Exact Calculation of Normalized Maximum Likelihood Code Length Using Fourier Analysis

TL;DR

This paper introduces a Fourier analysis-based method for efficiently calculating the normalized maximum likelihood code length, improving accuracy and applicability for various statistical models.

Contribution

It presents a novel Fourier analysis approach for exact and asymptotic calculation of normalized maximum likelihood code length, enhancing model selection techniques.

Findings

Provides a non-asymptotic formula for exponential family models

Offers an asymptotic formula for general parametric models

Improves computational efficiency and theoretical understanding

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.