生成式多用途采样器用于加权M估计
Generative Multiple-purpose Sampler for Weighted M-estimation
AI总结：
本文提出生成式多用途采样器（GMS），通过单一优化生成加权M估计解，显著降低计算成本，并引入权重乘法多层感知器加速收敛，支持多种统计程序。
摘要：
为了克服诸如自助法和交叉验证等各种数据扰动程序的计算瓶颈，我们提出了生成式多用途采样器（GMS），它构建一个生成器函数，从一组给定的权重和调谐参数中产生加权M估计量的解。GMS通过单一优化实现，无需重复评估加权损失的最小化器，因此能够显著减少计算时间。我们证明，GMS框架使得各种在传统框架下不可行的统计程序得以实现，例如迭代自助法、惩罚似然的自助交叉验证、非参数最大似然的自助经验贝叶斯等。为了构建计算高效的生成器函数，我们还提出了一种新型的神经网络形式，称为“权重乘法多层感知器”，以实现快速收敛。我们的数值结果表明，与传统的神经网络结构相比，这种新的神经网络结构在速度上享有几个数量级的优势。我们提供了一个名为GMS的R包，该包在Pytorch下运行以实现所提出的方法，并允许用户提供自定义损失函数以适应他们感兴趣的模型。
英文摘要：
To overcome the computational bottleneck of various data perturbation procedures such as the bootstrap and cross validations, we propose the Generative Multiple-purpose Sampler (GMS), which constructs a generator function to produce solutions of weighted M-estimators from a set of given weights and tuning parameters. The GMS is implemented by a single optimization without having to repeatedly evaluate the minimizers of weighted losses, and is thus capable of significantly reducing the computational time. We demonstrate that the GMS framework enables the implementation of various statistical procedures that would be unfeasible in a conventional framework, such as the iterated bootstrap, bootstrapped cross-validation for penalized likelihood, bootstrapped empirical Bayes with nonparametric maximum likelihood, etc. To construct a computationally efficient generator function, we also propose a novel form of neural network called the \emph{weight multiplicative multilayer perceptron} to achieve fast convergence. Our numerical results demonstrate that the new neural network structure enjoys a few orders of magnitude speed advantage in comparison to the conventional one. An R package called GMS is provided, which runs under Pytorch to implement the proposed methods and allows the user to provide a customized loss function to tailor to their own models of interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
