Covariance Shrinkage via Stochastic Interpolation
We recast classical shrinkage of high-dimensional covariance estimators as empirical risk minimization over a parametric stochastic interpolant between a source and a target distribution. This formalism recovers known shrinkage estimators as special cases and reveals three distinct mechanisms for reducing statistical risk: (i) Scheduling: the interpolant schedule determines the class of admissible covariances, and hence the achievable risk. (ii) Flow maps and couplings: whereas naive constructions amount to assuming independence between the distributions, specific coupling structures (e.g., solutions of optimal transport problems) can lower the empirical risk. Moreover, non-linear flow ma...
| Authors | Mathieu Chalvidal, Florentin Coeurdoux, Eric Vanden-Eijnden |
|---|---|
| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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