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arXiv Machine Learning By Kihun Rhee

When Is the Sharp Covariance Envelope Tight? Feature-Only Geometry for Volume-Sampled Least Squares

Read the original on arXiv Machine Learning →

The paper extends prior work on volume sampling by providing a Loewner envelope for the centered coefficient covariance in least‑squares regression with a fixed pool of features and responses. It characterizes when this envelope is tight, linking tightness to strict spectral properties of residuals, and introduces a residual‑augmented change of measure to derive a one‑sided slack bound. The results also offer geometric insights at the boundary and demonstrate non‑vacuous certificates through frozen‑feature examples, focusing on conditional centered, full‑Gram‑whitened covariance rather than population generalization.

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