Nonconvex Theory of $M$-estimators with Decomposable Regularizers
Authors: Weiwei Liu
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper advances the theory of regularized M-estimator with decomposable regularizers from convex to nonconvex. Our main results show that the estimation errors still lie in a restricted set and we can recover the convergence rates of the estimation error when the loss function is nonconvex. Moreover, we apply our main results to two nonconvex models: corrected linear regression and ℓ1-penalized Lasso estimator. Our key technical analysis of two examples is to prove that with high probability, a form of the restricted strong convexity (RSC) condition and dual norm bound hold. |
| Researcher Affiliation | Academia | 1School of Computer Science, National Engineering Research Center for Multimedia Software, Institute of Artificial Intelligence and Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan University, Wuhan, China. Correspondence to: Weiwei Liu <EMAIL>. |
| Pseudocode | No | The paper presents theoretical proofs and theorems, but does not include any explicitly labeled pseudocode or algorithm blocks. The methods are described mathematically. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to a code repository or mention code in supplementary materials. |
| Open Datasets | No | The paper uses theoretical models such as 'corrupted linear model with additive noise' and 'Gaussian linear model' with assumptions like 'i.i.d. observations' and 'random matrices X, W Rn d are sub-Gaussian'. It does not refer to or provide access information for any specific public or open datasets. |
| Dataset Splits | No | The paper focuses on theoretical analysis and does not use specific empirical datasets, therefore, there is no mention of dataset splits (e.g., training, validation, test splits). |
| Hardware Specification | No | The paper is theoretical in nature and does not describe any experimental setup or the specific hardware used to conduct experiments. |
| Software Dependencies | No | The paper is a theoretical work focusing on mathematical proofs and doesn't describe any software implementations or dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and presents mathematical proofs and derivations. It does not include details on experimental setup, hyperparameters, or training configurations. |