# Causal isotonic calibration for heterogeneous treatment effects

## TL;DR

This paper introduces causal isotonic calibration, a nonparametric method for calibrating heterogeneous treatment effect predictors, and a data-efficient cross-calibration variant that ensures robust, distribution-free calibration with minimal data requirements.

## Contribution

It presents a novel calibration method that can be applied to any black-box predictor, with theoretical guarantees under weak conditions, improving treatment effect estimation accuracy.

## Key findings

- Achieves fast doubly-robust calibration rates
- Works without assuming monotonicity
- Can be wrapped around any black-box model

## Abstract

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.