Conformal Interval Regression (CPS)

Regression in Calibrated Explanations is conformal interval regression implemented via Conformal Predictive Systems (CPS).

  • Canonical semantics: Point regression + calibrated uncertainty intervals = conformal regression.

  • Interval control: The specific interval width is controlled by low_high_percentiles.

Percentile or interval regression semantics note

  • Calibration prerequisites: fit on x_proper, y_proper and calibrate on held-out x_cal, y_cal.

  • Mode-specific guarantees: CPS returns calibrated percentile intervals for requested low_high_percentiles.

  • Assumptions: calibration and deployment data are exchangeable or distribution-matched.

  • Explicit non-guarantees: no guarantee under drift or fixed interval width across subpopulations.

  • Explanation-envelope limits: feature-level interval effects summarize model behavior under perturbation.

  • Formal semantics: Calibrated interval semantics.

Supported signatures

Method

Description

predict(x)

Point regression estimate

predict(x, uq_interval=True, ...)

Point estimate + CPS parameterised interval

explain_factual(x, ...)

Factual explanation with CPS intervals

explore_alternatives(x, ...)

Alternative explanations with CPS intervals

Controlling the interval: low_high_percentiles

The low_high_percentiles parameter (tuple (low, high)) governs the CPS interval.

  • Default: (5, 95) → 90% central interval.

  • One-sided: (-np.inf, 95) or (5, np.inf).

Examples

1. Point prediction + 90% conformal interval

# Returns median, low (5th percentile), and high (95th percentile)
prediction, (low, high) = explainer.predict(
    x_test,
    uq_interval=True,
    low_high_percentiles=(5, 95)
)
print(f"Prediction: {prediction[0]} Interval: {low[0]} – {high[0]}")

2. Explanation with specific interval settings

You can request explanations with arbitrary confidence levels by strictly passing the percentiles:

# Explain with a 50% central interval (25th - 75th percentiles)
explanation = explainer.explain_factual(
    x_test,
    low_high_percentiles=(25, 75)
)

Key semantics

  • Prediction Interval: The interval returned by predict(..., uq_interval=True) is the conformal interval derived from the CPS.

  • Rule Intervals: The explanation envelopes on feature weights in explain_factual rules are also derived from the underlying CPS calibration.

Entry-point tier: Tier 2.