Extension to high-dimensional regression and classification

Extend the Fibonacci Ensemble framework to high-dimensional regression and classification by developing refined control of effective dimension and spectral truncation for the Fibonacci conic hull and the second-order recursive ensemble operator, and adapt Fibonacci ensembles to margin-based classification losses by analyzing the interplay between golden-ratio weights, margin distributions, and generalization bounds.

Background

The paper focuses on one-dimensional regression with smooth base learners to develop and visualize the geometry of Fibonacci weighting, orthogonalization, and spectral recursion. It acknowledges that higher-dimensional hypothesis spaces introduce complex spectral behavior and effective dimension challenges for random features and polynomial bases.

In the Future Work section, the authors point out the need to extend the Fibonacci conic hull and recursive operator analysis to high-dimensional settings and to classification tasks, emphasizing the necessity of careful treatment of margins and generalization under golden-ratio weighting.