论文标题
从自动模型的角度估算过度参数化模型
Estimation of Over-parameterized Models from an Auto-Modeling Perspective
论文作者
论文摘要
从模型构建的角度来看，我们提出了适合过度参数化模型的范式转移。从哲学上讲，心态是将模型拟合到未来的观察结果，而不是观察到的样本。从技术上讲，给定一种生成未来观察的插补方法，我们通过根据其样本对应物和自适应$ \ textit {duality函数} $优化了所需预期损耗函数的近似来拟合这些未来观察结果。所需的插补方法还使用相同的估计技术开发，并采用自适应$ m $ $ n $ n $ bootstrap方法开发。我们用许多正常均值问题，$ n <p $线性回归和基于神经网络的MNIST数字图像分类来说明其应用程序。数值结果表明了其在这些不同应用中的出色性能。在主要的说明性方面，本文对该主题的理论方面进行了深入的研究。最后，关于一些开放问题的评论。
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.
