Conformal Prediction for Nonparametric Instrumental Regression

2026-03-26

AI Summary

This work proposes a novel framework based on conditional conformal inference to construct prediction intervals for nonparametric instrumental variable (NPIV) regression that are distribution-free and offer finite-sample coverage guarantees—features absent in existing methods. By reformulating the conditional coverage problem as marginal coverage over a user-specified class of instrumental variable perturbations, the approach yields valid prediction intervals compatible with any NPIV estimator, including sieve two-stage least squares and neural network-based minimax estimators. The method provides, for the first time, distribution-free finite-sample coverage guarantees for NPIV regression while allowing practitioners to tailor the perturbation class to reflect domain-specific assumptions, thereby balancing flexibility with rigorous theoretical validity.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: State Estimation

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• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We propose a method for constructing distribution-free prediction intervals in nonparametric instrumental variable regression (NPIV), with finite-sample coverage guarantees. Building on the conditional guarantee framework in conformal inference, we reformulate conditional coverage as marginal coverage over a class of IV shifts $\mathcal{F}$. Our method can be combined with any NPIV estimator, including sieve 2SLS and other machine-learning-based NPIV methods such as neural networks minimax approaches. Our theoretical analysis establishes distribution-free, finite-sample coverage over a practitioner-chosen class of IV shifts.

Problem

• Conformal Prediction
• Nonparametric Instrumental Regression
• Prediction Intervals
• Finite-sample Coverage
• Instrumental Variable

Innovation

• Conformal Prediction
• Nonparametric Instrumental Regression
• Finite-sample Coverage
• Distribution-free Inference
• IV Shifts