# Information criteria for non-normalized models

arXiv: https://arxiv.org/abs/1905.05976 · HTML: https://mlsanity.com/paper/1905.05976/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 3 of 3)

- [Optimizing the Noise in Self-Supervised Learning: from Importance Sampling to Noise-Contrastive Estimation](https://mlsanity.com/paper/2301.09696/) (2023)
- [Sparse Bayesian Correntropy Learning for Robust Muscle Activity Reconstruction from Noisy Brain Recordings](https://mlsanity.com/paper/2404.15309/) (2024)
- [ReLeVAnT: Relevance Lexical Vectors for Accurate Legal Text Classification](https://mlsanity.com/paper/2604.22292/) (2026)

## Abstract (arXiv)

Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant, such as noise contrastive estimation (NCE) and score matching. However, model selection methods for general non-normalized models have not been proposed so far. In this study, we develop information criteria for non-normalized models estimated by NCE or score matching. They are approximately unbiased estimators of discrepancy measures for non-normalized models. Simulation results and applications to real data demonstrate that the proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner.