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arXiv Machine Learning By Trenton Lau, Gary P. T. Choi

The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling

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The paper develops a rigorous framework for computing the Normalized Maximum Likelihood (NML) codelength for regular path‑differentiable Lipschitz (PDL) estimators, which include non‑smooth models such as Lasso and Sparse SVMs. By leveraging geometric measure theory and a novel Propose‑and‑Project Metropolis‑Hastings sampler, the authors provide a method to exactly evaluate the stochastic complexity for these non‑smooth estimators and demonstrate its scalability to high‑dimensional settings. The study shows that the exact NML criterion can match cross‑validation performance while being more data‑efficient, offering a theoretically grounded alternative for model selection in modern machine learning.

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