# Extrapolation-Aware Nonparametric Statistical Inference

arXiv: https://arxiv.org/abs/2402.09758 · HTML: https://mlsanity.com/paper/2402.09758/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 11 of 11)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [First Steps Toward Understanding the Extrapolation of Nonlinear Models to Unseen Domains](https://mlsanity.com/paper/2211.11719/) (2022)
- [Identifying Representations for Intervention Extrapolation](https://mlsanity.com/paper/2310.04295/) (2023)
- [Learning stable and predictive structures in kinetic systems: Benefits of a causal approach](https://mlsanity.com/paper/1810.11776/) (2018)
- [Local Gaussian process extrapolation for BART models with applications to causal inference](https://mlsanity.com/paper/2204.10963/) (2022)
- [Perturbation-based Effect Measures for Compositional Data](https://mlsanity.com/paper/2311.18501/) (2023)
- [Average partial effect estimation using double machine learning](https://mlsanity.com/paper/2308.09207/) (2023)

## Built on by (most cited first, 5 of 5)

- [Progression: an extrapolation principle for regression](https://mlsanity.com/paper/2410.23246/) (2024)
- [Regularizing Extrapolation in Causal Inference](https://mlsanity.com/paper/2509.17180/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Learning to Extrapolate to New Tasks: A Relational Approach to Task Extrapolation](https://mlsanity.com/paper/2605.30132/) (2026)
- [Distributional Extrapolation for Interactions](https://mlsanity.com/paper/2608.19849/) (2026)

## Abstract (arXiv)

We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. While extrapolating is straightforward in parametric models, it becomes challenging in nonparametric models. In this work, we extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions that can be combined with existing inference techniques to draw extrapolation-aware conclusions. The proposed class of extrapolation assumptions stipulate that the conditional function attains its minimal and maximal directional derivative, in each direction, within the observed support. We illustrate how the framework applies to several statistical applications including prediction and uncertainty quantification. We furthermore propose a consistent estimation procedure that can be used to adjust existing nonparametric estimates to account for extrapolation by providing lower and upper extrapolation bounds. The procedure is empirically evaluated on both simulated and real-world data.