# Estimation of Over-parameterized Models from an Auto-Modeling Perspective Source: [Estimation of Over-parameterized Models from an Auto-Modeling Perspective]() Collection index: [llms.txt]() Data updated: 2025-10-25T17:46:19.187Z Authors: Yiran Jiang, Chuanhai Liu Published: 2022-06-03T21:24:50.000Z ## Abstract From a model-building perspective, we propose a paradigm shift for fitting over-parameterized models. Philosophically, the mindset is to fit models to future observations rather than to the observed sample. Technically, given an imputation method to generate future observations, we fit over-parameterized models to these future observations by optimizing an approximation of the desired expected loss function based on its sample counterpart and an adaptive $\\textit{duality function}$. The required imputation method is also developed using the same estimation technique with an adaptive $m$-out-of-$n$ bootstrap approach. We illustrate its applications with the many-normal-means problem, $n \< p$ linear regression, and neural network-based image classification of MNIST digits. The numerical results demonstrate its superior performance across these diverse applications. While primarily expository, the paper conducts an in-depth investigation into the theoretical aspects of the topic. It concludes with remarks on some open problems. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()