The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling
The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provided a calculation method for smooth models, this framework collapses for the non-smooth estimators ubiquitous in modern machine learning (e.g., Lasso, Sparse SVMs). In this work, we provide a rigorous framework for computing the NML for regular path-differentiable Lipschitz (PDL) estimators. By applying classical geometric measure theory and bridging the coarea formula with conservative Jacobians, we prove that the stochastic complexity for non-smooth models is well-posed and theoretically consistent with the outp...
| Authors | Trenton Lau, Gary P. T. Choi |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 30 September 2026 |
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