The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression
Updated 6 h ago · first seen 11 Sept 2026
paper_01M294FTBVHMYR127E1X1F8N4H
- Published
- 11 Sept 2026
- T1 · 6 h ago
- arXiv
- 2607.24041
- T1 · 6 h ago
- Category
- math.ST
- T1 · 6 h ago
Abstract
-cross Abstract: Over-parameterized linear regression has been widely studied over the last decade. However, most existing works assume that the covariates are independent and that their covariance matrices are non-degenerate. In this paper, we relax both assumptions and derive deterministic equivalents for the prediction risk in a vanishing-ridge regime. We show that degeneracy of the covariance matrices and dependence can lead to multiple descent, and characterize where the corresponding peaks can occur. Our proofs use a novel graph representation of the variance profile. We show that maximum matchings and the Dulmage--Mendelsohn decomposition of the associated bipartite graph identify the configurations at which the variance becomes singular.
Authors 4
Kevin Han Huang, Haoyu Ye, Somak Laha, Morgane Austern
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
- Arxiv announce type
- replace
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
- arXiv id
- 2607.24041
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
- Categories
- math.ST, cs.LG, stat.ML, stat.TH
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
- Primary category
- math.ST
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
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T19
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6 h ago
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- Authors
- Kevin Han Huang, Haoyu Ye, Somak Laha
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- New paperPaperThe Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression
New paper: The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 4 h ago | 1 |
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