STRIDE: Subset-Free Functional Decomposition for XAI in Tabular Settings

Most explainable AI (XAI) frameworks are limited in their expressiveness, summarizing complex feature effects as single scalar values \phi_i. This approach answers "what" features are important but fails to reveal "how" they interact. Furthermore, methods that attempt to capture interactions, like those based on Shapley values, often face an exponential computational cost. We present STRIDE, a scalable framework that addresses both limitations by reframing explanation as a subset-enumeration-free, orthogonal "functional decomposition" in a Reproducing Kernel Hilbert Space (RKHS). In the tabular setups we study, STRIDE analytically computes functional components f_S(x_S) via a recursive kernel-centering procedure. The approach is model-agnostic and theoretically grounded with results on orthogonality and L^2 convergence. In tabular benchmarks (10 datasets, median over 10 seeds), STRIDE attains a 3.0 times median speedup over TreeSHAP and a mean R^2=0.93 for reconstruction. We also introduce "component surgery", a diagnostic that isolates a learned interaction and quantifies its contribution; on California Housing, removing a single interaction reduces test R^2 from 0.019 to 0.027.