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Conformal Thresholded Intervals for Efficient Regression

AAAI 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Conformal prediction sets · 6 citations (OpenAlex)

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Proposes Conformal Thresholded Intervals (CTI), which thresholds multi-output quantile regression interquantile intervals by length to build small conformal prediction sets for regression with marginal coverage guarantees.

Problem

Conformal regression methods typically produce interval prediction sets that are suboptimal for skewed or non-unimodal conditional distributions, while full conditional density methods are complex to tune; the goal is the smallest valid prediction set with guaranteed coverage.

Approach

Train multi-output quantile regression on K equiprobable quantiles, define interquantile intervals, and keep those with length at most a calibrated threshold t (score = interval length), so that short intervals (high estimated density) are included, approximating the Neyman-Pearson optimal set without estimating the full conditional density.

Key results

• On the synthetic triangular data, theoretical expected set sizes are 0.317 for CTI versus 0.342 for CHR and 0.376 for CQR at alpha=0.1.
• CTI(RF) gives the smallest set size on most real datasets, e.g., meps19 1.760 vs 2.388 for CHR(RF) and 2.923 for CQR, with coverage near 0.90.
• On the small star dataset (n=2161), CQR (0.181) slightly outperforms CTI (0.186 RF), which the authors attribute to limited data for multi-output quantile regression.

Measured effects reported in the paper

Surprising findings

• On the star dataset, plain CQR outperforms both CTI and CHR, showing the method depends on quantile regression quality with small samples.

Limitations

• Current implementation does not guarantee prediction sets are intervals (non-convex sets possible).
• Performance depends on quality of multi-output quantile regression; small datasets hurt performance.
• Theoretical optimality requires accurate quantile estimates and smoothness assumptions; some proofs are informal.

Experimental setup

Datasets: synthetic triangular distribution (n=10000) bike bio blog community concrete facebook1 facebook2 homes meps19 meps20 meps21

Benchmarks: synthetic bike bio blog community concrete facebook1 facebook2 homes meps19 meps20 meps21

Metrics: coverage prediction set size

Baselines: CQR CHR Split conformal

Builds on: conformal quantile regression conformal histogram regression split conformal prediction least ambiguous set classification

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