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Here C(n, Id) = c r Tr(IS) logn n + B1 logγ B1p Tr(IS) ! · log n n

Then, for all β, it holds that |(ES[ℓ(x, y, β)] − ℓn(β)) − (ES[ℓ(x, y, β0)] − ℓn(β0))| ≤ min ( 2B0 r log n n , C(n, Id) ∥β − β0∥2 + B2 r log n n ∥β − β0∥2 2 + B3 ∥β − β0∥3 2 )

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Principled Out-of-Distribution Generalization via Simplicity

stat.ML · 2025-05-28 · conditional · novelty 5.0

Under the assumption that the out-of-distribution-generalizing model is the simplest source-consistent parameter, regularized maximum likelihood recovers it with near-1/n excess risk (constant gap) or n^{-1+2/(3τ)} (vanishing gap).

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  • Principled Out-of-Distribution Generalization via Simplicity stat.ML · 2025-05-28 · conditional · none · ref 7

    Under the assumption that the out-of-distribution-generalizing model is the simplest source-consistent parameter, regularized maximum likelihood recovers it with near-1/n excess risk (constant gap) or n^{-1+2/(3τ)} (vanishing gap).