Spectral Certificates and Projection-DPP Rounding for Determinantal MAP Selection
Selecting a fixed-size subset that maximizes the determinant of a positive semidefinite kernel is the MAP problem for a size-constrained determinantal point process and the classical maximum-entropy sampling problem. Although this discrete problem is NP-hard, a classical spectral bound gives an efficiently computable ceiling using the leading eigenvalues. The same ceiling is the exact optimum of the associated Stiefel relaxation, so the continuous problem is already solved by the leading eigenspace. We study what this eigenspace implies for discrete rounding. The leading eigenvectors induce a projection determinantal point process whose probability for a subset equals its squared coordina...
| Authors | Richard Yi Da Xu |
|---|---|
| Primary category | cs.LG |
| Published | 17 June 2026 |
| Last updated at source | 17 August 2026 |
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