_query, low_high_percentiles=(10, np.Inf))  # lower bounded, 90% condfidence

How to read the output:

exp = explanations[0]
median = exp.prediction['predict']    # point estimate (CPS median)
low    = exp.prediction['low']        # e.g., 5th percentile
high   = exp.prediction['high']       # e.g., 95th percentile
# Invariant (ADR-021 §4): low <= median <= high

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Mode 3: Thresholded Probabilistic Regression

Use when: you want the calibrated probability that the output exceeds a threshold.

explanations = explainer.explain_factual(X_query, threshold=50.0)              # scalar
explanations = explainer.explain_factual(X_query, threshold=(40.0, 60.0))      # two-sided

Key difference from Mode 2:

• The predict value is a probability (0-1), not a value in y-space.
• The interval bounds are probability bounds, not regression value bounds.
• Do NOT mix low_high_percentiles and threshold in the same call.

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Calibration Engine (Context — ADR-021)

Mode	Engine	What is calibrated
Classification	Venn-Abers only	P(class=k) with interval
Regression (percentile)	CPS only	Percentile bands
Regression (threshold)	CPS -> Venn-Abers	P(y <= t) with interval

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Choosing Interval Width

Goal	Setting
Standard 90% interval	low_high_percentiles=(5, 95) (default)
Tighter 80% interval	low_high_percentiles=(10, 90)
Tight 50% IQR	low_high_percentiles=(25, 75)
Wider 98% interval	low_high_percentiles=(1, 99)

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Alternatives in Regression

alternatives = explainer.explore_alternatives(X_query, threshold=50.0)
alternatives = explainer.explore_alternatives(X_query, low_high_percentiles=(10, 90))

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Out of Scope

• Classification interval semantics (see ce-factual-explain).
• Building the pipeline (see ce-pipeline-builder).
• Persisting the calibrated regression model (see ce-serializer-impl).

Evaluation Checklist

• Mode correctly identified (percentile vs threshold).
• low_high_percentiles and threshold not used simultaneously.
• Interval invariant low <= predict <= high verified.
• Correct semantic interpretation of predict stated (probability vs y-value).
• Calibration set size and expected interval width proportional.
• If DifficultyEstimator used: estimator is fitted=True before assignment.
• If DifficultyEstimator used: interval widths vary per instance (not uniform).
• set_difficulty_estimator(None) tested if removal path is needed.