Spectral Path Regression: Directional Chebyshev Harmonics for Interpretable Tabular Learning

TL;DR

This paper introduces spectral path regression using directional Chebyshev harmonics, enabling interpretable, efficient, and accurate tabular data modeling without high-dimensional complexity.

Contribution

It proposes a novel spectral regression method with directional harmonic modes that improves interpretability and efficiency over traditional tensor-product bases.

Findings

Achieves accuracy competitive with strong nonlinear models.

Models are compact, computationally efficient, and interpretable.

Reduces training to a single closed-form ridge solution.

Abstract

Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that is poorly matched to real tabular data. We address this by replacing tensorised oscillations with directional harmonic modes of the form $\cos(\mathbf{m}^{\top}\arccos(\mathbf{x}))$, which organise multivariate structure by direction in angular space rather than by coordinate index. This representation yields a discrete spectral regression model in which complexity is controlled by selecting a small number of structured frequency vectors (spectral paths), and training reduces to a single closed-form ridge solve with no iterative optimisation. Experiments on standard continuous-feature tabular regression benchmarks show that the resulting models achieve accuracy competitive with strong nonlinear baselines while remaining compact, computationally efficient, and explicitly interpretable through analytic expressions of learned feature interactions.