论文标题
模型维修：强大的过度参数统计模型的恢复
Model Repair: Robust Recovery of Over-Parameterized Statistical Models
论文作者
论文摘要
引入了一种新型的强大估计问题，目的是恢复从数据估算后已损坏的统计模型。提出了仅使用设计而不是用于在监督学习环境中适合模型的响应值的模型“修复”模型的方法。开发了理论，该理论揭示了模型修复所需的两种重要成分 - 统计模型必须过度参数化，并且估计器必须结合冗余。特别是，基于随机梯度下降的估计器非常适合模型修复，但稀疏的估计器通常不可修复。在提出问题并建立了与鲁棒估计有关的关键技术引理之后，提出了一系列结果，用于修复过度参数的线性模型，随机特征模型和人工神经网络。提供了证实并说明理论发现的模拟研究。
A new type of robust estimation problem is introduced where the goal is to recover a statistical model that has been corrupted after it has been estimated from data. Methods are proposed for "repairing" the model using only the design and not the response values used to fit the model in a supervised learning setting. Theory is developed which reveals that two important ingredients are necessary for model repair---the statistical model must be over-parameterized, and the estimator must incorporate redundancy. In particular, estimators based on stochastic gradient descent are seen to be well suited to model repair, but sparse estimators are not in general repairable. After formulating the problem and establishing a key technical lemma related to robust estimation, a series of results are presented for repair of over-parameterized linear models, random feature models, and artificial neural networks. Simulation studies are presented that corroborate and illustrate the theoretical findings.
