# Bayesian Properties of Normalized Maximum Likelihood and its Fast Computation

arXiv: https://arxiv.org/abs/1401.7116 · HTML: https://mlsanity.com/paper/1401.7116/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2014.

## Built on by (most cited first, 1 of 1)

- [Point Prediction for Streaming Data](https://mlsanity.com/paper/2408.01318/) (2024)

## Abstract (arXiv)

The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-like representation as a mixture of the component models, even in finite samples, though the weights of linear combination may be both positive and negative. This representation addresses in part the relationship between MDL and Bayes modeling. This representation has the advantage of speeding the calculation of marginals and conditionals required for coding and prediction applications.