Structural interpretability in SVMs with truncated orthogonal polynomial kernels

TL;DR

This paper introduces ORCA, a post-training interpretability framework for SVMs with truncated orthogonal polynomial kernels, revealing structural model aspects beyond accuracy.

Contribution

It proposes a novel diagnostic method that analyzes the distribution of the RKHS norm across interaction orders without retraining or surrogate models.

Findings

ORCA provides insights into model complexity not captured by accuracy.

The methodology is demonstrated on synthetic and real datasets.

It quantifies contributions of different interaction levels in the model.

Abstract

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product orthonormal basis, the fitted decision function can be expanded exactly in intrinsic RKHS coordinates. This leads to Orthogonal Representation Contribution Analysis (ORCA), a diagnostic framework based on normalized Orthogonal Kernel Contribution (OKC) indices. These indices quantify how the squared RKHS norm of the classifier is distributed across interaction orders, total polynomial degrees, marginal coordinate effects, and pairwise contributions. The methodology is fully post-training and requires neither surrogate models nor retraining. We illustrate its diagnostic value on a synthetic double-spiral problem and on a real five-dimensional echocardiogram dataset. The results show that the proposed indices reveal structural aspects of model complexity that are not captured by predictive accuracy alone.