Conformal Prediction for Nonparametric Instrumental Regression

TL;DR

This paper introduces a conformal prediction method for nonparametric instrumental variable regression that provides finite-sample, distribution-free coverage guarantees, adaptable to various NPIV estimators including neural networks.

Contribution

It reformulates conditional coverage as marginal coverage over IV shifts and integrates conformal inference with any NPIV estimator, ensuring finite-sample guarantees.

Findings

Provides distribution-free, finite-sample coverage guarantees

Compatible with multiple NPIV estimation methods including neural networks

Reformulates conditional coverage as marginal coverage over IV shifts

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.