Predictive Interval Models for Non-parametric Regression

TL;DR

This paper introduces a novel method for constructing reliable two-sided predictive intervals in non-parametric regression without assuming constant variance, using tolerance intervals and a new hyper-parameter tuning approach.

Contribution

It presents a new approach to generate minimal reliable predictive intervals for non-parametric regression, including a model test and a comparison measure.

Findings

Our method produces more reliable intervals than existing methods.

The approach effectively balances interval size and coverage.

Experiments demonstrate improved precision and effectiveness.

Abstract

Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We name such intervals predictive intervals. This work presents a new method to find two-sided predictive intervals for non-parametric least squares regression without the homoscedasticity assumption. Our predictive intervals are built by using tolerance intervals on prediction errors in the query point's neighborhood. We proposed a predictive interval model test and we also used it as a constraint in our hyper-parameter tuning algorithm. This gives an algorithm that finds the smallest reliable predictive intervals for a given dataset. We also introduce a measure for comparing different interval prediction methods yielding intervals having different size and coverage. These experiments show that our methods are more reliable, effective and precise than other interval prediction methods.