# A Unified Descriptive-Complexity Framework for Model Selection under Correlated Designs

arXiv: https://arxiv.org/abs/2608.26618 · HTML: https://mlsanity.com/paper/2608.26618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 66 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Builds on (most cited first, 1 of 1)

- [Best subset selection is robust against design dependence](https://mlsanity.com/paper/2007.01478/) (2020)

## Abstract (arXiv)

Model selection becomes particularly challenging under strong predictor dependence and model-class uncertainty, especially when there are exponentially many models. We propose a Descriptive-Complexity Information Criterion (DCIC) that regularizes large candidate model collections through Kraft-admissible code lengths. Under sub-Weibull noise, we establish selection consistency through approximation-error separation without relying on RIP-type conditions, together with nonasymptotic oracle risk bounds that remain valid under model misspecification. The same coding principle places heterogeneous classes on a common complexity scale at a small additional class-identification cost. This extension yields class--model recovery under suitable identifiability conditions and risk adaptation across classes. We further develop a complexity-guided search path that makes the computation--statistics trade-off explicit. Large penalties yield polynomial-size retained search regions with high probability, whereas smaller penalties sharpen the oracle risk benchmark. Numerical experiments illustrate stable support recovery and favorable estimation performance under strong dependence and model-class uncertainty.