Extrapolation-Aware Nonparametric Statistical Inference

TL;DR

This paper introduces a framework for nonparametric statistical inference that explicitly accounts for extrapolation outside the observed data support, providing bounds and adjustments to improve inference validity.

Contribution

It extends nonparametric models to incorporate extrapolation assumptions, enabling more reliable inference when evaluating functions outside the data support.

Findings

Proposes a class of extrapolation assumptions for nonparametric inference.

Develops a consistent estimation procedure for extrapolation bounds.

Empirically demonstrates the method on simulated and real data.

Abstract

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.