The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling
arXiv:2605.24477v1 Announce Type: new Abstract: 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 wi
The proliferation of non-smooth models in modern machine learning necessitates a robust theoretical framework for complexity, and this research addresses a fundamental gap.
This work provides a rigorous foundation for evaluating the complexity of ubiquitous non-smooth machine learning models, which is critical for model selection, generalization bounds, and efficient universal coding.
The ability to accurately compute Normalized Maximum Likelihood for non-smooth models enhances theoretical understanding and practical application of universal coding principles in advanced AI systems.
- · Machine Learning Researchers
- · AI algorithm developers
- · Sectors using complex ML models
- · Researchers relying on ad-hoc complexity metrics
- · Those resistant to geometric measure theory
Improved theoretical understanding and design of machine learning algorithms for non-smooth estimators.
More reliable model selection criteria and enhanced generalization capabilities for complex AI systems.
Accelerated development of more robust and efficient AI agents and automated decision-making systems.
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