Exact Calculation of Normalized Maximum Likelihood Code Length Using Fourier Analysis

2018/01/11 by Atsushi Suzuki, Suzuki, Atsushi, Kenji Yamanishi +1 · 1 citation
Computer Science · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #FOS: Mathematics #Machine Learning and Algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1801.03705

openalex publication_date 2018/01/11 · openalex created_date 2018/01/26 · openalex updated_date 2026/07/28

Abstract

The normalized maximum likelihood code length has been widely used in model selection, and its favorable properties, such as its consistency and the upper bound of its statistical risk, have been demonstrated. This paper proposes a novel methodology for calculating the normalized maximum likelihood code length on the basis of Fourier analysis. Our methodology provides an efficient non-asymptotic calculation formula for exponential family models and an asymptotic calculation formula for general parametric models with a weaker assumption compared to that in previous work.

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