# Detecting Signs of Model Change with Continuous Model Selection Based on Descriptive Dimensionality

arXiv: https://arxiv.org/abs/2302.12127 · HTML: https://mlsanity.com/paper/2302.12127/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 4 of 4)

- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [Model Selection Techniques -- An Overview](https://mlsanity.com/paper/1810.09583/) (2018)
- [Graph based Entropy for Detecting Explanatory Signs of Changes in Market](https://mlsanity.com/paper/1811.12165/) (2018)
- [Detecting Change Signs with Differential MDL Change Statistics for COVID-19 Pandemic Analysis](https://mlsanity.com/paper/2007.15179/) (2020)

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

- [Foundation of Calculating Normalized Maximum Likelihood for Continuous Probability Models](https://mlsanity.com/paper/2409.08387/) (2024)
- [Normalized Maximum Likelihood Code-Length on Riemannian Data Spaces](https://mlsanity.com/paper/2508.21466/) (2025)
- [Clustering Change Sign Detection by Fusing Mixture Complexity](https://mlsanity.com/paper/2403.18269/) (2024)

## Abstract (arXiv)

We address the issue of detecting changes of models that lie behind a data stream. The model refers to an integer-valued structural information such as the number of free parameters in a parametric model. Specifically we are concerned with the problem of how we can detect signs of model changes earlier than they are actualized. To this end, we employ em continuous model selection on the basis of the notion of em descriptive dimensionality~(Ddim). It is a real-valued model dimensionality, which is designed for quantifying the model dimensionality in the model transition period. Continuous model selection is to determine the real-valued model dimensionality in terms of Ddim from a given data. We propose a novel methodology for detecting signs of model changes by tracking the rise-up of Ddim in a data stream. We apply this methodology to detecting signs of changes of the number of clusters in a Gaussian mixture model and those of the order in an auto regression model. With synthetic and real data sets, we empirically demonstrate its effectiveness by showing that it is able to visualize well how rapidly model dimensionality moves in the transition period and to raise early warning signals of model changes earlier than they are detected with existing methods.