SPARK: A General Goodness-of-Fit Assessment via Residual Projection

2026-09-29

AI Summary

This study addresses the challenge of goodness-of-fit assessment for black-box models and the limitations of traditional parametric tests when applied to high-dimensional, flexible learners. To this end, we propose SPARK, a general testing framework that projects residuals onto near-orthogonal directions via kernel functions to extract residual signals, combined with a debiasing strategy. The method accommodates both continuous and binary responses alongside predictors of arbitrary dimensionality. We establish the asymptotic properties of the test statistic and prove bootstrap consistency. Simulation studies and real-data analyses validate the effectiveness and flexibility of the proposed approach, demonstrating its capacity to significantly enhance accuracy evaluation for complex machine learning models.

Abstract

Goodness-of-fit testing is a basic tool for assessing whether a fitted procedure has captured the systematic information contained in the covariates. While traditional theory has largely focused on parametric regression models, modern data analysis increasingly relies on flexible black-box learners, whose predictive success alone is insufficient to assess model accuracy. In this paper, we propose SPARK, a general framework for goodness-of-fit testing that applies to traditional statistical models and general black-box learning procedures, continuous and binary responses, and low- and high-dimensional predictors. Based on a debiasing strategy, the residuals from an initial fit of a learning procedure are projected onto nearly orthogonal directions to extract any remaining signal. To capture information across all projection directions, we propose a kernel-based projection method and establish both its asymptotic properties and the consistency of a bootstrap procedure. Comprehensive simulations and real data analyses illustrate the effectiveness and flexibility of our proposed method.

Problem

• Goodness-of-fit testing
• Black-box learners
• Residual projection
• High-dimensional predictors

Innovation

• Goodness-of-fit testing
• Residual projection
• Debiasing strategy
• Kernel-based projection
• Black-box learners