High-dimensional ridgeless least squares interpolation under spiked covariance structures
This paper investigates the asymptotic behavior of the out-of-sample prediction risk of the high-dimensional ridgeless least-squares estimator when the feature dimension $p$ and the sample size $n$ grow proportionally. We consider a generalized spiked population covariance model with multiple latent factors, where the number of spiked eigenvalues may remain finite or increase with $n$, and the spiked eigenvalues may be bounded or diverge at arbitrary rates. Beyond characterizing the impact of covariance spectra, we reveal a new mechanism underlying benign overfitting: the prediction behavior of ridgeless interpolation is fundamentally governed by the alignment between the regression coeff...
| Authors | Zhijun Liu, Dandan Jiang |
|---|---|
| Primary category | math.ST |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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