Navigating interpretability and alpha control in GF-KCSD testing with measurement error: A Kernel approach

The Gradient-Free Kernel Conditional Stein Discrepancy (GF-KCSD), presented in our prior work, represents a significant advancement in goodness-of-fit testing for conditional distributions. This method offers a robust alternative to previous gradient-based techniques, specially when the gradient calculation is intractable or computationally expensive. In this study, we explore previously unexamined aspects of GF-KCSD, with a particular focus on critical values and test power—essential components for effective hypothesis testing. We also present novel investigation on the impact of measurement errors on the performance of GF-KCSD in comparison to established benchmarks, enhancing our understanding of its resilience to these errors. Through controlled experiments using synthetic data, we demonstrate GF-KCSD's superior ability to control type-I error rates and maintain high statistical power, even in the presence of measurement inaccuracies. Our empirical evaluation extends to real-world datasets, including brain MRI data. The findings confirm that GF-KCSD performs comparably to KCSD in hypothesis testing effectiveness while requiring significantly less computational time. This demonstrates GF-KCSD's capability as an efficient tool for analyzing complex data, enhancing its value for scenarios that demand rapid and robust statistical analysis.