A Unified Descriptive-Complexity Framework for Model Selection under Correlated Designs
Read the original on arXiv Machine Learning →The paper introduces the Descriptive‑Complexity Information Criterion (DCIC), a new framework for selecting models when predictors are highly correlated and the model class is uncertain. DCIC uses Kraft‑admissible code lengths to regularize large collections of candidate models, achieving selection consistency under sub‑Weibull noise without requiring RIP‑type conditions and providing non‑asymptotic oracle risk bounds even when the model is misspecified. The approach also unifies heterogeneous model classes on a common complexity scale, enables class–model recovery under identifiability conditions, and offers a complexity‑guided search path that balances computational effort with statistical accuracy, as demonstrated by numerical experiments.
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