Online Supervised Dimension Reduction with Random Features: Diagnostics and Computational Trade-offs

Abstract:Accurate optimization of a supervised spectral objective need not produce an accurate population subspace or a better predictive representation. We investigate these distinctions for Online Kernel Supervised Principal Component Analysis (OKSPCA), which combines a centered cross-moment in finite random-feature coordinates with an Adam-style orthonormal basis update for an established objective. Fixed-map consistency, concentration and perturbation results describe the estimator and its exact subspace; same-target comparisons then assess the practical iterate separately. Across six predictive benchmarks, performance depends on the declared pipeline: replacing the tracker with the exact empirical target leaves the two regression deficits largely unchanged. Direct classification-rank models capture nearly all terminal objective energy on average, but a saved intermediate state exhibits substantial geometric deviation; a controlled sample-size study further separates empirical accuracy from population recovery. In distinct numerical-service workloads, exact on-request computation is faster in the tested classification settings, whereas Adam saves time relative to the tested full thin-SVD service for some dense wider-regression requests, alongside persistent geometric error. These diagnostics limit explanations based solely on terminal optimization accuracy and distinguish numerical cost from quality, rank coverage and freshness; they establish neither practical-tracker convergence nor predictive or deployment benefits from basis availability.

Machine Learning (stat.ML); Machine Learning (cs.LG); Computation (stat.CO)

arXiv:2609.20454 [stat.ML]

(or arXiv:2609.20454v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.20454 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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